6th Class Mathematics Fractions

Fractions

• A fraction is a part of a whole.

• In the fraction \[\frac{6}{7}\] ,6 is called the numerator and 7 is called the denominator.

• The denominator is the number of equal parts into which a whole is divided.

• The numerator is the number of parts considered of the whole.

• Types of fractions

Like fractions: Fractions with the same denominators.

e.g., \[\frac{4}{5},\frac{6}{5},\frac{3}{5}\]

Unlike fractions: Fractions with different denominators,

e.g.,\[\frac{1}{2},\frac{9}{4},\frac{3}{7}\]

Proper fractions: Fractions in which the denominator is greater than the numerator.

e.g.,\[\frac{2}{9},\frac{5}{6},\frac{2}{3}\]

Improper fractions: Fractions in which the numerator is greater than or equal to the denominator.

e.g., \[\frac{9}{2},\frac{6}{5},\frac{3}{2},\frac{7}{7}\]

Mixed fractions: Fractions with a whole number part and a fractional part are called mixed fractions.

e.g.,\[1\frac{1}{2},2\frac{2}{3},3\frac{1}{4}\]

• Fractions can be represented on the number line. Every fraction has a point associated with it on the number line.

• Conversion of an improper fraction to a mixed fraction

\[\frac{13}{5}=2\frac{3}{5}\left[ Q\frac{R}{D}\,from \right]\]

• Conversion of a mixed fraction to an improper fraction

De = Denominator, Nu = Numerator, WN = Whole Number

\[3\frac{1}{4}=\frac{\left( De\times WN \right)+Nu}{De}=\frac{\left( 4\times 3 \right)+1}{4}=\frac{12+1}{4}=\frac{13}{4}\]

• Equivalent fractions: All fractions that have the same value are called equivalent fractions.

• Equivalent fractions of a given fraction can be written by multiplying (or dividing) the numerator and the denominator by the same number.

• Simplification of fractions: Reducing a fraction to its lowest terms is called simplification of the fraction. Dividing the numerator and the denominator of a fraction by a common factor reduces it into its lowest terms. The H.C.F of the numerator and denominator of a fraction in its simplest form is 1.

• (a) Comparing like fractions: Among like fractions. The fraction with greater numerator is greater.

(b) Comparing unlike fractions: Unlike fractions are first converted into like fractions by writing their equivalent fractions and then compared.

e.g., Compare \[\frac{a}{b\,}\,and\,\frac{c}{d}\]

(i) If ad > bc, then \[\frac{a}{b\,}\,>\,\frac{c}{d}\].

(ii) If ad < bc, then \[\frac{a}{b\,}\,<\frac{c}{d}\]

(iii) If ad = be, then \[\frac{a}{b\,}\,=\frac{c}{d}\]

• Add or subtract like fractions: To add or subtract two or more like fractions, we add or subtract the numerators and write the result over the common denominator.

e.g.,\[\frac{7}{8}+\frac{3}{8}-\frac{5}{8}=\frac{7+3-5}{8}=\frac{10-5}{8}=\frac{5}{8}\]

• Add or subtract unlike fractions:

To add or subtract two or more unlike fractions, we change them to like fractions and then add or subtract. To add or subtract unlike fractions, follow the steps given below.

(i) Change the mixed fractions (if any) to improper fractions.

(ii) Change all the fractions into like fractions (by taking L.C.M. of the denominators).

(iii) Add or subtract the numerators and write the result over the common denominator.

(iv) Reduce this fraction to the simplest form and then convert it into mixed fraction (if needed).