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Standard VI

Mathematics

Equivalent Fractions

State which o...

Question

State which of the following are true

\frac{5}{8} = \frac{25}{40}

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\frac{6}{7} = \frac{12}{27}

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\frac{2}{7} = \frac{4}{14}

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\frac{- 8}{7} = \frac{- 72}{56}

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Solution

The correct options are
A $\frac{5}{8} = \frac{25}{40}$
C $\frac{2}{7} = \frac{4}{14}$
Option (A)
$\frac{25}{40} = \frac{5 \times 5}{5 \times 8} = \frac{5}{8}$
True

Option(B)
$\frac{12}{27} = \frac{3 \times 4}{3 \times 9} \neq \frac{6}{7}$
False

Option (C)
$\frac{4}{14} = \frac{2 \times 2}{2 \times 7} = \frac{2}{7}$
True

Option(D)
$- \frac{72}{56} = \frac{8 \times 9}{8 \times 7} \neq - \frac{8}{7}$
False

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Similar questions

Q. Find the value of

A

2 + 3 = 8

3 + 7 = 27

4 + 5 = 32

5 + 8 = 60

6 + 7 = 72

7 + 8 = A

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

Q. Are the following expressions polynomials?

(1) 21 − 8a + a²
(2) n³ − 6n² + 13
(3)

8 x^{2} - x^{\frac{7}{2}}

(4)

\frac{- 13}{9}

(5)

n - \frac{1}{n}

(6)

\frac{2}{5} a^{3} - 7 a + 19

(7) 51
(8) 9 − 5b² + b⁴
(9)

12 + \frac{10}{p^{- 2}}

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. Which of the following will come next in the following series?

919829873987649876559876546987654

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State which of the following are true

The correct options are A 58=2540 C 27=414Option (A)2540=5×55×8=58TrueOption(B)1227=3×43×9≠67FalseOption (C)414=2×22×7=27TrueOption(D)−7256=8×98×7≠−87False