ratio problem solving grade 7

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• 7th Grade Ratio And Proportions Worksheets

7th Grade Ratio and Proportion Worksheets help students learn to compare two similar sizes by giving them a ratio. When both ratios are the same in an equation, they are called proportions. Ratio and proportions are based on numbers and fractions and are the basis for several mathematical concepts. Ratios and Proportion Worksheets help 7th graders understand concepts such as how to express ratios in their simplest form, compare ratios, arrange ratios in ascending or descending order, proportions, and the proportional mean between numbers. Practice questions feature  tables, graphs, word problems, and stimulating visuals to keep students engaged while learning. ...Read More Read Less

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Choose math worksheets by topic, benefits of 7th grade ratio and proportions worksheets.

The Ratio and Proportion Worksheets are essential learning materials for 7th graders. Regular practice with these worksheets can help students increase their understanding of these crucial topics. 

Instilling reasoning using logic:

Children can develop a keen sense of reasoning as they practice and solve problems using the Online Ratio and Proportion Worksheets. The printable worksheets cover various topics to help students understand the basics of rations and proportions and learn to use what they have learned in their daily life. 

Approaching cautiously :

The step-by-step 7th Grade Ratio and Proportions worksheets start with simple tasks that gradually increase in difficulty level. Students learn to solve these problems at their own pace and apply the concepts to real life situations.  

Studying in their own time:

The Ratio and Proportion Worksheets provide children with multi-level problems they can do either in the classroom or at home to help them understand the concepts of this topic.

Trying different formats:

7th Grade Online Ratios and Proportions Worksheets were designed to keep students engaged and eliminate monotonous studying. Worksheets are interactive, and give students interesting visual examples to help them understand the concepts being reviewed and build their confidence. 

Grade 7 Ratio and Proportions Worksheets Explained

Ratio proportion worksheets for 7 th grade are designed to teach young students the basics of ratio and proportions quickly and effectively. Worksheets often contain tables of equivalent rates with two rows. Each row represents values for an item.

Below is a basic table where students need to figure out proportions and ratios from two given Kilometer and Hour values. The worksheets are arranged in order of difficulty, so the first worksheet will feature simpler problems to introduce these concepts. The proportion/ratio is defined in the beginning of the worksheets.

7th Grade Ratio and Proportion worksheets challenge students to figure out the equivalent values for one of the items across multiple, equal proportions or ratios.

Moving up in difficulty,  the table's structure stays the same, but the provided values move to the middle of the table.

The most complex problems on the worksheets feature some values in one of the rows and some in the other. Again, students need to understand the unit rates to complete these.

Some ratio proportion worksheets may contain traditional mathematical problems. These are designed to reflect real-life situations as much as possible. This helps students learn perspective and apply mathematics in practical life problems.

• 7 th Grade Ratio and Proportion worksheets feature problems such as:

Q1: If x: y = 2:3, then what should be 2x + 3y: 4x + 5y?

Answer: If x: y = 2:3, then x/y = 2/3, or 3x = 2y, or x = 2y/3.

Applying this formula to the bigger ratio, 2x + 3y = (2 x 2y/3) + 3y = 13y/3

And 4x + 5y = (4 x 2y/3) + 5y = 23y/3

So 2x + 3y: 4x + 5y = 13y/3 / 23y/3 = 13/23 = 13:23

Q2: If a 6 feet tall tree casts a shadow of 15 meters, how tall a shadow will a pole 30 meters high cast?

Here, the proportion of the tree’s height to its shadow is 6:15, which can be simplified to 2:5.

So, we present this equivalency problem as:

2:5 = 30:x (assuming x is the height of the shadow cast)

or, 2/5 = 30/x

or, x/30 = 5/2

or, x = 30 x 5/2 = 75

The answer is 75 meters.

By practicing using Grade 7 Ratio and Proportions Worksheets, students are encouraged to solve these expressive problems in simpler forms, find the difference between ratios, order ratios in either up or down formation, and proportionally average between numbers. The worksheets also illustrate problems that use algebraic variables that relate to real world mathematical problems.

What are 7th grade ratio and proportions worksheets about?

The 7th grade ratio and proportions worksheets are free fun and interactive printable worksheets that contain questions and stepwise solutions based on ratio and proportion that enhance the knowledge about the concept and self assessment skill.

What is the difference between ratio and proportion?

The ratio is the mathematical term to represent the comparison of two numbers and it is represented by either a/b or a : b but proportion is the equation that tells whether the two ratios are equal or not.

What are equivalent ratios?

The equivalent ratios are the ratios that describe the same relationship between numbers. The value of equivalent ratios is equivalent.

How can we find whether the ratios are proportional?

The ratios, whether proportional or not can be determined in three ways, first is finding the values of the ratios, second is using cross product property, and third is using the equivalent ratio table. You will find good practice questions in grade 7 ratio and proportions worksheets.

How are grade 7 ratio and proportions worksheets beneficial for students?

The 7th-grade ratio and proportions worksheets for students are free and printable worksheets which means the student can appear for the worksheets as many times as he/she wants and can print them also so, no need for internet connectivity for solving worksheets. The worksheet has questions based on ratio and proportion that will reinforce the knowledge of the topic and by solving real-life questions students can also apply the concept to real-life needs. In worksheets, there are different types of questions, solving those questions students have an encouraging feeling and can trace their progress. That will help in analytical thinking skill.

