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Understand and Describe Ratios

Students learn what a ratio is and how to use ratio language to describe a relationship between two quantities. They write ratios in three forms (a:b, a to b, a/b) and interpret what each ratio means in context, including part-to-part and part-to-whole relationships.

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Understand and Describe Ratios

Grade 6 · Ratios and Rates · question 1 of 3

0 of 20

20 rungs. A star at the top.

16 : 6 = 8 :

How it is taught

0:00 of 4:13

A ratio compares two quantities in order.

Equivalent ratios simplify to the same comparison.

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.

9 : 10 = 54 : ___ — 60. 54 is 9 × 6, so the other term is 10 × 6 = 60.

3 apples to 5 oranges

A fruit bowl has three apples and five oranges. How can we describe this in math?

Let's count. One, two, three apples.

And one, two, three, four, five oranges.

A ratio compares two amounts. The ratio of apples to oranges is three to five.

We can write it with a colon: three colon five.

Or with the word 'to': three to five.

Or as a fraction: three over five. Same ratio, three different forms.

3 apples and 5 orangesRatio: apples to orangesPart-to-whole: apples to all fruitThree forms, one ratio●●●3 apples●●●●●5 orangeswith a colon3 : 5with the word 'to'3 to 5as a fraction35part-to-part: 3 apples : 5 oranges8 pieces of fruit in allapples to all fruit = 3 : 8RATIO3 : 5apples to oranges
Grade 6 · Comparing two quantities with ratios

This is a part-to-part ratio — it compares one part to another part.

Now let's count all the fruit. Three plus five is eight pieces of fruit in all.

The ratio of apples to all fruit is three to eight. That's a part-to-whole ratio.

So three apples and five oranges gives us a three-to-five ratio. Ratios let us compare amounts in a clear way!

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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