Fractions (Including Problems)
ICSE Class 7 · Mathematics · Chapter 3
What this chapter covers
- Fractions and mixed numbers
- Fraction as an operator ('of')
- Multiplication of fractions
- Reciprocal of a fraction
- Division of fractions
- Word problems on fractions
Key points
- A fraction (a)/(b) names a of b equal parts of a whole, and it also means a ÷ b.
- Change mixed numbers into improper fractions before you multiply or divide them.
- A fraction used as an operator acts on a quantity, and "of" means multiply.
- To find a fraction of a quantity, divide by the denominator and multiply by the numerator.
- The product of two fractions is the product of the numerators over the product of the denominators.
- Cancel common factors before multiplying to keep the numbers small.
- Multiplying by a proper fraction makes a positive number smaller.
- The reciprocal of a non-zero fraction is that fraction turned upside down, and a number times its reciprocal is 1.
- Zero has no reciprocal, and 1 is its own reciprocal.
- To divide by a fraction, multiply the dividend by the reciprocal of the divisor.
- Dividing by a proper fraction makes a positive number bigger.
- To find a whole when a fraction of it is known, divide the known part by the fraction.
- In word problems, read for the clue words, convert mixed numbers, simplify, give units and check that the answer makes sense.
Questions answered
Find (3)/(4) of 56.
(56 ÷ 4) × 3 = 14 × 3 = 42.
How many minutes are there in (7)/(10) of an hour?
(60 ÷ 10) × 7 = 42 minutes.
Multiply 3(1)/(3) × 2(1)/(4).
(10)/(3) × (9)/(4) = (90)/(12) = (15)/(2) = 7(1)/(2).
Write the reciprocal of 4(2)/(5).
4(2)/(5) = (22)/(5), so its reciprocal is (5)/(22).
Explain why 0 has no reciprocal.
A reciprocal must multiply with the number to give 1, but any number multiplied by 0 gives 0. So no number can be the reciprocal of 0.
Divide 6 ÷ (2)/(3).
6 × (3)/(2) = 9.
Without working out the answers, say which is larger: 15 × (4)/(5) or 15 ÷ (4)/(5). Then check.
15 ÷ (4)/(5) is larger, because dividing by a proper fraction makes a number bigger while multiplying by it makes the number smaller. Checking: 15 × (4)/(5) = (60)/(5) = 12, and 15 ÷ (4)/(5) = 15 × (5)/(4) = (75)/(4) = 18(3)/(4). Since 18(3)/(4) is greater than 12, the quotient is the larger value.
A jug holds 1(1)/(2) litres of lassi. How many glasses of (3)/(10) litre each can be filled from it?
(3)/(2) ÷ (3)/(10) = (3)/(2) × (10)/(3) = 5 glasses.