Ratio and Proportion Worksheets 7th Grade

Ratio and proportion worksheets 7th grade help students in practicing questions on expressing ratios in the simplest form, simplifying ratios, comparing ratios, arranging ratios in the ascending order or descending order, proportion, and also mean proportional between numbers. These worksheets also help students in practicing questions involving tables, graphs, word problems, etc.

Benefits of 7th Grade Ratio and Proportion Worksheets

Ratio and proportion worksheets 7th grade deal with the logical and reasoning aspect of mathematics and help students in real-life scenarios as well. The stepwise approach of these worksheets makes students solve a variety of questions with ease. Students can study at their own pace and can solve problems with a gradually increasing difficulty level. As these worksheets are also interactive, students can rely on visual simulations to promote a better understanding of the topic.

Printable PDFs for Grade 7 Ratio and Proportion Worksheets

7th Grade Ratio and Proportion worksheets are available as PDFs that can be downloaded for free, enabling students to access them offline.

• Math 7th Grade Ratio and Proportion Worksheet
• 7th Grade Ratio and Proportion Math Worksheet
• Seventh Grade Ratio and Proportion Worksheet
• Grade 7 Math Ratio and Proportion Worksheet

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Ratio Word Problem Worksheets

We are delighted to share this set of extensively well-researched ratio word problem worksheets which will help students in grade 5 through grade 8 to grasp the basics of ratio calculations. These printable worksheets include simple theme-based ratio word problems, finding the ratio between two quantities, word problems that require children to find a part from the whole, part-to-part, a whole from the part, reading pictographs, bar graphs, and pie graphs. Click on the free icon to sample our worksheets.

Express in ratio: Read the themes

Look at the vivid themes and answer the word problems in these 5th grade worksheets. Express in ratio and reduce it to the lowest term. Use the answer key to verify your responses.

• Download the set

Find the ratio between two quantities

This set of well-researched ratio word problem pdf worksheets includes factual and educative real-life scenarios. Find the ratio between the two quantities. Express your answer in the simplest form.

Ratio word problems: Part-to-part

Based on the data given in these colorful worksheets, read and answer the extremely engaging part-to-part ratio word problems that ensue. You have an option to download this set of worksheets in a single click.

Ratio word problems: A part from the whole

This collection of ratio word problems printable worksheets will require 6th grade and 7th grade students to find the parts from the given ratio and the whole. Set up the simple equation and solve the word problems.

Ratio word problems: The whole from the part

Based on one part of the number and the ratio provided in these word problems, the children need to find the share of the other part and the whole. There are five word problems in each worksheet.

Ratio word problems: Mixed bag

This set of assorted word problems for 7th grade and 8th grade students contains a mix of finding part-to-part, part-to-whole, and finding the ratio. Some word problems may require you to find the ratio based on the increase or decrease in quantity and vice versa.

Finding the Ratio from Pictographs

Use the key to find the total of each item. Read the pictograph and answer the word problems. The word problems are based on finding ratio between the quantities. Do not forget to reduce the ratio to the lowest term.

Finding the Ratio from Bar Graphs

The data provided in these bar graphs are borrowed from real-life scenarios. Read the bar graphs and write the ratio in the simplest form.

Finding the Ratio from Pie Graphs

The printable worksheet pdfs in this section contain ratio word problems based on pie graphs. Read the pie graph, find the ratio and solve the word problems.

Related Worksheets

» Proportions

» Fractions

» Fraction Word Problems

» Decimal Word Problems

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Grade 7 - Ratios and Proportional Relationships

Standard 7.RP.A.2a - Practice identifying if two ratios form a proportion.

Included Skills:

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

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Here you will learn about ratios, including how to write a ratio, simplifying ratios, unit rate math and how to solve problems involving ratios and rates.

Students will first learn about ratios as part of ratios and proportions in 6 th grade and 7 th grade.

What is a ratio?

A ratio is a multiplicative relationship between two or more quantities.

Ratios are written in the form a : b, which is read as “a to b”, where a and b are normally integers, fractions, or decimals.

The order of the quantities in the ratio is important.

For example,

If there are 10 boys in a class and 15 girls, the ratio of boys to girls is 10 : 15 which is read as “10 to 15.” This is an example of a part to part ratio. You could also say the ratio of total students to girls is 15 : 25. This is an example of a part to whole ratio.

Step-by-step guide: How to write a ratio

Since a ratio represents a relationship, there is always more than one way to show it.

This includes unit rate math – which creates equivalent ratios where one part of the ratio is 1.

You can use unit rates to compare different quantities.

A grocery store sells a bag of 6 bananas for \$ 2.34 and a bag of 4 bananas for \$ 1.44.

Which bag has the better unit price?

Unit price means the price per 1 unit. In this case, the units are bananas. Divide each ratio to find the price for 1 banana.

The bag of 4 bananas is \$ 0.36 per banana, which is cheaper than the bag of 6 bananas which is \$ 0.39 per banana.

