Solving proportions

Two equal fractions, one unknown. Find the multiplier from one side and apply it to the other.

01 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Solving proportions v1

Solve for x:

3 / 4 = x / 12

x =

Solving proportions v2

Solve for x:

5 / 8 = 25 / x

x =

Solving proportions v3

Solve for x:

x / 15 = 4 / 5

x =

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 How to Solve It

a / b = c / d
find what multiplies one side, apply to the other

Three of the four numbers are given. Look at the side with both numbers; figure out what multiplier turns the known top into the new top (or known bottom into the new bottom). Apply the same multiplier to the other side to solve for x.

Solve 3/4 = x/12.

The denominators are 4 on the left and 12 on the right. What times 4 gives 12? 3. So the multiplier is 3.

3 \times 3 = 9

Apply the same multiplier to the top: 3 × 3 = 9. Answer: x = 9.

Solve 5/8 = 25/x.

This time the multiplier is on the top. What times 5 gives 25? 5. So the multiplier is 5.

8 \times 5 = 40

Apply 5 to the bottom: 8 × 5 = 40. Answer: x = 40.

Solve x/15 = 4/5.

Here the unknown is on the LEFT. Look at the denominators: 15 and 5. 5 × 3 = 15, so the multiplier going from right to left is 3.

4 \times 3 = 12

Apply 3 to the top of the right side, then carry it across: x = 12.

▸ COMMON SLIPStudents grab the multiplier from one side but then add it to the other instead of multiplying. If 4 × 3 = 12, then 3 × 3 = 9, not 3 + 3 = 6. The same operation has to apply to both top and bottom — that's what keeps the proportion balanced.

04 Practice — Step by Step

Walk through this practice problem one step at a time. Each step unlocks the next.

Find the multiplier.

Practice problem: Solve 2/5 = x/20. Look at the bottoms — what number do you multiply 5 by to get 20?

multiplier =

Apply the multiplier.

The multiplier is 4. Apply it to the top of the left side: 2 × 4 = ?

answer =

State the answer.

What is x?

x =

▸ NICE WORK

You walked the proportion move end to end.

Same three steps every time: find the multiplier from one side, apply it to the other, state the answer. The unknown can sit on top or bottom, left or right; the move is identical.

Q2 Q4