IMOClass 3 › Fractions (Intro)

Fractions (Intro)

Half, Third, Fourth & the Parts of a Fraction

A fraction shows equal parts of a whole. If a chapati is cut into 2 equal parts, each part is one-half (½). Into 3 equal parts gives one-third (⅓), and into 4 equal parts gives one-fourth (¼).

In a fraction the top number is the numerator (how many parts we take) and the bottom number is the denominator (how many equal parts in all). In ¾ the numerator is 3 and the denominator is 4.

Example 1: A pizza is cut into 4 equal slices. What fraction is 1 slice?
1 out of 4 equal parts = ¼ (one-fourth).
Example 2: In the fraction ⅖, what is the denominator?
The bottom number is 5, so the denominator is 5.
Quick recap
  • A fraction shows equal parts of a whole.
  • Numerator = parts taken (top); denominator = total equal parts (bottom).
✓ Quick check
Which fraction means one-half?
One-half is written ½.
What is the numerator in ⅗?
The top number of ⅗ is 3.

Like Fractions & Comparing Unit Fractions

Like fractions have the same denominator, such as ⅖ and ⅗. A unit fraction has 1 as the numerator, such as ½, ⅓ and ¼.

For unit fractions, the smaller the denominator, the larger the fraction — because the whole is split into fewer, bigger pieces. So ½ > ⅓ > ¼ > ⅕.

Example 1: Which is bigger, ½ or ¼?
½ is bigger — halves are larger pieces than fourths.
Example 2: Are ⅖ and ⅗ like fractions?
Yes — they share the same denominator, 5.
Quick recap
  • Like fractions have the same denominator.
  • For unit fractions, a smaller denominator means a bigger fraction.
✓ Quick check
Which is the largest fraction?
Among unit fractions, ½ has the smallest denominator, so it is the largest.
Which pair are like fractions?
⅓ and ⅔ share the denominator 3, so they are like fractions.

Adding & Subtracting Like Fractions

To add or subtract like fractions, keep the denominator the same and only add or subtract the numerators. For example, ⅖ + ⅕ = ⅗, and ¾ − ¼ = 2/4, which is the same as ½.

This works because the pieces are all the same size, so we simply count how many pieces we have.

Example 1: Add ⅖ + ⅕.
Add numerators: 2 + 1 = 3, keep denominator 5 → ⅗.
Example 2: Subtract ¾ − ¼.
3 − 1 = 2, so 2/4, which equals ½.
Quick recap
  • Add/subtract only the numerators; keep the denominator.
  • 2/4 is the same as ½.
✓ Quick check
What is ⅕ + ⅖?
1 + 2 = 3 over 5 → ⅗.
What is ⅘ − ⅖?
4 − 2 = 2 over 5 → ⅖.
Ready to test this chapter?
Take the Chapter Test →