Revision notes
Find out how many pieces fit, learn reciprocals, and divide any fraction using keep, change, flip.
Mama Ngozi pours 3 litres of zobo into cups that each hold 14 of a litre. Each litre fills 4 cups, so 3 litres fill 12 cups. She has just worked out 3 ÷ 14 = 12 — dividing by a fraction!
6 ÷ 2 asks: how many 2s fit into 6? In the same way, 3 ÷ 14 asks: how many quarters fit into 3?
There are 4 quarters in each whole, so 3 × 4 = 12 quarters. Dividing by 14 gives the same answer as multiplying by 4.
That is why dividing by a fraction smaller than 1 gives a bigger answer.
🔑 Key idea: Dividing by 14 is the same as multiplying by 4.
The reciprocal of a fraction is the fraction turned upside down. The reciprocal of 23 is 32.
The reciprocal of a whole number like 5 is 15, because 5 = 51.
For a mixed number, change it to an improper fraction first: 123 = 53, so its reciprocal is 35. A number times its reciprocal always equals 1.
🔑 Key idea: Reciprocal = upside down. Number × reciprocal = 1.
To divide by a fraction, multiply by its reciprocal. Keep the first fraction, change ÷ to ×, flip the second fraction.
34 ÷ 25 = 34 × 52 = 158 = 178.
Mixed numbers become improper fractions first: 212 ÷ 34 = 52 × 43 = 206 = 313. Only flip the SECOND number.
🔑 Key idea: Keep the first, change ÷ to ×, flip the second.
Work out 16 ÷ 59.
Step 1: Keep, change, flip
16 ÷ 59 = 16 × 95
Why? Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
Step 2: Multiply across
= 930
Step 3: Simplify
= 310
Answer: 310
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.