Step-by-step guide: Unit rate math

Unit rates are not the only types of equivalent ratios. When simplifying fractions, use the common factors to divide all the numbers in a ratio until they cannot be divided further to write the ratio in lowest terms.

The ratio of red counters to blue counters is 16 : 12.

You can simplify the ratio to lowest terms by finding the greatest common factor \textbf{(GCF)} of each of the numbers in the ratio.

Factors of 16 \text{:} \, 1, 2, 4, 8, 16

Factor of 12 \text{:} \, 1, 2, 3, 4, 6, 12

The greatest common factor is 4. To simplify the ratio, you divide both sides by 4.

Step-by-step guide: Simplifying ratios

Another way to write ratios is by using fraction notation.

Fraction notation can be used to show a part to whole ratio relationships.

The bar model below shows the ratio of blue : red as 3 : 2 (3 to 2). There are 3 blue blocks, 2 red blocks and 5 blocks in total.

This part to whole relationship allows us to make statements like…

• \cfrac{3}{5} of the blocks are blue
• \cfrac{2}{5} of the blocks are red
• \cfrac{5}{5} of the blocks are blue or red

The ratio of blue : red as 3 : 2 can also be shown as a part to part fraction…

The fractions show the ratio relationship BETWEEN the blue and red blocks. This allows us to make statements like…

• The number of blue blocks is \cfrac{3}{2} larger than red
• The number of red blocks is \cfrac{2}{3} the amount of blue

Step-by-step guide: Ratio to fraction

Ratios can also be written with percents.

The ratio of pencils to crayons is 4 : 6.

The ratio has 10 parts, so the fractions are

\cfrac{4}{10} : \cfrac{6}{10}.

The numerator represents the numbers of the ratio, which show how many pencils or crayons there are. The denominator represents the total number of pencils and crayons.

You may be able to recognize what the fractions are as percents or you may need to use long division to help convert your fractions.

\cfrac{4}{10}=40 \%, so 40 \% are pencils.

\cfrac{6}{10}=60 \%, so 60 \% are crayons.

Step-by-step guide: Ratio to percent

Solving problems with ratios is common in the real world. One place that this shows up is in calculating exchange rates. An exchange rate is the rate at which the money of one country can be exchanged for the money of another country.

Using a currency’s exchange rate you can convert between US dollars and foreign currencies.

To convert from US dollars (USD) to Japanese yen (JPY), you must multiply by the exchange rate.

So \$ 15 \; USD would be ¥2,134.35 \; JPY because,

\$ 15 \; USD \times 142.29=¥ 2,134 .35 \; JPY.

Step-by-step guide: How to calculate exchange rates

All the skills above are examples of ratio problem solving. When solving problems with ratios, it is important to ask:

• What is the ratio involved?
• What order are the quantities in the ratio?
• What is the total amount / what is the part of the total amount known?
• What are you trying to calculate ?

In the classroom, ratio problem solving often comes in the form of real world scenarios or word problems.

\cfrac{8}{10} students are right handed. What is the ratio of left handed students to right handed students? (2 : 8)

Step-by-step guide: Ratio problem solving

[FREE] Ratio Worksheet (Grade 6 and 7)

Use this quiz to assess your 6th and 7th grade students’ understanding of ratios. Covers 10+ questions with answers on ratio topics to identify areas of strength and support!

Common Core State Standards

How does this relate to 6 th grade math and 7 th grade math?

• Grade 6 – Ratios and Proportions (6.RP.A.1) Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2 : 1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
• Grade 6 – Ratios and Proportions (6.RP.A.2) Understand the concept of a unit rate \cfrac{a}{b} associated with a ratio a : b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is \cfrac{3}{4} cup of flour for each cup of sugar.” “We paid \$ 75 for 15 hamburgers, which is a rate of \$ 5 per hamburger.”
• Grade 6 – Ratios and Proportions (6.RP.A.3) Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
• Grade 6 – Ratios and Proportions (6.RP.A.3b) Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
• Grade 7 – Ratios and Proportions (7.RP.A.1) Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks \cfrac{1}{2} mile in each \cfrac{1}{4} hour, compute the unit rate as the complex fraction \cfrac{\cfrac{1}{2}}{\cfrac{1}{4}} miles per hour, equivalently 2 miles per hour.

How to work with a ratio

There are a lot of ways to work with a ratio. For more specific step-by-step guides, check out the ratio pages linked in the “What are ratios?” section above or read through the examples below.

Ratio examples

Example 1: how to write a ratio.

Write the ratio of apples to pears.

• Identify the different quantities being compared and their order.

There are 5 pears and 2 apples.

The order of the ratio is apples to pears.

2 Write the ratio using a colon.

Apples : Pears

\hspace{0.7cm} 5 : 2

3 Check if the ratio can be simplified.

5 and 2 only have a common factor of 1, so this ratio is already in its lowest terms (simplest form).

Example 2: unit rate calculation – decimal

A car travels 303 miles in 6 hours. If the car travels the same number of miles each hour, what is the miles per hour rate?

Write the original rate.

303 miles in 6 hours → 303 : 6.

Use multiplication or division to create a unit rate.

The miles ‘per hour’ refers to 1 hour. Divide each side of the rate by 6, to create a rate for 1 hour.

