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Build Tables of Equivalent Ratios

Students use ratio tables to find missing values by extending a given ratio. They recognize that every row in a ratio table represents an equivalent ratio and use multiplication or division to scale ratios up or down to solve missing-value problems.

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Build Tables of Equivalent Ratios

Grade 6 · Ratios and Rates · question 1 of 3

0 of 20

20 rungs. A star at the top.

: 4 = 14 : 8

How it is taught

0:00 of 4:09

Equivalent ratios come from multiplying both parts by the same number.

Adding the same amount to both parts is not the same.

Read it: Equal ratios in a table

3 adults for every 8 children. The table keeps that ratio in every column: 6 to 16, 9 to 24, 12 to 32. Each column is 3 : 8 times a number.

  1. Put the ratio in the first column: 3 adults over 8 children.
  2. Find the factor: 12 adults is 3 adults × 4.
  3. Multiply the other row by the same factor: 8 × 4 = 32 children.

Every column is the first column times a number, so each one keeps the ratio 3 : 8.

Multiplying both terms by 4 makes 4 groups of 3 adults and 8 children: 12 adults, 32 children.

Dividing both terms by the same number works the other way: 12 : 32 = 3 : 8.

Equal ratios multiply or divide both terms by the same number; they never add the same number.

Adding 9 to both terms and writing 3 : 8 = 12 : 17.

12 is 3 × 4, so the other term is 8 × 4 = 32: 3 : 8 = 12 : 32.

11 : 13 = 55 : ___ — 65. 55 is 11 × 5, so the other term is 13 × 5 = 65.

2:3 → ?:12 (cookie recipe)

Our cookie recipe uses two cups of flour for every three cookies. How much flour do we need for twelve cookies?

Let's build a ratio table. Flour on the left, cookies on the right.

Our starting ratio is two to three. That's row one.

Double both sides: two times two is four cups, three times two is six cookies.

Triple the recipe: six cups of flour for nine cookies.

Multiply by four: eight cups of flour for twelve cookies.

There it is! Twelve cookies need eight cups of flour.

Notice: we multiplied BOTH sides by four. Every row is an equivalent ratio to two to three.

How much flour for 12 cookies?Recipe: 2 cups flour → 3 cookiesRatio TableFlour (cups)Cookies2346×269×3812×4×4×4Same multiplier on both sides → equivalent ratioANSWER8 cupsfor 12 cookies
Grade 6 · Scaling a recipe with a ratio table

Eight cups of flour makes twelve cookies. Ratio tables let us scale any recipe!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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