Grade 6 (age 11-12)

Proportion & Proportional Distribution

A proportion links two equal ratios with an equals sign, and the product of the outer terms always matches the product of the inner terms. Proportional distribution splits a whole by a set ratio, so 40 candies shared in 3 to 5 become 15 and 25. It shows up often in daily life, from doubling a recipe to splitting an allowance between siblings. Here you can balance a proportion on a scale and watch a pie chart divide the whole by the ratio you choose.

What is a Proportion?

⚖️ Connect Two Equal Ratios with =!

①2:3 = 4:6 → both equal 2/3

②Like a balance staying level

③Outer product = inner product is key!

a (outer)2

b (inner)3

c (inner)4

Proportional Distribution

🍰 Divide the Whole by a Given Ratio

①Divide 40 candies in 3:5

②Whole = (3+5=8) groups

③1 group = 40÷8 = 5; A=15, B=25

A ratio3

B ratio5

Total amount40

Summary

Property of Proportion

a : b = c : d → a × d = b × c

Outer product = inner product

Proportional Distribution

A's share = Total × aa+b

When dividing whole by a:b, A's share

🎯 Key Points

①Proportion: two equal ratios

②Solve unknowns via outer product = inner product

③Proportional distribution: split a whole by ratio

④Verify: sum of shares = total

⑤Real life: recipe scaling, map scale, allowance sharing

Examples & Unit Review

Example 1

Find □ in the proportion 3 : 4 = 9 : □.

In a proportion, the product of the outer terms equals the product of the inner terms: 3 × □ = 4 × 9.

3 × □ = 36, so □ = 36 ÷ 3 = 12.

▸ □ = 12

In a proportion, the product of the two outer terms equals the product of the two inner terms.

Example 2

Share 40 candies between two siblings in a 3 : 5 ratio. How many does each get?

Treat the whole as 3 + 5 = 8 parts. One part = 40 ÷ 8 = 5.

Older = 5 × 3 = 15, younger = 5 × 5 = 25.

▸ Older 15, younger 25

Proportional sharing splits the whole into as many parts as the sum of the ratio.

Unit Review

What is □ in the proportion 2 : 5 = □ : 20?

①8

②10

③50

④4

▸ ① 8

Outer product = inner product: 2 × 20 = 5 × □.

40 = 5 × □, so □ = 40 ÷ 5 = 8.

← Previous

Ratio & Rate

Percentage