Grade 6 (age 11-12)

grade 6 Ratio & Rate

Ratio & Rate

A ratio compares two amounts with the symbol :, and a rate is the size of the compared amount against the base. We write the comparison of 3 and 4 as 3 : 4, and the same value can also appear as the fraction 3/4 or the decimal 0.75. From mixing juice with water to the scale on a map, ratios and rates show up all around daily life. The house of this chapter is ratio and rate. Percentage is rate×100; the percentage house is the next chapter. 2 times 3:5 gives 6:10, the same ratio.

What is a Ratio?

⚖️ Comparing Two Numbers

①Mixing 3 cups juice with 5 cups water

②Juice to water ratio = 3 : 5

③Read as "3 to 5"!

④Same ratio: 3:5 = 6:10 (double both sides)

⑤Discount, batting average, and interest rate are all rates

A amount3

B amount5

What is Percentage?

💯 Ratio Based on 100

①Set the whole as 100

②Express the part as a number

③65% means 65 out of 100 cells!

④Compared amount/base is the same idea as part/whole.

Percentage65%

Summary

Rate

Rate = Compared amountBase

Compared amount divided by the base

Percentage

Percentage(%) = Rate × 100

Rate multiplied by 100 = percent (%)

🎯 Key Points

①Ratio: compare two numbers with ':' (3:5)

②Rate: size of compared amount vs the base

③Percentage: rate expressed as %

④Equal ratios are the same (3:5 = 6:10)

⑤Discount, batting average, interest rate are all rates!

Examples & Unit Review

Example 1

There are 12 boys and 8 girls. Find the ratio of girls to boys.

The reference quantity comes after "to". Boys 12 is the reference and girls 8 is compared, so write 8 : 12.

Divide 8 and 12 by 4 to get 2 : 3.

▸ 2 : 3

In a ratio a : b, the second term b is the reference. Divide by a common number to simplify.

Example 2

Out of 20 students, 9 wear glasses. Express the rate as a fraction and a decimal.

Rate = compared ÷ reference = 9 ÷ 20 = 9/20.

9/20 = 45/100 = 0.45.

▸ 9/20 = 0.45

A rate is the size of the compared amount when the reference is taken as 1.

Unit Review

Express the rate of a compared amount 15 to a reference 25 as a decimal.

①0.6

②0.4

③1.6

④0.06

▸ ① 0.6

Rate = compared ÷ reference = 15 ÷ 25.

15 ÷ 25 = 0.6.

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Variables and Expressions

Proportion & Proportional Distribution