Ratios and rates: how to help your child practice

What are ratios and rates?

A ratio compares two quantities. If a bag has 4 red marbles and 6 blue marbles, the ratio of red to blue is 4 to 6, written 4:6 or 4/6. Ratios simplify like fractions, so 4:6 is the same as 2:3: for every 2 red marbles there are 3 blue ones.

A rate is a ratio of two different kinds of units, like miles and hours. A unit rate is a rate "per 1": 150 miles in 3 hours is 50 miles per hour. Unit rates are how kids compare prices, speeds and recipes.

In most US schools, 6th graders write ratios, use ratio tables and find unit rates, and 7th graders find unit rates with fractions, solve proportions and use them for percents. The 6th grade guide shows what else comes up that year, and the math topic guide shows how ratios grow out of multiplication and fractions.

How do you solve ratio and rate problems, step by step?

Two tools cover most homework problems.

A ratio table. A recipe uses 2 cups of flour for every 3 eggs. How much flour for 12 eggs?

1. Write the ratio as the first column: 2 flour, 3 eggs.
2. Multiply both numbers by the same amount to make new columns: 4 and 6, 6 and 9, 8 and 12.
3. Read off the answer: 12 eggs need 8 cups of flour.

A unit rate. A car goes 150 miles in 3 hours.

1. Write it as a fraction with the "per" unit on the bottom: 150 miles / 3 hours.
2. Divide so the bottom becomes 1: 150 ÷ 3 = 50.
3. Name the units: 50 miles per hour.

Unit rates make comparing easy. 6 pencils for $3.00 is $0.50 each, and 10 pencils for $4.50 is $0.45 each, so the 10-pack is the better buy. In 7th grade the numbers can be fractions: walking 1/2 mile in 1/4 hour is (1/2) ÷ (1/4) = 2 miles per hour.

What ratios and rates mistakes do kids make most?

Writing the ratio backward

Asked for the ratio of red to blue with 4 red and 6 blue marbles, a child writes 3:2. The order of the words sets the order of the numbers, so it's 4:6, or 2:3. Have your child label each number ("2 red : 3 blue") before simplifying.

Adding instead of multiplying

For 2 cups of flour per 3 eggs, a child sees that 3 eggs became 12 (9 more) and adds 9 to the flour too, answering 11 cups. Ratios grow by multiplying: 3 × 4 = 12, so 2 × 4 = 8 cups.

Dividing the wrong way for a unit rate

For 150 miles in 3 hours, a child divides 3 ÷ 150 and gets 0.02. That's hours per mile, not miles per hour. The unit after "per" goes on the bottom: 150 ÷ 3 = 50 miles per hour.

How can you practice ratios and rates at home in 10 minutes?

Ratios are everywhere in a kitchen or a grocery store, so use them.

• Minutes 1–3: scale a recipe. If lemonade is 1 cup of lemon juice to 4 cups of water, how much juice for 12 cups of water? (3 cups.) Have your child build a ratio table to show it.
• Minutes 4–8: five mixed problems. One ratio in simplest form (12 boys to 9 girls), one unit rate (84 pages in 4 minutes), one better buy, one missing value in a ratio table, and, for 7th graders, one unit rate with fractions.
• Minutes 9–10: check a real price. Look at a shelf tag or receipt and work out a price per ounce: a 12-ounce box for $3.60 is $0.30 per ounce.

Use new numbers each night so your child is practicing the method, not the answers.

How can Easy Twin help with ratios and rates?

Scan your child's ratios worksheet and Easy Twin makes a twin with the same kinds of questions and new numbers. Every question comes with two hints and worked steps, visuals like tables and bar graphs are redrawn with new data, and your child can play the twin as a quest or you can print it with an answer key.

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