How to write a ratio

Here you will learn about how to write a ratio, including how to write and simplify ratios.

Students will first learn about how to write a ratio as part of ratios and proportions in 6 th grade.

What is writing a ratio?

Writing a ratio is a way of showing the constant relationship between two or more quantities. The quantities can be in the same or different units.

Ratios can be commonly written 3 different ways:

1. Ratios are most commonly written in the form a: b.

2. As a common fraction \frac{a}{b}.

3. Using the word ‘to’, e.g. a to b.

Example 1

In a class of students, there are 13 boys and 17 girls.

The ratio of boys to girls can be written as 13:17.

The ratio of girls to boys can be written as 17:13.

The ratio of total students to boys can be written as 30:13.

Example 2

In a recipe, there are three eggs, one onion, and two tomatoes. The ratio of eggs to onions is 3:1.

Example 3

There are 7 yellow squares and 5 blue squares. There are 12 squares in total.

The ratio of yellow to blue squares is 7:5.

The ratio of blue to yellow squares is 5:7.

The ratio of yellow squares to the total number of squares is 7:12.

The ratio of blue squares to the total number of squares is 5:12.

After you have written a ratio, like in the examples above, it is possible that the ratio can be simplified by writing an equivalent ratio. When a ratio is fully simplified, the parts of the ratio are all integers with no common factors.

What is writing a ratio?

Common Core State Standards

How does this relate to 6 th grade math?

• Grade 6 – Ratios and Proportional Relationships (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 Proportional Relationships (6.RP.A.2)
  Understand the concept of a unit rate 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.”

How to write a ratio

In order to write a ratio:

1. Identify the different quantities being compared and their order.
2. Write the ratio using a colon.
3. Check if the ratio can be simplified.

How to write a ratio examples

Example 1: writing a ratio about an everyday life situation

Ms. Holly is looking after 7 children. She has 5 toys in her nursery. Write the ratio of children to toys.

1. Identify the different quantities being compared and their order.

There are 7 children and 5 toys.

The order of the ratio is children to toys.

2Write the ratio using a colon.

Children : Toys

\hspace{0.9cm}7 : 5

3Check if the ratio can be simplified.

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

Example 2: writing a ratio about a real life situation

On a farm there are 20 pigs, 8 cows and 124 chickens. Write the ratio of chickens to cows in lowest terms.

Check if the ratio can be simplified.

124 and 8 have common factors of 1, 2 and 4 so this ratio can be simplified.

The ratio of chickens to cows in lowest terms is 31:2.

Example 3: writing a ratio from a picture

Use the diagram below to write the ratio of white counters to the total number of counters in lowest terms.

Check if the ratio can be simplified.

16 and 24 have common factors of 1, 2, 4 and 8 so this ratio can be simplified.

The ratio of white counters to total counters in lowest terms is 2:3.

Example 4: writing a ratio from a graph

The bar chart shows the number of left handed and right handed people in a group.

Write the ratio of left handed people to the total number of people in lowest terms.

Check if the ratio can be simplified.

32 and 80 have common factors of 1, 2, 4, 8 and 16 so this ratio can be simplified.

The ratio of left handed people to the total number of people in its lowest terms is 2:5.

Example 5: writing a ratio from a word problem

In a fridge there are three different types of drinks in bottles: water, tea and lemonade. There are 3 bottles of tea and 2 bottles of lemonade. There are 8 bottles in total. What is the ratio of bottles of lemonade to bottles of water?

Example 6: writing an algebraic ratio from a word problem

Amy is a years old. Imran is 12 years older than Amy. Write the ratio of Imran’s age to Amy’s age.

Teaching tips for how to write a ratio

• Worksheets are a good way for students to practice writing ratios, but be sure to include worksheets that show the ratios in a variety of formats. This can include written statements, pictures or graphs. Also choose worksheets that have questions that ask for unsimplified and simplified ratios.

Easy mistakes to make

• Writing the parts of the ratio in the wrong order
  When a ratio is written, the order is very important. Remember to read the problem carefully to ensure you get the order right.
  For example,
  There are 12 dogs and 13 cats. What is the ratio of cats to dogs?
  A common mistake would be to write 12:13 because this is the order in which the numbers are presented in the information. However, the question asks for the ratio of ‘cats to dogs’, so the correct answer is 13:12 because there are 13 cats and 12 dogs.

• Confusing wholes and parts
  Take the ratio of boys to girls 5:4. This ratio shows two parts. If asked, what is the ratio of boys to total students, the parts need to be added to find the whole. Since 5 + 4 = 9, there are 9 students in all. The ratio of boys to total students is 5:9.

• Confusing fractions and ratios in fraction form
  Ratios can also be written as fractions, but this does not typically happen until later to avoid confusion. When students are ready to write a ratio in fraction form, the numerator and the denominator represent the two values being compared. It is important to note that the fraction form of a ratio does NOT always represent a part-whole relationship.
  For example,
  The ratio of dogs to cats is \cfrac{6}{4} .
  The ratio is written the same as an improper fraction, but it is not appropriate to read this ratio as “6 fourths .” The numerator of the fraction represents the dogs 6, and the denominator of the fraction represents the cats 4. This ratio is read as “6 to 4” or “6 dogs to 4 cats.”

Related ratio lessons

• Ratio
• Unit rate math
• Simplifying ratios
• Ratio to percent
• Ratio to fraction
• How to calculate exchange rates
• Ratio problem solving
• Dividing ratios
• How to find the unit rate
• Ratio scale
• Constant of proportionality

The next lessons are

• Proportion
• Converting fractions, decimals and percentages
• Percent

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