ICSE Class 7 Maths Chapter 04 Fraction

Chapter 4: Fraction

Including Problems Based On Fractions

4.1 Basic Concept

If an apple is divided into five equal parts; each part is said to be one-fifth \(\frac{1}{5}\) of the whole apple. And, if out of these five equal parts, 2 parts are eaten; we say two-fifth \(\frac{2}{5}\) of the apple is eaten or three-fifth \(\frac{3}{5}\) of the apple is left.

The numbers \(\frac{1}{5}\), \(\frac{2}{5}\) and \(\frac{3}{5}\) used in the statement, given above, are called fractions.

Each of these fractions indicates a part of the whole.

In fraction \(\frac{a}{b}\), \(a\) is called the numerator and \(b\) is called the denominator of the fraction.

Fraction = Numerator / Denominator

Every fraction can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\) i.e. denominator is not equal to zero.

Teacher's Note

Fractions are used every day when splitting bills at restaurants, dividing pizza slices among friends, or measuring ingredients while cooking.

4.2 Classification Of Fractions

If the numerator is equal to the denominator, the fraction is equal to unity (one).

e.g. \(\frac{4}{4} = 1\), \(\frac{-3}{-3} = 1\), \(\frac{49}{49} = 1\) and so on.

Important : (a) \(\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100}\), a decimal fraction.

(b) \(\frac{81}{500} = \frac{81 \times 2}{500 \times 2} = \frac{162}{1000}\), a decimal fraction.

If the denominator of a fraction can be expressed as 10 or as some higher power of 10, it is a decimal fraction.

Teacher's Note

Classification helps us understand which fractions are easier to work with in calculations, such as decimal fractions being useful for money and measurements.

4.3 Reducing A Given Fraction To Its Lowest Term

Steps

First of all find H.C.F. of both the terms (numerator and denominator) of the given fraction. Then divide each term by this H.C.F.

Example 2

Reduce : (i) \(\frac{48}{60}\) (ii) \(\frac{18}{27}\) to their lowest terms.

Solution

(i) Since, H.C.F. of terms 48 and 60 = 12.

\(\frac{48}{60} = \frac{48 \div 12}{60 \div 12}\) [Dividing each term by 12]

\(= \frac{4}{5}\)

(ii) Since, H.C.F. of 18 and 27 is 9

\(\frac{18}{27} = \frac{18 \div 9}{27 \div 9} = \frac{2}{3}\)

Alternative Method

Resolve both the numerator and the denominator into prime factors, then cancel out the common factors among both.

Since, \(48 = 2 \times 2 \times 2 \times 2 \times 3\) and \(60 = 2 \times 2 \times 3 \times 5\)

\(\frac{48}{60} = \frac{\cancel{2} \times \cancel{2} \times 2 \times 2 \times \cancel{3}}{\cancel{2} \times \cancel{2} \times \cancel{3} \times 5}\) [Cancelling out the common factors]

\(= \frac{2 \times 2}{5} = \frac{4}{5}\)

Teacher's Note

Reducing fractions to lowest terms is like simplifying a recipe - using the simplest ingredients possible without changing the final result.

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