Use the unit rate to answer the question.

The car travels 50.5 miles each hour.

Example 3: simplifying ratios

Write the ratio 48 : 156 in lowest terms.

Calculate the greatest common factor of the parts of the ratio.

Factors of 48=1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 156=1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

GCF(48,156)=12

Divide each part of the ratio by the greatest common factor.

4 : 13 is in lowest terms.

Example 4: solving a problem involving ratio to percents

The ratio of adults to children in a park is 11 : 14.

One-fourth of the adults are women. What percent of the people in the park are men?

Add the parts of the ratio for the denominator of the fractions.

11+14=25. There are 25 parts in total. The denominator is 25.

Convert each part of the ratio to a fraction.

11 : 14 becomes \cfrac{11}{25} : \cfrac{14}{25}.

Convert the fractions to percents.

\begin{aligned}& \cfrac{11}{25}=\cfrac{44}{100}=44 \% \\\\ & \cfrac{14}{25}=\cfrac{56}{100}=56 \%\end{aligned}

You now know that 44 \% of the people are adults.

One-fourth of the adults are women.

\cfrac{1}{4} of 44 \%=11 \%.

11 \% of the people in the park are women and therefore 44-11=33 \% of the people are men.

Example 5: converting from KRW / USD

₩5,000 \; KRW is equal to \$ 3.85 \; USD. What is the exchange rate from \$ \; (USD) to ₩ \; (KRW)?

Use the information given to set up a rate.

When calculating the currency exchange rate from ₩ \; (KRW), you want to know how many ₩ \; (KRW) are equal to \$ 1 \; (USD). This is the ratio of ₩ to \$, so set up the rate as \cfrac{₩ 5,000}{\$ 3.85}.

Divide both parts by the base currency.

In this case, the base currency is \$ \; (USD), so divide both parts by 3.85, rounding the ₩ \; KRW is to the nearest whole:

\cfrac{₩ 5,000 \div 3.85}{\$ 3.85 \div 3.85}=\cfrac{₩ 1,299}{\$ 1}.

State the final exchange rate with the correct currency symbols.

The exchange rate from \$ \; (USD) to ₩ \; (KRW) is 1,299.

Example 6: ratio problem solving – mixed numbers

Fruit Salad Recipe:

• 2 \cfrac{1}{2} cups of blueberries
• 2 \cfrac{1}{5} cups of orange slices
• 1 \cfrac{1}{4} cups of strawberries
• 2 cups of apple slices

Write the ratio of the total cups of berries for every 1 cup of strawberries in the salad.

Identify key information within the question.

There are 1 \cfrac{1}{4} cups of strawberries and 2 \cfrac{1}{2} cups of blueberries.

Know what you are trying to calculate.

You need to create the ratio of the total cups of berries (strawberries and blueberries) for every 1 cup of strawberries.

Use prior knowledge to structure a solution.

First add 1 \cfrac{1}{4}+2 \cfrac{1}{2} to find the total cups of berries.

\begin{aligned}& 1 \cfrac{1}{4}+2 \cfrac{1}{2} \\\\ & =\cfrac{5}{4}+\cfrac{5}{2} \\\\ & =\cfrac{5}{4}+\cfrac{10}{4} \\\\ & =\cfrac{15}{4}\end{aligned}

Then write the ratio of total cups of berries to cups of strawberries.

\cfrac{15}{4} : \cfrac{5}{4}

Now multiply both sides of the ratio by \cfrac{4}{5}, to calculate the ratio of 1 cup of strawberries.

\cfrac{15}{4} \times \cfrac{4}{5} : \cfrac{5}{4} \times \cfrac{4}{5}

There are 3 total cups of berries for every 1 cup of strawberries.

*Note: To solve, you can also write the ratio \cfrac{15}{4} : \cfrac{5}{4} as the complex fraction \cfrac{\cfrac{15}{4}}{\cfrac{5}{4}} and find the quotient of the numerator and denominator.

Teaching tips for ratio

• There are many ways to engage students in ratios. One way is to introduce the golden ratio (based on Fibonacci’s sequence) and challenge students to look for it in the real world. Keep a chart or wall in the classroom for students to add any examples of this ratio that they find.
• Incorporate as many examples of ratios in the classroom as you can – even across subjects. For example, have students write ratios about the “Word of the day” – from an English or Science class. Such as “Write the ratio of nouns to adjectives” or “Write the ratio of words with the letter ‘e’ to total words.”
• As students work with ratios in different ways, keep track of successful solving strategies on a bulletin board or on chart paper. This allows students to see and utilize another students’ strategy, make connections between strategies and feel ownership in any ideas they help create.
• Be mindful of how to progress with ratio topics. Typically whole number ratios are introduced first, then ratios with rational numbers. Ratios that involve compare only fractional (or decimal values), such as \cfrac{2}{3} : \cfrac{5}{6} or 0.45 : 0.34 are the most difficult for students. As always, be mindful of your state’s curriculum when making decisions on when to introduce certain ratio topics.

