A quick reminder
A fraction a/b means a parts out of b equal parts. A proper fraction has a numerator smaller than its denominator (3/5); an improper fraction does not (7/4); a mixed fraction combines a whole number and a proper fraction (1¾ = 7/4).
To add or subtract fractions, first rewrite them with a common denominator: 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
Multiplying a fraction by a whole number
Multiply the numerator by the whole number and keep the denominator.
3 × 2/7 = 6/7, which is the same as 2/7 + 2/7 + 2/7.
"Of" means multiply
½ of 10 is 5, and ½ × 10 = 5. In general, "of" means multiplication.
Example. Riya has ₹60 and spends 2/5 of it. She spends 2/5 × 60 = 120/5 = ₹24.
Multiplying two fractions
Multiply the numerators, multiply the denominators, then simplify.
2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15
Cancelling first keeps the numbers small: 4/9 × 3/8 = (4 × 3)/(9 × 8). Cancel 4 with 8 (leaving 1 and 2) and 3 with 9 (leaving 1 and 3) to get 1/6.
Convert mixed fractions to improper fractions before multiplying: 1½ × 2⅓ = 3/2 × 7/3 = 7/2 = 3½.
When you multiply by a proper fraction, the answer is smaller than the number you started with: 1/2 × 1/3 = 1/6, which is smaller than both.
Reciprocals and division
Two numbers are reciprocals if their product is 1. The reciprocal of 3/7 is 7/3, the reciprocal of 5 is 1/5, and 1 is its own reciprocal. Zero has no reciprocal.
To divide by a fraction, multiply by its reciprocal.
6 ÷ 2/3 = 6 × 3/2 = 9. (There are nine 2/3-pieces in 6.)
3/4 ÷ 5 = 3/4 × 1/5 = 3/20
2/5 ÷ 4/15 = 2/5 × 15/4 = 30/20 = 3/2 = 1½
Multiplying decimals
Multiply as if there were no decimal points.
Count the total number of digits after the decimal point in both numbers.
Put that many digits after the decimal point in the answer.
Example. 2.5 × 1.3: 25 × 13 = 325. There are 1 + 1 = 2 decimal places, so the answer is 3.25.
Example. 0.06 × 0.4: 6 × 4 = 24, with 2 + 1 = 3 decimal places: 0.024.
Multiplying and dividing by 10, 100 and 1000
Operation | Rule | Example |
|---|---|---|
× 10, × 100, × 1000 | move the point 1, 2, 3 places right | 3.47 × 100 = 347 |
÷ 10, ÷ 100, ÷ 1000 | move the point 1, 2, 3 places left | 3.47 ÷ 100 = 0.0347 |
Dividing decimals
By a whole number: divide as usual and keep the decimal point in place. 7.5 ÷ 3 = 2.5.
By a decimal: make the divisor a whole number by multiplying both numbers by the same power of 10.
Example. 1.44 ÷ 0.12. Multiply both by 100: 144 ÷ 12 = 12.
Example. 6.5 ÷ 0.5. Multiply both by 10: 65 ÷ 5 = 13.
Common mistakes
Adding denominators when multiplying. 1/2 × 1/3 is 1/6, not 2/5.
Flipping the wrong fraction. In a ÷ b, only the divisor b is replaced by its reciprocal.
Lining up decimal points when multiplying. That rule is for addition and subtraction; for multiplication, count decimal places.
Summary
Multiply fractions straight across; "of" means multiply.
To divide by a fraction, multiply by its reciprocal.
In decimal multiplication, the answer has as many decimal places as the two numbers together.
To divide by a decimal, first make the divisor a whole number.