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Lesson · Grade 8 · Mathematics

Solving a proportion with equivalent ratios

  • Grade 8
  • Mathematics
  • 2 min 18 s
  • British Columbia
  • BC8-MA-11

A recipe uses 3 cups of flour for 2 loaves, and the video finds the flour for 7 loaves by solving the proportion 3/2 = x/7 two ways: with the scale factor (× 3.5) and with a ratio table through the unit rate of 1.5 cups a loaf, both giving 10.5 cups. It then shows why adding 5 to both terms (8 cups) is wrong, solves a percent as a proportion (18 out of 24 = 75 out of 100, so 75%, checked with 0.75 × 24 = 18), and ends on the recap: multiply or divide both terms by the same number.

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In one sentence

The question this lesson answers

A recipe uses 3 cups of flour for 2 loaves. How much flour do 7 loaves need?

A ratio compares two amounts, called its terms. Flour to loaves is 3 to 2, or 3 over 2.

Transcript

What the lesson says

A recipe uses 3 cups of flour for 2 loaves. How much flour do 7 loaves need?

A ratio compares two amounts, called its terms. Flour to loaves is 3 to 2, or 3 over 2.

Call the missing flour x. A proportion says two ratios are equal: 3 over 2 equals x over 7.

Equal ratios are called equivalent. To make one, multiply or divide both terms by the same number, not zero.

Method 1: the scale factor is the number we multiply both terms by. 2 times 3.5 is 7.

Multiply the flour by 3.5 too: 3 times 3.5 is 10.5 cups.

Method 2 is a ratio table, where each column is an equivalent ratio.

First find the unit rate, the flour for 1 loaf. Divide both terms by 2: 3 divided by 2 is 1.5.

Then multiply both terms by 7. 1.5 times 7 is 10.5 cups, the same answer.

A common mistake is adding. 2 plus 5 is 7, so some people add 5 to 3 as well and get 8 cups.

But 8 divided by 7 is about 1.14, not 1.5. Adding 5 changed the ratio.

A percent is a ratio out of 100, so a percent question is a proportion too.

You get 18 out of 24 questions right. So 18 over 24 equals x over 100.

Divide both terms by 6 to get 3 over 4. Then multiply both by 25 to get 75 over 100.

So 18 out of 24 is 75 percent. Check: 0.75 times 24 is 18.

To solve a proportion, multiply or divide both terms by the same number.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: numerical proportional reasoning (rates, ratio, proportions, and percent)BC8-MA-11

Previous: Rates and Unit Rates: How Much for OneNext: Sharing an Amount in a Ratio

The outcomes and strands follow the British Columbia curriculum.

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