Fractions represent parts of a whole. A fraction a/b means 'a parts out of b equal parts'. In Class 7, we go beyond basic fractions to learn multiplication and division of fractions and decimals.
- Types of Fractions:
- Proper fraction: numerator < denominator, e.g. 3/5
- Improper fraction: numerator ≥ denominator, e.g. 7/4
- Mixed number: whole part + fractional part, e.g. 1 and 3/4
Multiplication of Fractions:
To multiply two fractions, multiply their numerators together and their denominators together.
(a/b) x (c/d) = (a x c)/(b x d)
To multiply a fraction by a whole number, treat the whole number as a fraction with denominator 1.
Division of Fractions:
To divide by a fraction, multiply by its reciprocal.
(a/b) / (c/d) = (a/b) x (d/c) = (a x d)/(b x c)
Decimals:
A decimal is another way to write a fraction with denominator 10, 100, 1000, etc.
- 0.1 = 1/10, 0.01 = 1/100
- Multiplication of Decimals:
- Multiply as whole numbers, then count total decimal places in both numbers and place the decimal point accordingly.
- Multiplying by 10: move decimal point one place right.
- Multiplying by 0.1: move decimal point one place left.
- Division of Decimals:
- Dividing by 10: move decimal point one place left.
- To divide a decimal by another decimal, convert the divisor to a whole number by multiplying both dividend and divisor by 10 or 100 as needed.
Find 3/4 x 2/5.
= (3 x 2)/(4 x 5) = 6/20 = 3/10.
Find 2 and 1/3 x 1 and 1/2.
Convert to improper fractions: 7/3 x 3/2 = 21/6 = 7/2 = 3 and 1/2.
Find 5/6 divided by 2/3.
= 5/6 x 3/2 = 15/12 = 5/4 = 1 and 1/4.
Multiply 3.5 x 2.4.
35 x 24 = 840. Both numbers have 1 decimal place each (total 2). So 3.5 x 2.4 = 8.40.
Divide 0.48 by 0.6.
Multiply both by 10: 4.8 / 6 = 0.8.
A ribbon is 6 and 3/4 m long. How many pieces of 3/4 m can be cut from it?
6 and 3/4 / (3/4) = (27/4) x (4/3) = 108/12 = 9 pieces.
Find the area of a rectangle with length 4.5 cm and breadth 2.3 cm.
Area = 4.5 x 2.3. 45 x 23 = 1035. Two decimal places total: Area = 10.35 sq cm.
- Key Formulas:
- (a/b) x (c/d) = ac/bd
- (a/b) / (c/d) = (a x d)/(b x c)
Common mistakes
When dividing fractions, always invert the SECOND fraction (the divisor) and then multiply. Do not invert both. When multiplying decimals, count the total number of decimal places, not just one of the numbers.
Summary
Fractions and decimals are two ways to represent parts of a whole. Multiplication of fractions is straightforward (multiply numerator and denominator). Division means multiplying by the reciprocal. Decimal operations use similar ideas through place value.