Level 2 · Ages 8–11
Read it again any time, including while you work through the exercises.
Imagine two identical pizzas. The first is cut into 2 slices and you eat 1: you ate 1/2 of a pizza. The second is cut into 8 slices and you eat 4: you ate 4/8 of a pizza. Look closely: in both cases you ate exactly the same amount, half a pizza! So the fractions 1/2 and 4/8 are equal.
That is the key idea of this lesson: the same amount can be written with many different fractions. If you cut each slice into smaller pieces, you get more slices, but each slice is smaller: the total amount does not change. In numbers, this gives a golden rule: when you multiply (or divide) the numerator AND the denominator by the same non-zero number, the fraction keeps the same value. For example 1/2 = 2/4 = 3/6 = 4/8.
Simplifying a fraction means going the other way: dividing the top and the bottom by the same number to get a simpler form. 6/8 becomes 3/4 when you divide by 2. When you cannot simplify any further, the fraction is in lowest terms: its simplest form, the easiest to read and compare.
Watch out for the classic trap: adding the same number to the top and the bottom changes the value of the fraction! 1/2 and 2/3 are not equal at all (one half is not two thirds). Only multiplication and division keep the equality. Keep that rule in mind, your turn to play!
Simplify the fraction 6/8.
6 = 2 × 3 et 8 = 2 × 4
I look for a number that divides both 6 and 8: the number 2 works.
6/8 = (6 ÷ 2)/(8 ÷ 2)
I divide the numerator and the denominator by 2, the value does not change.
6/8 = 3/4
3 and 4 share no common divisor other than 1: the fraction is in lowest terms.
Result: 6/8 = 3/4
Show that 2/3 = 8/12.
3 × 4 = 12
I ask myself what to multiply 3 by to get 12: it is 4.
2 × 4 = 8
So I ALSO multiply the numerator by 4: each third is cut into 4 pieces.
2/3 = 8/12
Same amount, just cut more finely: the two fractions are equal.
Result: 2/3 = 8/12