Stage 8 · Fractions & decimals
Improper fractions and mixed numbers
Top ÷ bottom: quotient whole, remainder top.
How to do it
Method
Top ÷ bottom: quotient whole, remainder top
175 = 3 25 (5 × 3 = 15, 17 − 15 = 2)
One more example
2 34 = (2 × 4 + 3)/4 = 114
In full
A fraction whose top is at least its bottom is an improper fraction, like 175; a whole number and a proper fraction together make a mixed number, like 3 25, which is 3 + 25. Improper to mixed: divide the top by the bottom; the quotient is the whole part and the remainder is the new top, over the same bottom. 175: how many 5s in 17? 5 × 3 = 15, 17 − 15 = 2, so 175 = 3 25. A top that's a multiple of the bottom makes a whole number: 124 = 12 ÷ 4 = 3. Mixed to improper: the whole number times the bottom, plus the top, over the same bottom: 2 34 → 2 × 4 = 8, 8 + 3 = 11, so 2 34 = 114. Or split the mixed number: 2 34 = 2 + 34 = 84 + 34 = 114 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
5 18 = ?
Answer as an improper fraction
Show the answer and working
Answer: 5 18 = 418
5 18: the whole number times the denominator, plus the numerator, over the same denominator: 5 × 8 = 40, 40 + 1 = 41 → 418
Example 2
92 = 4 ?2
Show the answer and working
Answer: 92 = 4 12
92: divide the numerator by the denominator. How many 2s in 9? 2 × 4 = 8, 9 − 8 = 1; 92 = 4 12, the remainder is the numerator: 1
Example 3
92 = ? 12
Show the answer and working
Answer: 92 = 4 12
92: divide the numerator by the denominator. How many 2s in 9? 2 × 4 = 8, 9 − 8 = 1; 92 = 4 12, the quotient is the whole part: 4
Example 4
296 = 4 ?6
Show the answer and working
Answer: 296 = 4 56
296: divide the numerator by the denominator. How many 6s in 29? 6 × 4 = 24, 29 − 24 = 5; 296 = 4 56, the remainder is the numerator: 5
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