99
Multiplying a fraction by a whole number
Textbook: Part 3, lesson 99, pp. 87–89
GoalMultiplying a fraction by a whole number: the denominator stays, the numerator is multiplied.
New words
multiplication · ko‘paytirishwhole number (natural number) · natural sonrepeated addition · ko‘p martalik qo‘shishnumerator · surat
Explanation
Multiplying a fraction by a whole number is repeated addition: 2/5 × 3 = 2/5 + 2/5 + 2/5 = 6/5. So to multiply a fraction by a whole number, keep the denominator and multiply the numerator by that number. If the product is an improper fraction, take out the whole part: 6/5 = 1 1/5. The factors can swap places: 3 × 2/5 = 2/5 × 3.
Worked examples
3/8 × 4 = 12/8 = 1 4/8.
7/10 × 3 = 21/10 = 2 1/10.
Class activity
“Fraction steps”: on a number ray a child takes 4 steps of length 2/6. They write how far they went as a multiplication (2/6 × 4 = 8/6).
Practice
1
Work out 4/9 × 2.
8/9
2
Work out 5/12 × 5 and also write it as a mixed number.
25/12 = 2 1/12
3
Work out 3 × 7/10 and also write it as a mixed number.
21/10 = 2 1/10
4
One bunch of flowers needs 3/4 m of ribbon. How many metres are needed for 6 such bunches?
18/4 = 4 2/4
5
Each exercise lasts 1/6 of an hour. How many hours do 5 exercises last?
5/6