### Solved Examples

**Question 1: **A Pizza is cut into 8 equal pieces and shared by three children Jerome,
Jane and Robby. Jerome and Jane each got 3 pieces while little Robby got
2 pieces. Find the fraction of Pizza shared by

(a) Jerome and Jane.

(b) Jerome and Robby.

** Solution: **

While Jerome and Jane got $\frac{3}{8}$ of the Pizza, Robby got $\frac{2}{8}$ of it.

Fraction of Pizza shared by Jerome and Jane = $\frac{3}{8}$ + $\frac{3}{8}$ = $\frac{6}{8}$ = **$\frac{3}{4}$**

Like fractions added straight and the answer reduced.

Fraction of Pizza shared by Jerome and Robby = $\frac{3}{8}$ + $\frac{2}{8}$ = **$\frac{5}{8}$**

**Question 2: **More than two fractions can also be added applying the same methods discussed above.

Add

$\frac{2}{5}$,

$\frac{5}{6}$ and

$\frac{13}{15}$.

** Solution: **

We have unlike denominators here. The LCM of the denominators 5, 6 and 15 = 30.

The equivalent fractions to be used for addition with LCD = 30 are

$\frac{2}{5}$ = $\frac{12}{30}$, $\frac{5}{6}$ = $\frac{25}{30}$ and $\frac{13}{15}$ = $\frac{26}{30}$

$\frac{2}{5}$ + $\frac{5}{6}$ + $\frac{13}{15}$ = $\frac{12}{30}$ + $\frac{25}{30}$ + $\frac{26}{30}$ = $\frac{63}{30}$ = $\frac{21}{10}$ = 2$\frac{1}{10}$

The resulting sum is reduced and expressed as a mixed number.

**Question 3: **Mixed numbers can be added as fractions, by writing them as improper fractions.

Add

$3\frac{3}{4}$ and 2

$\frac{2}{5}$ ** Solution: **

Writing the mixed numbers as improper fractions we get 3$\frac{3}{4}$ = $\frac{15}{4}$ and 2$\frac{2}{5}$ = $\frac{12}{5}$

3$\frac{3}{4}$ + 2$\frac{2}{5}$ = $\frac{15}{4}$ + $\frac{12}{5}$

The LCD for the addition = 20. Hence,

3$\frac{3}{4}$ + 2$\frac{2}{5}$ = $\frac{15}{4}$ + $\frac{12}{5}$ = $\frac{75}{20}$ + $\frac{48}{20}$ = $\frac{123}{20}$ = 6$\frac{3}{20}$

Note here the sum is again given as a mixed number.

**Question 4: **Here are few examples in algebra.

$\frac{a}{c}$ +

$\frac{b}{c}$ =

$\frac{a+b}{c}$ ** Solution: **

Both the algebraic fractions have like denominators. The addition is
performed similar to the manner fractional numbers with like
denominators are added.

Algebraic fractions with unlike denominators are also added using common denominator as in the case of numerical fractions.

$\frac{1}{x}$ + $\frac{1}{y}$ = $\frac{y}{xy}$ + $\frac{x}{xy}$ = $\frac{x+y}{xy}$