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Percent Fraction to percent Multiplication and divisionLong division

Here you will learn about ratio to percent, including how to convert from ratios to percents and how to solve word problems involving converting ratios to percents.

Students will first learn about ratio to percent as part of ratio and proportion in 6 th grade.

**Ratio to percent** is when you use a given ratio to calculate a percent.

A ratio tells us how much there is of one thing in relation to another thing.

For example, if Olivia and Dean share some sweets in the ratio 3:2, then for every 3 sweets Olivia gets, Dean gets 2. You can use this information to write the percent of sweets Olivia and Dean each get.

To find the percent of sweets they each get, first convert the ratio into fractions.

The ratio 3:2 has 5 parts, so the fractions are

\cfrac{3}{5} : \cfrac{2}{5}

The numerator represents the numbers of the ratio, which show how many sweets Olivia and Dean each get. The denominator represents the total number of sweets that are present in the ratio. So out of every 5 sweets, Olivia gets 3 and Dean gets 5.

Olivia gets three-fifths of the sweets and Dean gets two-fifths. You can convert these fractions to percents.

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{3}{5}=60 \%, so Olivia gets 60 \% of the sweets.

\cfrac{2}{5}=40 \%, so Dean gets 40 \% of the sweets.

Each percent must include the percent sign \% (also known as percent symbol or percentage symbol).

How does this relate to 6 th grade math?

**Grade 6 – Ratio and Proportional Relationships (6.RP.A.3c)**

Find a percent of a quantity as a rate per 100 (for example, 30 \% of a quantity means \cfrac {30}{100} times the quantity); solve problems involving finding the whole, given a part and the percent.

In order to convert a ratio to a percent:

**Add the parts of the ratio for the denominator of the fractions.****Convert each part of the ratio to a fraction.****Convert the fractions to percents.**

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREEThe ratio of blue counters to red counters is 3:1. Write the ratio as percents.

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

3 + 1 = 4. There are 4 parts in total. The denominator is 4.

2**Convert each part of the ratio to a fraction.**

3:1 becomes \cfrac{3}{4}:\cfrac{1}{4} \, .

3**Convert the fractions to percents.**

\cfrac{3}{4} and \cfrac{1}{4} \, are common fractions for which you should already know the percent conversions.

\cfrac{3}{4} : \cfrac{1}{4}=75 \% : 25 \%

The ratio of green counters to yellow counters is 3:5. What percent of the counters are green?

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

3 + 5 = 8. There are 8 parts in total. The denominator is 8.

**Convert each part of the ratio to a fraction.**

3:5 becomes \cfrac{3}{8}:\cfrac{5}{8} \, .

**Convert the fractions to percents.**

3 \div 8=0.375

5 \div 8=0.625

0.375=37.5 \% and 0.625=62.5 \% therefore,

\cfrac{3}{8}:\cfrac{5}{8}=37.5 \% : 62.5 \%.

Order is important in ratios, and in this ratio, the number of green counters is first.

Therefore the percent of counters that are green is 37.5 \%.

A garden center sells three types of bulbs; daffodil, tulip and lily, in the ratio 6:9:5. What percent of the bulbs sold are tulips?

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

6 + 9 + 5 = 20. There are 20 parts in total. The denominator is 20.

**Convert each part of the ratio to a fraction.**

6:9:5 becomes \cfrac{6}{20}:\cfrac{9}{20}:\cfrac{5}{20} \, .

**Convert the fractions to percents.**

Writing each fraction with a denominator of 100,

\cfrac{6}{20}:\cfrac{9}{20}:\cfrac{5}{20}=\cfrac{30}{100}:\cfrac{45}{100}:\cfrac{25}{100}.

\cfrac{6}{20}:\cfrac{9}{20}:\cfrac{5}{20}=30 \% : 45 \% : 25 \%

This question asks about the number of tulips sold, which is the middle value. The percent that are tulips is 45 \%.

In April 2022, Ben and Jacob shared some money in the ratio of their ages. Ben was born in June 2014 and Jacob in January 2019. What percent of the money does Ben receive?

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

In April 2022, Ben is 7 and Jacob is 3. The ratio of their ages is 7:3.

7+3=10. There are 10 parts in total. The denominator is 10.

**Convert each part of the ratio to a fraction.**

7:3 becomes \cfrac{7}{10}:\cfrac{3}{10} \, .

**Convert the fractions to percents.**

\cfrac{7}{10} :\cfrac{3}{10} = 70 \% : 30 \%

Ben receives 70 \% of the money.

The ratio of adults to children in a park is 6:4.

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

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

6 + 4 = 10. There are 10 parts in total. The denominator is 10.

**Convert each part of the ratio to a fraction.**

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

**Convert the fractions to percents.**

\cfrac{6}{10} : \cfrac{4}{10} = 60 \% : 40 \%

You now know that 60 \% of the people are adults.

One-third of the adults are men.

\cfrac{1}{3} \, of \, 60 \% = 20 \%

20 \% of the people in the park are men, and therefore 60-20=40 \% of the people are women.

William and Matthew share some money in the ratio 3:7. Matthew gives two-fifths of his money to Ellie. Who receives the most money?

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

3 + 7 = 10. There are 10 parts in total. The denominator is 10.

**Convert each part of the ratio to a fraction.**

3:7 becomes \cfrac{3}{10}:\cfrac{7}{10} \, .

**Convert the fractions to percents.**

\cfrac{3}{10} : \cfrac{7}{10} = 30 \% : 70 \%

Now you know that William receives 30 \% and Matthew receives 70 \%. Matthew gives two-fifths of his money to Ellie. So you need to find two-fifths of 70 \%.

