19
Dividing fractions
Textbook, pp. 78–81
GoalKnow and apply the rule for dividing common fractions.
New words
quotient · bo‘linmadividend · bo‘linuvchidivisor · bo‘luvchireciprocal · teskari son
Explanation
To divide a fraction by a fraction, multiply the dividend by the reciprocal of the divisor: a/b : c/d = a/b · d/c. To divide a fraction by a natural number, multiply the denominator by it: 3/4 : 2 = 3/8. To divide a natural number by a fraction: 6 : 2/3 = 6 · 3/2 = 9. Mixed numbers are first turned into improper fractions. Dividing by 1/2 doubles a number, because there are two halves in one whole.
Worked examples
5/6 : 5/12 = 5/6 · 12/5 = (5 · 12)/(6 · 5) = 2.
2 1/4 : 3/8 = 9/4 · 8/3 = 72/12 = 6.
Class activity
“How many pieces?”: the teacher marks a paper strip as 3/4 m. Pupils cut it into pieces of 1/8 m, count the pieces and compare with the division.
Practice
1
Compute 3/4 : 9/16.
1 1/3
2
Compute 6 : 2/3.
9
3
3/4 kg of nuts is packed in bags of 1/8 kg each. How many bags are needed?
6
4
Why does dividing by 1/2 make a number twice as big?
One whole contains two halves, so each whole gives 2 pieces.