Writing ratios

Read a real-world situation, count the parts, write the ratio. Reduce when both numbers share a common factor.

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.

Writing ratios v1

A basket contains 5 green apples and 8 red apples.

Write the ratio of green apples to red apples.

ratio =

Writing ratios v2

A pet store has 7 dogs and 10 cats.

Write the ratio of cats to dogs.

ratio =

Writing ratios — reduces v3

A class has 6 boys and 9 girls.

Write the ratio of boys to girls in lowest terms.

ratio =

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

ratio of A to B → A / B
reduce by dividing top and bottom by their GCF

Order matters. "Green to red" is not the same as "red to green." Reduce only when both numbers share a common factor bigger than 1.

5 green apples, 8 red apples — green to red.

Pull the two counts straight from the sentence: green = 5, red = 8. The phrase "green to red" puts green on top.

5 / 8

5 and 8 share no common factor (other than 1), so this is already in lowest terms. Answer: 5/8.

7 dogs, 10 cats — cats to dogs.

Read carefully. The scenario lists dogs first, but the prompt asks for cats to dogs — so cats go on top. Counts: cats = 10, dogs = 7.

10 / 7

10 and 7 share no common factor (7 is prime), so this is already in lowest terms. Answer: 10/7.

6 boys, 9 girls — boys to girls.

Counts: boys = 6, girls = 9. "Boys to girls" → boys on top, girls on bottom.

6 / 9 = 2 / 3

Both 6 and 9 divide by 3. Divide top and bottom by 3 → 2/3.

▸ TWO COMMON SLIPS(1) Wrong order. Students write the ratio backwards: red to green when the prompt asked for green to red. Read the prompt twice to lock the order before writing anything down. (2) Forgetting to reduce. Students leave the answer as 6/9 instead of 2/3. Always check: do both numbers share a common factor? If yes, divide.

04 Practice — Step by Step

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

Count the first quantity.

Practice problem: A music store has 12 guitars and 18 keyboards. Write the ratio of guitars to keyboards in lowest terms. How many guitars are there?

guitars =

Count the second quantity.

Now pull the second number from the prompt. How many keyboards are there?

keyboards =

Write the ratio in lowest terms.

The ratio of guitars to keyboards is 12 / 18. Both 12 and 18 share a common factor of 6. Divide top and bottom by 6 — what's the ratio in lowest terms? Type your answer as a fraction (e.g. 3/4).

ratio =

▸ NICE WORK

You walked the ratio move end to end.

Same three steps every time: count the first quantity, count the second, write the ratio in the right order and reduce. ALEKS will give you different objects — apples, cats, students, cars — but the move is identical.

Q1 Q3