The H-C-F- of the fractions 8-21- 12-35 and 32-7 is

The correct option is A 4/105 8= 2 ^ 3 12= 2 ^ 2 × 3 32= 2 ^ 5 HCF(8,12,32)= 2 ^ 2 =4 21=3× 7 35=5× 7 7=1× 7 LCM ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

The H.C.F. of...

Question

The H.C.F. of the fractions $\frac{8}{21}$ , $\frac{12}{35}$ and $\frac{32}{7}$ is

\frac{4}{105}

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\frac{192}{7}

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\frac{4}{7}

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\frac{5}{109}

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Solution

The correct option is A $\frac{4}{105}$
$8 = 2^{3} 12 = 2^{2} \times 3 32 = 2^{5} H C F (8, 12, 32) = 2^{2} = 4 21 = 3 \times 7 35 = 5 \times 7 7 = 1 \times 7 L C M (21, 35, 7) = 3 \times 5 \times 7 = 105$
HCF of a fraction $=$ HCF of numerator / LCM of denominator

HCF of fraction $=$ $\frac{4}{105}$

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Similar questions

Verify each of the following :

(i) $(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} \times (\frac{12}{13} \times \frac{7}{18})$
(ii) $\frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36}) = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36}$
(iii) $(\frac{- 9}{5} \times \frac{- 10}{3}) \times \frac{21}{- 4} = \frac{- 9}{5} \times (\frac{- 10}{3} \times \frac{21}{- 4})$

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) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Slide the slider to the value of : (4 \times 8) \times 5 + (35 + 12) - 7

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

Find:

(i) (ii) (iii)

(iv) (v) (vi)

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The H.C.F. of the fractions 821, 1235 and 327 is

The correct option is A 41058=2312=22×332=25HCF(8,12,32)=22=421=3×735=5×77=1×7LCM(21,35,7)=3×5×7=105HCF of a fraction = HCF of numerator / LCM of denominatorHCF of fraction = 4105

The H.C.F. of the fractions $\frac{8}{21}$ , $\frac{12}{35}$ and $\frac{32}{7}$ is