MAT-144 · Mathematical Reasoning
Topic 01 · Linear Functions
Solving proportions
Two equal fractions, one unknown. Find the multiplier from one side and apply it to the other.
01
Worked Example Video
Every step of Solving proportions explained on video. Pause anywhere; the embed scrolls independently of the page.
YOUTUBE
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
Solve for x: 3 / 4 = x / 12
x =
✓
Right — the multiplier on the bottom is × 3 (4→12). Apply to the top: 3 × 3 = 9.
✗
Not quite. The bottom went from 4 to 12 — that's a multiplier of × 3. Apply the same multiplier to the top: 3 × 3 = 9.
Solving proportions
Solve for x: 5 / 8 = 25 / x
x =
✓
Right — this time the multiplier is on the top (5 → 25, × 5). Apply to the bottom: 8 × 5 = 40.
✗
The multiplier is on the top this time. 5 to 25 is × 5. Apply to the bottom: 8 × 5 = 40.
Solving proportions
Solve for x: x / 15 = 4 / 5
x =
✓
Right — the bottom went from 5 to 15 (× 3). Apply to the top: 4 × 3 = 12.
✗
The bottom went from 5 to 15 — that's × 3. Apply the same multiplier to the top: 4 × 3 = 12.
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
The Rule
Given a/b = c/d
find the multiplier from one side
Multiplier on the known side
apply it to the other side
Three of the four numbers are given. Look at whichever side has both numbers; figure out what multiplier turns one into the other. Apply the same multiplier to the other side to solve for x.
Common slip
Students divide when they should multiply. If the multiplier goes from 4 to 12 (times 3), and the top of the same side is 3, the top of the other side is 3 × 3, not 3 ÷ 3. The direction of the multiplier is the same on both sides.
04
Practice — Step by Step
Practice this problem step by step
Solve for x: 2 / 7 = x / 14
Find the multiplier
Look at the denominators. What multiplier turns 7 into 14?
Ask yourself: 7 times WHAT equals 14?
✓
Right — 7 × 2 = 14, so the multiplier is × 2. Apply the same multiplier to the top.
✗
Not quite — try again.
Apply the multiplier to the top
The top of the known side is 2. Multiply it by 2 (the same multiplier). What is x?
x =
The multiplier is × 2. The top of the known side is 2. What’s 2 × 2?
✓
Right. 2 × 2 = 4. So x = 4. Every proportion works the same way — find the multiplier on the known side, apply it to the unknown side.
✗
Not quite. 2 × 2 = 4. The multiplier on the bottom was × 2 (7 → 14); the same multiplier on the top gives 2 × 2 = 4.
🎉
You solved the proportion.
Same move every time: find the multiplier on the side with both numbers, apply it to the other side. Doesn’t matter whether the x is on top or bottom, or on the left or right — the multiplier logic is identical.