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FRACTIONS AND DECIMALS

Fractions Decimals

Types of Fractions Decimal Place Value Chart
1 1 1
Unit fractions: , , , etc. Hundreds Tens Ones Tenths Hundredths Thousandths
3 9 12 (100) (10) (1) 1 1 1
1 2 4 11
Proper fractions: , , , , etc. 10 100 1000
2 3 7 13
4 5 11 19
Improper fractions: , , , , etc. 2 4 5 2 4 3
3 2 7 8 245.243: Two hundred forty-five point two four three
3
1
5
Mixed fractions: 2 , 3 , 7 8 , 5 , etc. 1 1 1
7 4 11 9 2 × 100 + 4 × 10 + 5 × 1 + 2 × + 4 × + 3 ×
2 1 4 5
Like fractions: , , , , etc. 10 100 1000
7 7 7 7 Whole number Fractional part
1 2 4 5
Unlike fractions: , , , , etc.
8 9 10 7 Conversion of Fractions and Decimals
2 4 6 8
Equivalent fractions: , , , , etc.
3 6 9 12 Conversion of fractions to decimals:
(a) 4 = 0.4 (b) 8 = 0.08 (c) 27 = 0.027
Addition and Subtraction of Fractions 10 100 1000
Conversion of decimals to fractions:
For like fractions: 4
5
Addition of fraction = SumofNumerators (a) 0.5 = 10 (b) 1.24 = 124 (c) 0.004 = 1000
100
CommonDenominator
Subtraction of fractions =
Differenceof Numerators Like and Unlike Decimals
Like Decimals: Decimals having the same number of
CommonDenominator decimal places. E.g., 0.24, 5.73, 12.40, 127.00
For unlike fractions: Convert the fractions into like Unlike Decimals: Decimals having different number
fractions first, then add or subtract them same as of decimal places. E.g., 0.64, 26.8 and 124.568
like fractions.
Addition and Subtraction of Decimals
Multiplication and Division of Fractions Addition Subtraction
H T O • t O • t h th
Multiplication of a fraction by a whole number: 3 5 • 6 4 • 4 1 7
Product of a fraction and a whole number + 3 1 • 7 – 2 • 1 0 6

= Numerator × Whole Number 6 7 • 3 2 • 3 1 1
Denominator Multiplication and Division of Decimals
Multiplication of a fraction by another fraction: Multiplication of decimals by 10, 100 and 1000:

Product of two fractions = Product of Numerators E.g., (a) 45.8 × 10 = 458.0 (b) 65.149 × 100 = 6514.9
Multiplication of decimals by a whole number:
Product of Denominators
E.g., 36.35 × 6 = 218.1
Division of a fraction by a whole number: Multiplication of decimals by another decimals:
Fraction ÷ Whole number = Fraction × Reciprocal E.g., 12.45 × 1.2 = 14.940
of whole number
Division of a whole number by a fraction: Division of decimals by 10, 100 and 1000:
Whole number ÷ Fraction = Whole number (a) 47.8 ÷ 10 = 4.78 (b)65.2÷100 = 0.652
× Reciprocal of the (c) 583.0 ÷ 1000 = 0.583
fraction Division of decimals by a whole number:
Division of a fraction by another fraction: E.g., 15.52 ÷ 4 = 3.88
1st fraction ÷ 2nd fraction = 1st fraction × Reciprocal Division of decimals by another decimals:
of the 2nd fraction E.g., 7.75 ÷ 0.25 = 31

Mathematics-7 48