Easy mistakes to make

• Writing the ratio in the wrong order A common error is to write the parts of the ratio in the wrong order. For example, The number of dogs to cats is given as the ratio 12 : 13 but the solution is incorrectly written as 13 : 12.
• Confusing ratios and fractions You can write a ratio with fraction notation. A part to whole fraction will have the same fractional language as a fraction. However, a part to part fraction will not. For example, The ratio of boys to girls is 2 : 3. Two ways to express this ratio are \cfrac{2}{3} or \cfrac{2}{5}. However, you must be careful how you read these fractions. You can say “ \cfrac{2}{5} of the kids are boys” but you cannot say “ \cfrac{2}{3} of the kids are boys.” Instead, say “The number of boys is \cfrac{2}{3} the number of girls.”
• Not fully simplified A common error is to not find the greatest common factor when simplifying a ratio. For example, Simplify the ratio 12 : 18. Dividing both numbers by only 2 leaves a ratio of 6 : 9, which is not fully simplified. This can be simplified further by dividing by 3 to get the ratio 2 : 3, which is the correct answer. By dividing both numbers by the greatest common factor, 6, would get the ratio 2 : 3 in one step.

Practice ratio questions

1. 500 people attended a concert. There were 240 boys. What is the ratio of boys to girls who went to the concert?

There are 500 people and 240 boys.

500-240=260. There are 260 girls.

The order of the ratio is boys to girls.

Boys : Girls

2. A musical requires 200 costumes. 140 costumes are for the background dancers. The rest are for the lead roles. Write the ratio of the costumes for lead roles to background dancers in the simplest form.

There are 200 costumes. 140 costumes are for background dances.

200-140=60 lead role costumes

The ratio order of the ratio is lead roles to background dancers

Lead roles : Background dancers

\hspace{1cm} 60 : 140

The greatest common factor of 60 and 140 is 20\text{:}

3. A shop is selling the same pencils in two different packs.

Which statement correctly compares the packs?

Pack \textbf{A}\text{:} \; 5 pens cost \$ 6.20

Pack \textbf{B}\text{:} \; 4 pens cost \$ 4.88

Pack A is \$ 1.32 cheaper per pencil than Pack B.

Pack B is \$ 1.32 cheaper per pencil than Pack A.

Pack A is \$ 0.02 cheaper per pencil than Pack B.

Pack B is \$ 0.02 cheaper per pencil than Pack A.

Offer A\text{:} \; 5 pencils cost \$ 6.20 → 5 : \$ 6.20

Each pencil in Pack A costs \$ 1.24.

Offer B\text{:} \; 4 pencils for \$ 4.88 → 4 : \$4.88

Each pencil in Pack B costs \$ 1.22.

\$ 1.24-\$ 1.22=\$ 0.02.

Offer B costs \$ 0.02 cheaper than Offer A.

4. The fraction of bananas in a bowl is \cfrac{13}{20}. Calculate the ratio of bananas to other pieces of fruit in the bowl.

The total number of pieces of fruit is 20. The number of bananas is 13.

As a bar model, this looks like

The number of other pieces of fruit is therefore 7 (this is calculated by 20-13=7 or counting the number of red bars above).

The ratio of bananas to other pieces of fruit is therefore 13 : 7.

5. Given the exchange rate between US dollars (USD) and New Zealand dollars (NZD) is \$ 1 \; USD=\$ 1.63 \; NZD, convert \$ 50 \; USD to New Zealand dollars (NZD). Round to the nearest cent.

\$ 50 \, USD=\$ \rule{0.5cm}{0.15mm} \, NZD

Since each US dollar is equal to \$ 1.63 \, NZD, multiply the USD by 1.63 to find the number of \$ \, (NZD).

\$ 50 \, USD=\$ 81.50 \, NZD

6. A soap is made by combining lavender soap with lemon soap. Each bar of soap weighs 330 \, g. If the ratio of lavender to lemon is 4 : 7,   how many grams of lemon soap are in each bar?

As there are 7+4=11   shares within the ratio

330 \div 11=30 \, g   per share

The amount of Lemon in the soap is equal to 7 \times 30=210 \, g

While the term ratio is used in a variety of ways in the real world, the definition of ratio in math is the comparison of two or more values that have a constant relationship. Some examples of ratios are “ 2 dogs to 5 cats” or “ 24 miles per hour.”

A rate is a special type of ratio that compares different units. They are not synonyms, since not all ratios are rates. However, all rates are ratios, so they can be called by either name.

Ratio understanding is expanded to include more complex comparisons that involve exponents, variables and/or polynomials. This extends to include ratio relationships in proportions and linear equations. As students progress in their learning, they will become comfortable graphing, creating tables and equations that represent ratio relationships.

The next lessons are

• Converting fractions, decimals and percentages

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Welcome to our Ratio Word Problems page. Here you will find our range of 6th Grade Ratio Problem worksheets which will help your child apply and practice their Math skills to solve a range of ratio problems.

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Here you will find a range of problem solving worksheets about ratio.

The sheets involve using and applying knowledge to ratios to solve problems.

The sheets have been put in order of difficulty, with the easiest first. They are aimed at students in 6th grade.

Each problem sheet comes complete with an answer sheet.

