Fractions
Category : 6th Class
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.,\[1\frac{1}{2},2\frac{2}{3},3\frac{1}{4}\]
\[\frac{13}{5}=2\frac{3}{5}\left[ Q\frac{R}{D}\,from \right]\]
De = Denominator, Nu = Numerator, WN = Whole Number
\[3\frac{1}{4}=\frac{\left( De\times WN \right)+Nu}{De}=\frac{\left( 4\times 3 \right)+1}{4}=\frac{12+1}{4}=\frac{13}{4}\]
(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 \[\frac{a}{b\,}\,=\frac{c}{d}\]
e.g.,\[\frac{7}{8}+\frac{3}{8}-\frac{5}{8}=\frac{7+3-5}{8}=\frac{10-5}{8}=\frac{5}{8}\]
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).
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