15
Multiplying fractions and mixed numbers
Textbook, pp. 59–64
GoalKnow and use the rule for multiplying common fractions and mixed numbers.
New words
multiplying fractions · kasrlarni ko‘paytirishproduct · ko‘paytmaimproper fraction · noto‘g‘ri kasrreduction (cancelling) · qisqartirish
Explanation
To multiply a fraction by a fraction, multiply the numerators to get the numerator and the denominators to get the denominator: a/b · c/d = (a · c)/(b · d). To multiply a natural number by a fraction, multiply it by the numerator: 5 · 2/3 = 10/3. Mixed numbers are first turned into improper fractions and then multiplied. To make work easier, cancel numerators and denominators before multiplying. The product of proper fractions is smaller than each factor.
Worked examples
3/4 · 2/9: cancel first: 3 and 9 by 3, 2 and 4 by 2. We get (1 · 1)/(2 · 3) = 1/6.
2 1/3 · 1 1/2 = 7/3 · 3/2 = 7/2 = 3 1/2.
Class activity
“Cancelling race”: two teams get fraction products; they cancel first and then multiply. The team that reaches the right answer in the fewest steps scores.
Practice
1
Compute 5/6 · 3/10.
1/4
2
Compute 4 · 5/8.
2 1/2
3
Compute 1 2/3 · 2 1/4.
3 3/4
4
Why is 1/2 · 1/2 = 1/4 smaller than a half?
We take half of a half, only part of 1/2. Multiplying by a proper fraction makes the number smaller.