Using these sheets will help your child to:

• apply their ratio skills;
• apply their knowledge of fractions;
• solve a range of word problems.
• Ratio Problems 1
• PDF version
• Ratio Problems 2
• Ratio Problems 3
• Ratio Problems 4

Ratio and Probability Problems

• Ration and Probability Problems 1
• Sheet 1 Answers
• Ration and Probability Problems 2
• Sheet 2 Answers

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Ratio & Unit Rate Worksheets

These sheets are a great way to introduce ratio of one object to another using visual aids.

The sheets in this section are at a more basic level than those on this page.

We also have some ratio and proportion worksheets to help learn these interrelated concepts.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets
• Unit Rate Problems 6th Grade

6th Grade Percentage Worksheets

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Percentage of Numbers Worksheets
• Money Percentage Worksheets
• 6th Grade Percent Word Problems

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7th Grade Ratio Word Problems

The following are some examples and solutions 7th Grade Math Word Problems that deals with fractions and percents.

Related Topics: More Math Word Problems Algebra Word Problems More Singapore Math Word Problems 7th Grade Math Word Problems 1

These are Grade 7 word problems from a Singapore text. The problems are solved both algebra (the way it is generally done in the US) and using block diagrams (the way it was shown in the Singapore text). You can then decide which one you prefer.

Singapore Math 5 (A Grade 7 Algebra Word Problem from a Singapore text) Example: Ivan went to a store and spent 1/3 of his money on a book. He then spent 2/5 of his remaining money on a computer game. After that, he then spent 1/4 of his remaining money on a CD. Finally, he spent 1/6 of the remaining money on a candy bar. After buying the four items, he was left with $15. How much money did he have originally, that is, before he purchased the book?

Example: Mr. Lee bought a bag of snacks. 3/4 of the snacks are yogurt bars and the remaining snacks are chocolate bars. His sons will share the chocolate bars equally among themselves and his daughters will share the yogurt bars equally among themselves. Each son got 1/8 of the snacks, while each daughter got 1/4 of the snacks. a) How many sons and daughters does Mr. Lee have? b) If each son got 3 chocolate bars and each daughter got 6 yogurt bars, how many snacks did Mr. Lee buy?

Example: There are 600 children on a field. 30% of them were boys. After 5 teams of boys join the children on the field, the percentage of children who were boys increased to 40%. How many boys were there in the 5 teams altogether?

Seventh Grade Singapore Problem Example: Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

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Arinjay Academy » Maths » Ratio and Proportion Problems and Solutions for Class 7

Ratio and Proportion Problems and Solutions for Class 7

Ratio and proportion problems and solutions for class 7, deals with various concepts which are as under:-.

• Convert Ratio into its simplest form
• Ratio of two quantities, by converting them into same units
• Equivalent ratios
• Find the numbers when their ratio and sum are given
• Divide sum of money between two persons when ratio are given
• Comparison of ratios
• Are the given ratio in proportion
• Are the given number are in proportion
• Find the value of y when four numbers are in proportion
• Finding Ratio A : B : C
• Finding Ratio A : B : C if Ratio A : B and B : C given
• Converting Ratio into another Ratio
• Finding ratio of present ages
• Finding ratio of ages of persons after some years
• Finding ratio of ages of persons some year ago.
• Third proportional value
• Mean proportional value
• Continued proportion

In order to convert the given ratio to Simplest Form, we should follow the following steps : –

• Find the HCF of both the numerator and denominator
• Dividing Both numbers by their HCF

The result is the ratio in its simplest form.

Question 1 :

Convert the ratio 66 : 18 in its simplest form

HCF of 66 and 18 is 6

Since, 66 : 18

Hence, the simplest form of 66 : 18 is 11 : 3

Ratio and Proportion Problems and Solutions for Class 7 –  Ratio of two quantities, by converting them into same units

Question 2 :

Find the ratio of 48 min to 4 hours

Taking both the quantities in same unit, we have

4 hours = ( 4 x 60 ) = 240 min

The equation now becomes 48 min : 240 min

Hence, the required ratio is 1 : 5

Ratio and Proportion Problems and Solutions for Class 7 – Equivalent ratios

In order to find Equivalent Ratios of any given ratio, we multiply or divide the numerator and denominator of the ratio by the same non zero number.

Question 3 :

Find the Equivalent ratio of 6 : 7 ?

On multiplying or dividing each term of a ratio by the same non zero number, we get a ratio equivalent to the given ratio

Both numerator and denominator of given fraction is multiplied by same non zero number i.e 4

24/28 is an equivalent ratio of 6/7

7/6 is not an equivalent ratio of 6/7. As both 6 and 7 are not mutiply by

same non zero number

25/21 is not an equivalent ratio of 6/7. As both 6 and 7 are not mutiply

by same non zero number

22/21 is not an equivalent ratio of 6/7. As both 6 and 7 are not mutiply

Ratio and Proportion Problems and Solutions for Class 7 – Find the numbers when their ratio and sum are given

Question 4 :

Two numbers are in the ratio 5 : 7 and their sum is 120. Find the numbers?

