Egypt Primary 4 Mathematics, Week 18: Equivalent fractions on the fraction wall

Comparing and equivalent fractions

Week 18 · Comparing and equivalent fractions · 3 lessons

Equivalent fractions on the fraction wall

Discover Mathematics P4: Term 2, Unit 9, Lessons 8–12

GoalFind equivalent fractions with the fraction wall and with multiplying and dividing.

New words

equivalent fractions · different fractions that name the same amountfraction wall · a chart of bars of the same length cut into different equal partssplit · to cut each part into smaller equal parts

Explanation

Equivalent fractions are different names for the same amount. Look at the fraction wall: the shaded part of the half bar ends in the same place as 2 fourths, 3 sixths, 4 eighths and 6 twelfths. So 1/2 = 2/4 = 3/6 = 4/8 = 6/12. When we cut every part into 2 equal parts, the number of shaded parts doubles and the number of all parts doubles: 1/2 becomes 2/4. If we cut every part into 3 equal parts, 1/2 becomes 3/6. In other words, multiply the numerator and the denominator by the same number. We may also divide both by the same number: 6/8 = 3/4. The amount stays the same, only the size and number of the parts change.

Worked examples

Fraction	1/2	2/4	3/6	4/8	6/12
Multiply by	1	2	3	4	6

Write fractions equal to 1/2. On the wall, half is the same length as 2/4, 3/6, 4/8 and 6/12. Pattern: each numerator is half of its denominator.

Find a fraction equal to 2/3 with denominator 12. 3 × 4 = 12, so multiply the numerator by 4 too: 2 × 4 = 8. So 2/3 = 8/12. On the wall, two thirds is the same length as 4/6 and 8/12.

Is 6/8 equal to 3/4? Divide the numerator and the denominator by 2: 6 ÷ 2 = 3 and 8 ÷ 2 = 4. Yes, 6/8 = 3/4. On the wall, 6 eighths and 3 fourths end at the same place.

Class activity

Build a fraction wall. On squared paper draw bars of the same length cut into halves, thirds, fourths, sixths and eighths. Colour 1/2 on each bar and see which fractions end at the same place.

Practice

Find the missing number: 1/2 = __/10.

Find the missing number: 3/4 = __/12.

Simplify 4/6 by dividing the numerator and denominator by 2.

Is 3/6 equal to 4/8? Explain.

Salma says 1/3 = 2/4 because she added 1 to the numerator and to the denominator. What is wrong? Find a fraction equal to 1/3 with denominator 6.