Dividing a fraction by a fraction the standard way
Discover Mathematics P6: Term 2, Unit 8, Lessons 3–4
GoalDivide fractions and mixed numbers with the standard algorithm, simplifying before multiplying.
New words
algorithm · a set of steps that always gives the answerimproper fraction · a fraction whose top is bigger than or equal to its bottommixed number · a whole number and a fraction together, like 1 1/2simplify · to divide the top and the bottom by the same number
Explanation
To divide a fraction by a fraction, follow four steps. One, turn mixed numbers into improper fractions. Two, keep the first fraction and change ÷ to ×. Three, turn the second fraction into its reciprocal. Four, multiply the tops and the bottoms, and simplify. It is easier to simplify before multiplying: a top number and a bottom number can be divided by the same number even if they are in different fractions. At the end, check that the answer makes sense by estimating: if the divisor is smaller than the first fraction, the answer is more than 1.
ƒFormula
a/b ÷ c/d = a/b × d/c
Worked examples
2/3 ÷ 4/9 = 2/3 × 9/4. Simplify first: 9 and 3 are both divisible by 3, and 2 and 4 are both divisible by 2. We get 1/1 × 3/2 = 3/2 = 1 1/2. Estimate: 4/9 is smaller than 2/3, so the answer is more than 1.
A mixed number: 1 1/2 ÷ 3/4. First 1 1/2 = 3/2. Then 3/2 × 4/3: simplify 3 with 3 and 4 with 2, which gives 1/1 × 2/1 = 2.
A story. A jug holds 3/4 L and each glass holds 3/16 L. How many glasses can be filled? 3/4 ÷ 3/16 = 3/4 × 16/3 = 4. Check: 4 × 3/16 = 12/16 = 3/4 L.
Class activity
Fraction division duel. Each player writes two fractions (tops and bottoms up to 12) on paper. The players swap papers and divide. The one with the answer closer to 2 scores a point. Check each answer by multiplying it by the divisor.
Practice
1
Find 3/5 ÷ 3/10.
3/5 × 10/3 = 2.
2
Find 5/6 ÷ 1/3.
5/6 × 3 = 15/6 = 5/2 = 2 1/2.
3
Find 2 1/4 ÷ 3/8.
2 1/4 = 9/4. Then 9/4 × 8/3 = 72/12 = 6.
4
How many pieces of ribbon of 3/20 m can be cut from 3/4 m?
3/4 ÷ 3/20 = 3/4 × 20/3 = 5 pieces.
5
Without calculating fully, is 4/5 ÷ 2/3 more or less than 1? Then find it.
More than 1, because 4/5 is bigger than 2/3. 4/5 × 3/2 = 12/10 = 6/5 = 1 1/5.