Let the required number be 5a and 7a

Since the sum of these two numbers is given, we can say that

5a + 7a = 120

So, the first number is 5a = 5 x 10

Second number is 7a = 7 x 10

Hence, two numbers are 50 and 70

Ratio and Proportion Problems and Solutions for Class 7 – Divide sum of money between two persons when ratio are given

Question 5 :

Divide ₹ 2000 between X and Y in the ratio 5 : 3

Total money = ₹ 2000

Given ratio = 5 : 3

Sum of ratio terms = ( 5 + 3 )

Give: 5/8 part of ₹ 2000 to X

Give: 3/8 part of ₹ 2000 to Y

X ‘s share = ₹ ( 2000 x 5/8) = ₹ 1250

Y ‘s share = ₹ ( 2000 x 3/8) = ₹ 750

Ratio and Proportion Problems and Solutions for Class 7 – Divide sum of money among three persons when ratio are given

Question 6 :

Divide ₹ 5000 among X , Y and Z in the ratio 1 : 2 : 7

Total money = ₹ 5000

Given ratio = 1 : 2 : 7

Sum of ratio terms = ( 1 + 2 + 7 )

Share of X = ₹ ( 5000 x 1/10) = ₹ 500

Share of Y = ₹ ( 5000 x 2/10) = ₹ 1000

Share of Z = ₹ ( 5000 x 7/10) = ₹ 3500

Ratio and Proportion Problems and Solutions for Class 7 – Comparison of ratios

To Compare two Ratios, we should follow the following steps : –

• Write both the Ratios as Fractions
• Convert both the Fractions into Like Fraction:- – Find the L.C.M of denominator of both the Fractions – Make the denominator of each fraction equal to their L.C.M.
• In case of Like fractions, the number whose numerator is greater is larger.

Question 7 :

Compare the ratios ( 3 : 4 ) and ( 4 : 3 )

We can write

( 3 : 4 ) = 3/4 and ( 4 : 3 ) = 4/3

Now, let us compare 3/4 and 4/3

LCM of 4 and 3 is 12

Making the denominator of each fraction equal to 12

In case of Like fractions, the number whose numerator is greater is larger. Hence we can say 9/12 < 16/12

That is, 3/4 < 4/3

Hence, ( 3 : 4 ) < ( 4 : 3 )

Ratio and Proportion Examples With Answers –  Proportion

When Two Ratios are equal then we say that they are in Proportion and use the symbol “: :” or “=” to equate two ratios.

Four Numbers in Proportion

Let a, b, c, d are four numbers said to be in proportion. then, a : b = c : d  or a : b :: c : d here a and d are called the extreme terms or extremes. b and c are called the middle terms or means. When Four numbers are in proportion then, Product of extremes = Product of means. i.e, In proportion a : b :: c : d, (a x d) = (b x c)

Ratio and Proportion Problems and Solutions for Class 7 – Are the given ratio in proportion

Question 8 :

Are the ratios 15 m : 45 m and 30 km : 90 km in proportion?

We have 15 m : 45 m

30 km : 90 km

Since, the ratios 15 m : 45 m and 30 km : 90 km are equal to 1/3. So, they are in proportion.

Ratio and Proportion Problems and Solutions for Class 7 – Are the given number are in proportion

Question 9 :

Are 3, 6, 5, 15 in proportion?

Product of means = Product of extremes

Here, Means are 6 and 5

Extremes are 3 and 15

Product of extremes = 3 x 15 = 45

Product of means = 6 x 5 = 30

Since, Product of extremes ≠ Product of means

Hence, 3 , 6 , 5 , 15 are not in Proportion

Ratio and Proportion Problems and Solutions for Class 7 – Find the value of y when four numbers are in proportion

Question 10 :

If 20 : 12 : : y : 6, find the value of y?

We know that, Product of means = Product of extremes

In the given numbers, we can say that 12 , y are means and 20 , 6 are extremes

12 x y = 20 x 6

Hence, y = 10

Question 11 :

If 45 : y : : y : 5, find the value of y?

Clearly, Product of means = Product of extremes

y x y = 45 x 5

y² = 45 x 5

Hence, y = 15

Ratio and Proportion Problems and Solutions for Class 7 – Finding Ratio A : B : C

Question 12 :

If 3A = 5B = 4C , find A : B : C?

3A = 5B = 4C = k

This implies that 3A = k

Also if 5B = k

Further, if 4C = k

A : B : C = k/3 : k/5 : k/4

LCM of 3 , 5 , 4 is 60

Multiplying each of the ratio by 60/k we get the ratios as

= 20 : 12 : 15

Hence, A : B : C = 20 : 12 : 15

Ratio and Proportion Problems and Solutions for Class 7 – Finding Ratio A : B : C if Ratio A : B and B : C given

Question 13 :

If A : B = 4 : 9 and B : C = 12 : 2, find A : B : C

Given A : B = 4 : 9

and B : C = 12 : 2

To find A : B : C we have to make the value of common term in both the ratios equal

that is, B = 9

For this B : C = 1 : 2/12 ( On dividing each term by 12 )

B : C = ( 9 : 2/12 x 9 ) (On multiplying each term by 9 )

B : C = 9 : 18/12

We get, B : C = 9 : 3/2

Since, A = B = 4 : 9 and B : C = 9 : 3/2

Therefore, A : B : C = 4 : 9 : 3/2

Hence, A : B : C = 8 : 18 : 3 (Multiplying each term by 2 )

Ratio and Proportion Problems and Solutions for Class 7 – Converting Ratio into another Ratio

Question 14 :

What must be added to each term of the ratio 7 : 9 so that the new ratio becomes 7 : 8 ?

