Fractions & Decimals • Topic 1 of 5

Equivalent Fractions & Simplifying

Two fractions are equivalent when they represent the same value: 2/3, 4/6 and 6/9 are all one point on the number line. You generate equivalents by multiplying (or dividing) top and bottom by the same nonzero number — that keeps the value because you are multiplying by a disguised 1. To simplify (reduce to lowest terms), divide the numerator and denominator by their GCD; a fraction is fully reduced when the two are coprime. On the GRE this matters for speed and for matching answer choices, which are usually given in lowest terms. It also drives Quantitative Comparison: to compare 12/18 with 2/3 you do not need a calculator — reduce 12/18 to 2/3 and see they are equal. Always simplify before you compute; smaller numbers mean fewer slips.

✅ Solved examples

1. Reduce 18/24 to lowest terms.
GCD(18, 24) = 6. Divide both by 6: 18/24 = 3/4.
2. Fill the blank: 3/5 = ?/45.
The denominator went from 5 to 45, a ×9. Apply the same to the top: 3 × 9 = 27. So 3/5 = 27/45.
3. Reduce 84/144 to lowest terms.
GCD(84, 144) = 12. 84/12 = 7, 144/12 = 12. So 84/144 = 7/12.
4. Quantitative Comparison. Quantity A: 15/25. Quantity B: 3/5. Which is greater?
Reduce 15/25 by GCD 5 → 3/5. Quantity A = Quantity B; they are equal.

✏️ Practice — try these, take hints as needed

1. Reduce 20/50 to lowest terms.
GCD(20, 50) = 10.
Divide both.
2/5.
2/5
2. Fill the blank: 2/7 = ?/56.
7 → 56 is ×8.
Do the same on top.
2 × 8.
16
3. Reduce 45/60 to lowest terms.
GCD(45, 60) = 15.
45/15, 60/15.
Simplify.
3/4
4. Is 9/12 equal to 6/8?
Reduce both.
9/12 = 3/4.
6/8 = 3/4.
Yes
5. Reduce 121/132 to lowest terms.
GCD is 11.
121/11 = 11.
132/11 = 12.
11/12

📝 Topic test — 8 questions

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