Arithmetic (Beginner) · Quick Reference

Proportion Cheat Sheet

Arithmetic (Beginner) · Lesson 12/21

In one line: a proportion states that two ratios are equal. Proportions let us solve for an unknown quantity when we know a relationship holds.

Key Ideas

1What is a Proportion. An equation of the form a/b = c/d, stating two ratios are equal.

2Cross Multiplication. In a/b = c/d, cross multiply to get a x d = b x c, then solve for the unknown.

3Direct Proportion. As one quantity increases, the other increases at the same rate (y = kx).

4Inverse Proportion. As one quantity increases, the other decreases proportionally (xy = k, a constant).

5Unit Rate Method. Find the value for one unit first, then scale up or down to find the value needed.

Solve for x: 3/4 = x/20.

x = 15

If 5 pens cost $10, how much do 8 pens cost (direct proportion)?

$16

4 workers finish a job in 6 days. How many days would 8 workers take (inverse proportion)?

3 days

If a/b = c/d, then a x d = b x c

Solve for x: 2/5 = x/25.

x = 10

If 3 apples cost $6, how much do 7 apples cost?

$14

Solve for x: x/4 = 9/12.

x = 3