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Choose all the common denominators for
(1)/(4) and
(7)/(10).
A. 10
B. 20
C. 24
D. 32
E. 40

Choose all the common denominators for $\frac{1}{4}$ and $\frac{7}{10}$ . $\newline$ A. $10$ $\newline$ B. $20$ $\newline$ C. $24$ $\newline$ D. $32$ $\newline$ E. $40$

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Least common denominator

Full solution

Q. Choose all the common denominators for

\frac{1}{4}

and

\frac{7}{10}

.

\newline

A.

10

\newline

B.

20

\newline

C.

24

\newline

D.

32

\newline

E.

40

Find Common Denominators: To find common denominators for the fractions $(1)/(4)$ and $(7)/(10)$ , we need to find multiples of the denominators $4$ and $10$ that are the same.
Multiples of $4$ : The first few multiples of $4$ are $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \ldots$
Multiples of $10$ : The first few multiples of $10$ are $10$ , $20$ , $30$ , $40$ , $50$ , $60$ , $70$ , $80$ , $90$ , $100$ , ...
Identify Common Multiples: Now we look for the common multiples from the lists above. The common multiples of $4$ and $10$ within the given options are $20$ and $40$ .
Check Option A: We check the options given in the problem to see which ones are common multiples of $4$ and $10$ . Option A ( $10$ ) is not a multiple of $4$ , so it is not a common denominator.
Check Option B: Option B ( $20$ ) is a multiple of both $4$ and $10$ , so it is a common denominator.
Check Option C: Option C ( $24$ ) is a multiple of $4$ but not a multiple of $10$ , so it is not a common denominator.
Check Option D: Option D ( $32$ ) is a multiple of $4$ but not a multiple of $10$ , so it is not a common denominator.
Check Option E: Option E ( $40$ ) is a multiple of both $4$ and $10$ , so it is a common denominator.

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