CBSE Class 7 Mathematics Fractions and Decimals Notes Set 05

Types of Fractions

A fraction names a part of a whole: numerator over denominator. A proper fraction has numerator less than denominator (value below 1); an improper fraction has numerator greater than or equal to the denominator; a mixed number combines a whole number with a proper fraction, so 7/3 = 2 1/3.
Like fractions have the same denominator and unlike fractions do not. Fractions with equal value, such as 2/3 and 16/24, are equivalent.

Comparing, Adding and Subtracting

To compare or add unlike fractions, rewrite them with a common denominator (the LCM of the denominators). Then compare numerators, or add or subtract numerators and keep the denominator.
For mixed numbers either add whole parts and fractional parts separately or convert to improper fractions. Always reduce the answer to lowest terms.

Multiplication and Division of Fractions

Multiply numerators together and denominators together, cancelling common factors first. 'Of' means multiplication, so 1/6 of 24 = 4. The product of two proper fractions is smaller than either of them.
The reciprocal of a/b is b/a. To divide by a fraction, multiply by its reciprocal. Convert mixed numbers to improper fractions before multiplying or dividing.

Decimals

Multiplying by 10, 100 or 1000 shifts the decimal point right by 1, 2 or 3 places; dividing shifts it left. To multiply decimals, multiply as whole numbers and give the product as many decimal places as both factors together. To divide by a decimal, shift the point in both numbers until the divisor is whole.
Units: 1 km = 10 hm = 1000 m, 1 g = 10 dg, 1 kg = 1000 g, 1 cl = 10 ml.

Worked Example

Divide \( 3\frac23 \) by \( 2\frac12 \). Convert: 11/3 ÷ 5/2. Multiply by the reciprocal: 11/3 × 2/5 = 22/15 = 1 7/15.