\cfrac{2}{5} \, of \, 70 \% = \cfrac{2}{5} \times \cfrac{70}{1}=\cfrac{140}{5}

\cfrac{140}{5}=28 \%

Matthew gave Ellie 28 \%.

Subtract to find what percent Matthew has left.

70 \% - 28 \%=42 \%

The question asks who receives the most money – William, Matthew, or Ellie.

William has 30 \%, Matthew has 42 \%, and Ellie has 28 \%.

Matthew receives the most money.

- Start by explaining the concept of ratios and percents using familiar situations that students can relate to. For example, you can talk about how a recipe uses a ratio of ingredients, and then show how to convert those ratios into percentages for easier understanding. Another example is to create ratios using the number of students in your classroom.

- Instead of just providing study materials, utilize educational apps or online tools that allow students to practice converting ratios to percents interactively, such as a percentage calculator or a ratio calculator. This adds a modern and engaging dimension to the learning process.

- Give students a worksheet with solved examples and ask them to work backward to find the starting ratio. Students can calculate the ratio given the fractional form or percentage value first.

- For students who are struggling with ratio to percentage conversions, give them activities with commonly used ratios and provide a percentage table to use. Ask them to explain why the original ratio and percentage both represent the relationship. Then model how to convert the ratio to a percentage. With time, students can begin to identify the relationships and solve calculations on their own.

**Confusing ratios and fractions**

For example, the ratio 2:3 is expressed as the fraction \cfrac{2}{3} and not \cfrac{2}{5} \, .

This is a misunderstanding of the sum of the parts of the ratio. Be careful with what the question is asking as the denominator may be the part or the whole amount.

**Writing the ratio in the wrong order**Order is important in ratio questions and you must maintain the original order throughout your work and answer.

1) Convert the following ratio to a percent: 1:4

80 \% : 20 \%

10 \% : 40 \%

20 \% : 80 \%

40 \% : 10 \%

This ratio has 5 parts in total, therefore

1:4=\cfrac{1}{5}:\cfrac{4}{5} \, .

Converting to percents,

\cfrac{1}{5}:\cfrac{4}{5}=20 \% : 80 \% \, .

2) The ratio of podcast subscribers that are men to podcast subscribers that are women is 9:11. What percent of podcast subscribers are men?

9 \%

90 \%

55 \%

45 \%

This ratio has 20 parts, therefore

9:11=\cfrac{9}{20}:\cfrac{11}{20} \, .

Converting to percents,

\cfrac{9}{20}:\cfrac{11}{20}=45 \% : 55 \% \, .

45 \% of podcast subscribers are men.

3) The ratio of teachers to students on a school trip is 1:7. What percent of those on the trip are students?

87.5 \%

70 \%

10 \%

12.5 \%

The total number of parts in this ratio is 8, therefore

1:7=\cfrac{1}{8}:\cfrac{7}{8} \, .

Converting to percents,

\cfrac{1}{8}:\cfrac{7}{8}=12.5 \% : 87.5 \% \, .

87.5 \% of those on the trip are students.

4) Sam, Katrina and Alex share some sweets in the ratio 11:8:6. What percent of the sweets does Sam get?

24 \%

55 \%

11 \%

44 \%

The total number of parts in this ratio is 25, therefore

11:8:6=\cfrac{11}{25}:\cfrac{8}{25}:\cfrac{6}{25} \, .

Converting to percents,

\cfrac{11}{25}:\cfrac{8}{25}:\cfrac{6}{25}=44 \% : 32 \% : 24 \% \, .

Sam gets 44 \% of the sweets.

5) The ratio of the number of boys to girls on an olympiad team is 7:3. One-fifth of the boys wear glasses. What percent of the olympiad team are boys that wear glasses?

70 \%

14 \%

30 \%

20 \%

The total number of parts in this ratio is 10, therefore

7:3=\cfrac{7}{10}:\cfrac{3}{10} \, .

Converting to percents,

\cfrac{7}{10}:\cfrac{3}{10}=70 \% : 30 \% \, .

70 \% of the olympiad team are boys and one-fifth of the boys wear glasses.

\cfrac{1}{5} of 70 \% = 14 \%

14 \% of the olympiad team are boys who wear glasses.

6) Tony and Anne share some money in the ratio 23:27.

Anne gives a quarter of her share to her friend James.

What percent of the money does James get?

5.75 \%

11.5 \%

23 \%

46 \%

The total number of parts in this ratio is 50, therefore

23:27=\cfrac{23}{50}:\cfrac{27}{50} \, .

Converting to percents,

\cfrac{23}{50}:\cfrac{27}{50}=46 \% : 54 \% \, .

Anne gets 46 \% of the money and gives one quarter of her share to James.

\cfrac{1}{4} \, of \, 46 \% = 11.5 \%

James gets 11.5 \% of the money.

To convert ratios to percents, first add the parts of the ratio to get the denominator of the fractions, then convert each part of the ratio to a fraction. Finally, convert the fractions to percents.

The formula for converting a ratio to a percentage is: Percentage = (Numerator \div Denominator) \times 100. Note that this is used for a part-whole ratio.

To simplify a ratio, you divide both numbers in the ratio by their greatest common factor.

A percent is a specific type of ratio where the whole is represented as 100. A ratio can be converted into a percent or you can use percentage increase and percentage decrease to solve ratio problems.

No, ratios can involve any type of numbers, including decimals and fractions, as long as they represent the relationship between the quantities being compared.

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