Solve proportions

key notes :

Proportion says that two ratios (or fractions) are equal.

proportion 1/3 : 2/6

We see that 1-out-of-3 is equal to 2-out-of-6

The ratios are the same, so they are in proportion.

A rope’s length and weight are in proportion.

When 20m of rope weighs 1kg, then:

  • 40m of that rope weighs 2kg
  • 200m of that rope weighs 10kg
  • etc.
rope 20m / 1kg : 40m / 2kg

So:

20/1 = 40/2

Learn with an example

🔔 Solve for n in the proportion.

n/12 = 12/8

n = 

Solve for n in the proportion.

n/12 = 12/8

n/12 ( 12.8 ) = 12/8 ( 12.8 ) Multiply both sides by 12 · 8

8n = 12 · 12 Simplify

8n = 144 Simplify

n = 18 Divide both sides by 8

🔔 Solve for w in the proportion.

45/39 = 30/w

w = 

Solve for w in the proportion.

45/39 = 30/w

45/39 ( 39w ) = 30/w ( 39w ) Multiply both sides by 39w

45w = 39 · 30 Simplify

45w = 1,170 Simplify

w = 26 Divide both sides by 45

Solve for g in the proportion.

15/2 = 45/g

g =

Solve for g in the proportion.

15/2 = 45/g

15/2 (2g) = 45/g (2g) Multiply both sides by 2g

15g = 2 · 45 Simplify

15g = 90 Simplify

g = 6 Divide both sides by 15

Let’s Practice!