Let the required number to be added be ‘ a ‘

then, ( 7 + a ) : ( 9 + a ) = 7 : 8

8 ( 7 + a ) = 7 ( 9 + a )

56 + 8a = 63 + 7a

8a – 7a = 63 – 56

Hence, the required number is 7

Ratio and Proportion Problems and Solutions for Class 7 – Finding ratio of present ages

Question 15 :

Present age of Sanjay is 52 years and the age of his Daughter is 28 years. Find the ratio of present age of Daughter to the present age of Sanjay ?

Present age of Sanjay = 52 years

Present age of Daughter = 28 years

To find the ratio of present age of Daughter to the present age of Sanjay

Hence, the ratio of the present age of Daughter to Sanjay is 7 : 13

Ratio and Proportion Problems and Solutions for Class 7 – Finding ratio of ages of persons after some years

Question 16 :

Present age of Seema is 22 years and the age of her Brother is 26 years. Find the ratio of Seema’s age to her Brother’s age after 10 years.

Present age of Seema = 22 years

After 10 years Seema’s age = 22 + 10 = 32 years

Present age of Brother = 26 years

After 10 years Brother’s age = 26 + 10 = 36 years

Ratio of age of Seema and Brother after 10 years

Taking, HCF of 32 and 36 is 4

Hence, the ratio of Seema’s age to her Brother’s age after 10 years is 8 : 9

Ratio and Proportion Problems and Solutions for Class 7 – Finding ratio of ages of persons some year ago.

Question 17 :

Present age of Ritu is 23 years and the age of her Brother is 18 years. What was the ratio of Ritu’s age to her Brother’s age 3 years ago?

Present age of Ritu = 23 years

Ritu’s age 3 years ago = 23 – 3 = 20 years

Present age of Brother = 18 years

Brother’s age 3 years ago = 18 – 3 = 15 years

Ratio of age of Ritu and Brother 3 years ago

Hence, the ratio of Ritu’s age to Brother’s age is 4 : 3

Ratio and Proportion Problems and Solutions for Class 7 – Third proportional value

Let say a and b be two numbers and c is in third proportion with a and b

a : b = b : c

Question 18 :

Find the third proportion to 6 and 12?

Let, the third proportion to 6 and 12 be a

6 : 12 :: 12 : a

(Product of Extremes= Product of Means)

Here, Extremes are= 6 and a

Means are = 12 and 12

6 x a = 12 x 12

Hence, the value of ‘a’ is 24

Ratio and Proportion Problems and Solutions for Class 7 – Mean proportional value

Let say a and b be two numbers and c is mean proportional between a and b

a : c = c : b

Question 19 :

Find the mean proportional between 10 and 40 ?

Let, the mean proportional between 10 and 40 be ‘ a ‘

10 : a :: a : 40

(Product of extremes = Product of means)

Here, Extremes are 10 and 40

Means are a and a

10 x 40 = a x a

a² = 10 x 40 = 400

Hence, the value of ‘a’ is 20

Ratio and Proportion Problems and Solutions for Class 7 – Continued proportion

Three numbers are said to be in Continued Proportion if the ratio of first and second number is equal to the ratio of second and third number.

If a, b, c are in continued proportion

a : b : : b : c

Question 20 :

If 12, 42, a are in continued proportion, find the value of a?

Given –  12 , 42 , a are in continued proportion.

12 : 42 :: 42 : a

Here, Extremes are 12 and a

Means are 42 and 42

12 x a = 42 x 42

Hence, the value of ‘a’ is 147

Click here for Class 7 Chapterwise Explanations

NCERT Solutions for Class 7

Cbse notes for class 7, worksheets for class 7, 4 thoughts on “ratio and proportion problems and solutions for class 7”.

Amazing!! Helped me a lot in my test !! Thanks a lot

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Really nice worksheet there so many variety questions helps us to practice a lot .keep it up

Many Thanks Yuvraj

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Free Mathematics Tutorials

Grade 7 maths problems with answers.

Grade 7 math word problems with answers are presented. Some of these problems are challenging and need more time to solve. The Solutions and explanatiosn are included.

• In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
• In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
• If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?
• The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
• A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
• Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
• Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
• 15 cm is the height of water in a cylindrical container of radius r. What is the height of this quantity of water if it is poured into a cylindrical container of radius 2r?
• John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
• How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
• The rectangular playground in Tim's school is three times as long as it is wide. The area of the playground is 75 square meters. What is the primeter of the playground?
• John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
• N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? A) 1 1/2 B) 1 1/3 C) 5/3 D) 3/2
• In 2008, the world population is about 6,760,000,000. Write the 2008 world population in scientific notation.
• Calculate the circumference of a circular field whose radius is 5 centimeters.

Answers to the Above Problems

• 6 balls are blue
• 10 students are 10 years old
• x = 5/6 meter
• 20,000 square meters
• 368 square units
• 1250 meters per minute
• 78.74 inches
• 40 square meters
• 10π centimeters

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