MAT-144 · Mathematical Reasoning
Topic 01 · Linear Functions
Writing ratios
Read a real-world situation, count the parts, write the ratio. Reduce when both numbers share a common factor.
01
Worked Example Video
Every step of Writing ratios 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.
Writing ratios
A basket contains 5 green apples and 8 red apples. Write the ratio of green apples to red apples.
ratio =
✓
Right — “green to red” puts green on top. 5 and 8 share no common factor, so 5/8 is already in lowest terms.
✗
Not quite. “Green to red” means green on top, red on the bottom. Green = 5, red = 8 → 5/8. That’s already lowest terms.
Writing ratios
A pet store has 7 dogs and 10 cats. Write the ratio of cats to dogs.
ratio =
✓
Right — the sentence listed dogs first, but the prompt asks for cats to dogs — so cats go on top. 10 and 7 share no factor, so 10/7 is already reduced.
✗
Watch the order — the prompt asks for cats to dogs, so cats go on top even though the sentence listed dogs first. Cats = 10, dogs = 7 → 10/7.
Writing ratios — reduces
A class has 6 boys and 9 girls. Write the ratio of boys to girls in lowest terms.
ratio =
✓
Right — 6/9 both divide by 3, giving 2/3 in lowest terms.
✗
Not quite. Start with 6/9 (boys on top). Both 6 and 9 divide by 3: 6÷3 = 2, 9÷3 = 3. Reduced answer: 2/3.
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
Phrase reads “A to B”
write A / B
Both numbers share a common factor
divide both by their GCF
Order matters. “Green to red” is not the same as “red to green.” Only reduce when both numbers share a factor greater than 1.
Common slip
The scenario order in the sentence often doesn’t match the ratio the prompt is asking for. Read the phrase after “ratio of” carefully — the noun before the word “to” goes on top.
04
Practice — Step by Step
Practice this problem step by step
A parking lot has 12 cars and 8 trucks. Write the ratio of trucks to cars in lowest terms.
Set up the order
The prompt asks for trucks to cars. Which count goes on top?
In “trucks to cars,” trucks comes before the word “to” — so trucks go on top.
✓
Right — “trucks to cars” puts 8 on top and 12 on the bottom. Starting fraction: 8/12.
✗
Not quite — try again.
Find the GCF
What is the greatest common factor of 8 and 12?
The GCF is the largest number that divides both 8 and 12 evenly.
✓
Right — 4 is the biggest number that divides both. 8 ÷ 4 = 2, and 12 ÷ 4 = 3.
✗
Not quite — try again.
Write the reduced ratio
Divide both parts by 4. Type the ratio in lowest terms.
ratio =
8 divided by 4 goes on top; 12 divided by 4 goes on the bottom.
✓
Perfect. 8/12 reduces to 2/3. Same skill on any pair of counts: put the right one on top, then reduce if they share a factor.
✗
Not quite. 8 ÷ 4 = 2, and 12 ÷ 4 = 3. So the reduced ratio is 2/3.
🎉
You walked the ratio move end to end.
Every ratio problem is the same three moves: read the order the prompt asks for, put the right count on top, reduce if there’s a common factor. ALEKS will change the numbers and the objects (apples, dogs, students) — but the move is identical.