How to Simplify Fractions

18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4

Find the greatest common factor first — the largest number that divides both the numerator and the denominator. Every shared factor of 18 and 24 works, but 6 is the largest, so it finishes the job in one division: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The fraction 3/4 is the same amount as 18/24 with fewer, larger pieces.

For parents: Ask: “What is the biggest number that divides both the top and the bottom? Divide both by it, then look at the result once more.”

45/60 → shared factors 3, then 5 → GCF 15 → 3/4

With small numbers, list the factors of the smaller number and take the largest one that also divides the bigger number. With big numbers, use quick divisibility checks: if both are even, divide by 2 and repeat; if digit sums divide by 3, try 3; if both end in 0 or 5, try 5. Reducing in small steps is perfectly correct — dividing 45/60 by 3 and then by 5 lands on the same 3/4 as dividing by 15 once.

For parents: Say: “Two easy steps beat one impossible one. 45/60 ÷ 3 = 15/20, then ÷ 5 = 3/4.”

12/24 → 6/12 → still not done → 3/4 ✓

A fraction is in simplest form, or lowest terms, when 1 is the only whole number that divides both parts. The fastest finish check is to run 2, 3, and 5: if none of them divides both the numerator and the denominator, you are done. Watch 12/24 — one division by 2 gives 6/12, which looks finished but still shares 6. Run the check again until it passes.

For parents: Ask before the final answer: “Does anything still divide both numbers?” One extra check catches most lost points.

9/9 = 1 8/1 = 8 18/12 = 3/2 = 1 1/2

A fraction whose top and bottom match, like 9/9, reduces to 1 — every equal part is counted. A fraction with denominator 1, like 8/1, is already in lowest terms and simply equals 8. Improper fractions reduce by the same three steps; 18/12 reduces to 3/2 and then reads more naturally as the mixed number 1 1/2.

For parents: Say: “Reducing never changes whether a fraction is more or less than one — it only changes the size of the pieces.”

4 × 1/8 → cancel the 4 with the 8 → 1/2

In multi-step work, reducing early keeps every number small. That is exactly what cross-cancelling does in fraction multiplication. If you multiply first and reduce at the end, you still land on the same simplest form — 4/8 and 1/2 name the same amount. Early reducing is a convenience, not a different rule.

For parents: Say: “Cancel what you can see before multiplying; run the final check on whatever you end up with.”