Simplest form

What you will learn

• Find a common factor of the numerator and denominator
• Write a fraction in its simplest form
• Explain why simplifying does not change the amount

Models used: fraction strips, number sentences, stories.

Before you start

• Equivalent fractions

Simplest form

Four of eight equal parts are shaded. Can we name that same share using fewer, larger equal parts?

1. Four shaded parts out of eight equal parts.

   Start with four shaded eighths. Count the unshaded parts too: all eight belong to our one whole.

   4/8

   A simpler fraction must cover exactly this same length. We may regroup the pieces, but must not change the whole or its shaded share.

2. The lower strip groups the upper strip’s pieces in pairs. The blue lengths still match.

   Pair neighbouring eighths. Two small parts now make one larger part. Four shaded pieces become two shaded pairs; eight pieces become four pairs altogether.

   4/8 = (4 ÷ 2)/(8 ÷ 2) = 2/4

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   4/8 = 2/4: the same length, so the same amount.

3. The top has two shaded quarters. The bottom has one shaded half.

   Pair the quarters once more. Two shaded quarters become one half, and the four quarters become two halves.

   2/4 = (2 ÷ 2)/(4 ÷ 2) = 1/2

   Divide both counts by the same number because we regroup the shaded pieces and all the pieces in exactly the same way.

   2/4 = 1/2: the same length, so the same amount.

4. Different counts of parts; one unchanged shaded amount.

   We can stop at one half: 1 and 2 have no common factor greater than 1. Check the first strip against the last. Their shaded lengths have not changed.

   4/8 = 1/2

   Simplifying changes the fraction’s name, not its size. Dividing only the bottom number would change the share.

   4/8 = 1/2: the same length, so the same amount.

Worked example

Write 8/12 in its simplest form.

1. Find a number that divides both 8 and 12.

   Which number divides both 8 and 12?

   4

2. Divide both numbers by 4.

   8 ÷ 4 = 2 and 12 ÷ 4 = 3

   What is 8/12 in simplest form?

   2/3

3. Can 2 and 3 both be divided again? No, so this is simplest form.

   8/12 = 2/3

4. Check on the wall.

   8/12 = 2/3: the same length, so the same amount.

Common mistakes to discuss

• Subtracting from the numerator and denominator. 6/8 is not 5/7. Simplifying divides both numbers by the same factor: 6 ÷ 2 = 3 and 8 ÷ 2 = 4.
• Thinking a simplified fraction is a smaller amount. 3/4 and 6/8 shade exactly the same length. Only the size and number of pieces change.

Check your understanding

• spot a number that divides both parts of a fraction
• write 6/8 as 3/4
• check a simplified fraction on the fraction wall

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.