Numbers › Fractions

Fractions

A fraction is one whole, cut into equal pieces, with some of those pieces taken.

Fractions

Top counts the slices, bottom is total slices

Slices filled

Total slices

That's 38% of the pizza

How to read a fraction

A fraction has two parts. The bottom number is the denominator — it tells you how many equal pieces the whole is cut into. The top number is the numerator — how many of those pieces you have.

Equivalent fractions

1/2 and 2/4 and 4/8 all represent the same amount of pizza. They're equivalent: you've just sliced the same half into more pieces.

Why this matters

To compare or add fractions with different denominators, we usually rewrite them as equivalent fractions with the same denominator first. That's the whole trick.

Comparing fractions

Same denominator — compare the numerators. 3/8 < 5/8.
Same numerator — the smaller denominator is bigger. 1/3 > 1/8 (bigger slices).
Different both — find a common denominator first.

Adding fractions

With the same denominator, just add the numerators: 2/7 + 3/7 = 5/7. With different denominators, rewrite first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Improper fractions and mixed numbers

When the numerator is bigger than the denominator (like 7/4) you have more than one whole. You can rewrite it as a mixed number: 1 3/4.

Quick check

Which is bigger, 3/4 or 5/8?
Add: 1/4 + 1/2.
Write 9/4 as a mixed number.

Answers: 3/4 (it's 6/8), 3/4, and 2 1/4.