EQN-01-02

Fractions & Decimals

Add, compare, and simplify fractions, and convert fluently between fractions and decimals — the backbone of half the quantitative section.

~5 min read•Difficulty 2/5

Core ideas

A fraction a/b means "a parts out of b". To work with fractions you only ever need three moves:

Simplify — divide top and bottom by their greatest common factor (GCF).
Common denominator — to add or subtract, rewrite both fractions over the same bottom.
Multiply / divide — multiply straight across; to divide, multiply by the reciprocal (flip the second fraction).

Adding and subtracting

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Never add the denominators. The bottom tells you the size of the pieces, not a quantity to combine.

Multiplying and dividing

2/3 \times 3/5 = 6/15 = 2/5

3/4 \div 1/2 = 3/4 \times 2/1 = 6/4 = 3/2

Fractions ↔ decimals

A fraction is just a division $: 3/4 = 3 \div 4 = 0.75.$ Memorize the common ones $(1/2 = 0.5, 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 1/3 \approx 0.333)$ so you can compare instantly.

Comparing fractions fast

Cross-multiply: to compare a/b and c/d, compare $a \times d$ with $c \times b .$

3/5 vs 5/8 \to 3 \times 8 = 24 vs 5 \times 5 = 25 \to 25 is bigger, so 5/8 > 3/5

Worked examples

Example 1 (difficulty 2/5)

What is

2/3 + 1/4

◎ Predict the answer first:

Example 2 (difficulty 1/5)

Which is larger, 3/5 or 0.65 ?

◎ Predict the answer first:

Tips

When the answer choices are fractions, keep working in fractions; when they are decimals, convert early.
Always simplify your final fraction — the test almost always lists the simplest form.
To divide by a fraction, multiply by its reciprocal — "keep, flip, multiply".

Common mistakes

Adding denominators

: 1/2 + 1/3 = 2/5

Why: It looks symmetric to add tops and bottoms.

Fix: Find a common denominator first; only the numerators are added.

Forgetting to flip when dividing fractions

Why: Division and multiplication feel interchangeable under time pressure.

Fix: Dividing by a/b is the same as multiplying by b/a.

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