01Why this matters
Fractions appear in recipes, time and measurements. Understanding the size of the parts makes arithmetic more meaningful than memorising rules alone.
02See it
03Understand it
A fraction describes equal parts of a whole. The denominator counts the equal parts; the numerator counts the parts selected.
In 3/4, the whole is split into four equal parts and three are selected. Equivalent fractions have the same size: 1/2 = 2/4. Multiplying or dividing numerator and denominator by the same non-zero number preserves the value. To add fractions, give them a common denominator so that the parts have the same size.
04Guided example
Add 1/2 and 1/4 of the same cake.
- Divide the half into two quarter-sized pieces: 1/2 = 2/4.
- Now both fractions count quarters, so add their numerators: 2 + 1 = 3.
- Keep the common denominator: 2/4 + 1/4 = 3/4.
05Try it
06Practise it
07Use it in the real world
A recipe needs 3/4 cup of oats. A 1/4-cup measure fills it exactly three times. Doubling the recipe needs 6/4 = 1½ cups.
Go a little deeper
Dividing by a fraction asks how many of that size fit. There are six halves in three wholes, so 3 ÷ 1/2 = 6. A denominator cannot be zero.
08Quick check
09Summary
A fraction describes equal parts of a whole. The denominator counts the equal parts; the numerator counts the parts selected. Keep the common denominator: 2/4 + 1/4 = 3/4.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
a/c + b/c = (a + b)/c
a and b count parts; c is a common non-zero denominator.
a/b = (a × k)/(b × k), for non-zero b and k
Find this in the formula library →