Add the following fractions-a 712 and 38 b 916 and 712-

(a) 712 and 38 =14+924=2324 (b) 916 and 712 =27+2848=5548 ...

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Byju's Answer

Standard VI

Mathematics

Addition of Fractions

Add the follo...

Question

Add the following fractions.
(a) $\frac{7}{12}$ and $\frac{3}{8}$ (b) $\frac{9}{16}$ and $\frac{7}{12}$ .

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Solution

(a) $\frac{7}{12}$ and $\frac{3}{8}$
$= \frac{14 + 9}{24} = \frac{23}{24}$

(b) $\frac{9}{16}$ and $\frac{7}{12}$
$= \frac{27 + 28}{48} = \frac{55}{48}$

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Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Fill in the blanks.

(i) $(\frac{- 3}{17}) + (\frac{- 12}{5}) = (\frac{- 12}{5}) + (. . . . .)$

(ii) $- 9 + \frac{- 21}{8} = (. . . . . .) + (- 9)$

(iii) $(\frac{- 8}{13} + \frac{3}{7}) + (\frac{- 13}{4}) = (. . . . . .) + [\frac{3}{7} + (\frac{- 13}{4})]$

(iv) $- 12 + (\frac{7}{12} + \frac{- 9}{11}) = (- 12 + \frac{7}{12}) + (. . . . .)$

(v) $\frac{19}{- 5} + (\frac{- 3}{11} + \frac{- 7}{8}) = {\frac{19}{- 5} + (. . . . .)} + \frac{- 7}{8}$

(vi) $\frac{- 16}{7} + . . . . . = . . . . . . + \frac{- 16}{7} = \frac{- 16}{7}$

Q. Mark whether true or false.
(a) 8 (7 + 3) = 8 × 7 + 8 × 3 ____
(b) 12 (16 + 4) = 12 × 16 + 12 × 4 ____
(c) 14 (5 + 2) = 14 × 5 + 14 × 2 ____
(d) 9 (8 − 3) = 9 × 8 − 9 × 3 ____

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

Add the following rational numbers:
(i) $\frac{3}{4}$ and $\frac{- 3}{5}$
(ii) $\frac{5}{8}$ and $\frac{- 7}{12}$
(iii) $\frac{- 8}{9}$ and $\frac{11}{6}$
(iv) $\frac{- 5}{16}$ and $\frac{7}{24}$
(v) $\frac{7}{- 18}$ and $\frac{8}{27}$
(vi) $\frac{1}{- 12}$ and $\frac{2}{- 15}$
(vii) $- 1$ and $\frac{3}{4}$
(viii) $2$ and $\frac{- 5}{4}$
(ix) $0$ and $\frac{- 2}{5}$

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Add the following fractions.(a) 712 and 38 (b) 916 and 712.

(a) 712 and 38=14+924=2324(b) 916 and 712=27+2848=5548

Add the following fractions.
(a) $\frac{7}{12}$ and $\frac{3}{8}$ (b) $\frac{9}{16}$ and $\frac{7}{12}$ .

(a) $\frac{7}{12}$ and $\frac{3}{8}$
$= \frac{14 + 9}{24} = \frac{23}{24}$

(b) $\frac{9}{16}$ and $\frac{7}{12}$
$= \frac{27 + 28}{48} = \frac{55}{48}$