doing math

courses › Fractions, Decimals & Percents

Fraction basics

level 5 course

Simplify, find equivalent fractions, and compare them.

Best in your head · no pen, no calculator why?

Learn first (about 3 minutes)

Opens at level 5.

Sign in to start

Builds on: Times tables (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

A fraction is a division: 3/4 means 3 ÷ 4. The bottom number, the denominator, says how many equal parts make a whole. The top number, the numerator, says how many of those parts you have.

Multiply or divide the top and bottom by the same number and you get an equivalent fraction: the same amount, written differently. So 3/4, 6/8 and 15/20 are all equal. A fraction is in lowest terms when no number bigger than 1 divides both its top and its bottom.

Bigger numbers don't make a bigger fraction. To compare fractions, put them on one scale.

Techniques

Divide by a common factor

Simplifying a fraction to lowest terms.

  1. Find a number that divides both the top and the bottom.
  2. Divide both by it. The biggest such number, the greatest common factor, finishes in one step.
  3. Check again: if a number bigger than 1 still divides both, keep going.
worked example

Example: Simplify 24/36 to lowest terms.

  1. 12 divides both: 24 ÷ 12 = 2, and 36 ÷ 12 = 3.
  2. Only 1 divides both 2 and 3, so stop.

Answer: 2/3

Scale top and bottom together

Filling in the missing number in two equal fractions.

  1. Find the pair you know on both sides: the two tops or the two bottoms.
  2. Work out what the first was multiplied by to make the second.
  3. Multiply the other number by the same amount.
worked example

Example: Fill in the missing number: 2/3 = ?/18

  1. 3 became 18 by multiplying by 6.
  2. Multiply the top by 6 too: 2 × 6 = 12.

Answer: 12

Put them on one scale

Finding the largest or smallest of several fractions.

  1. Turn each fraction into a decimal by dividing the top by the bottom.
  2. Three decimal places are plenty.
  3. Compare the decimals, and ignore how big the numbers in the fractions look.
worked example

Example: Which fraction is largest: 7/12, 3/4, 5/8 or 2/3?

  1. 7/12 ≈ 0.583, 3/4 = 0.75, 5/8 = 0.625, 2/3 ≈ 0.667.
  2. The largest is 3/4.

Answer: 3/4

Tips by skill

  • TipSimplify a fraction: Divide the top and bottom by the biggest number that divides both. Then check that nothing bigger than 1 still does.
  • TipEquivalent fractions: Find what the known top or bottom was multiplied by, and multiply the other part by the same number.
  • TipWhich is largest?: Turn each fraction into a decimal by dividing top by bottom, then compare. Bigger numbers don't mean a bigger fraction.

Watch out for

  • Stopping before lowest terms. Halving 18/24 gives 9/12, but 3 still divides both, so keep going to 3/4.
  • Adding instead of multiplying. In 3/4 = ?/20 the bottom was multiplied by 5, so the top is 3 × 5, not 3 + 16.
  • Picking the fraction with the biggest numbers. 7/12 has bigger numbers than 2/3 but is the smaller amount.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

No rounds yet.