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Question
Fill in the blank using ‘>’, ‘<’ or ‘=’ :
`12/75` ______ `32/200`
Options
>
<
=
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Solution
`12/75 underlinebb(=) 32/200`
Explanation:
In order to compare fractions with different denominators, we will convert them to like fractions.
LCM of 75 and 200
| 2 | 75, 200 |
| 2 | 75, 100 |
| 2 | 75, 50 |
| 3 | 75, 25 |
| 5 | 25, 25 |
| 5 | 5, 5 |
| 1, 1 |
∴ LCM of 75 and 200 = 2 × 2 × 2 × 3 × 5 × 5 = 600
Now, converting each of the given fractions to equivalent fractions with denominator 600.
`(12 xx 8)/(75 xx 8) = 96/600` and `(32 xx 3)/(200 xx 3) = 96/600`
Clearly, `96/600 = 96/600`
∴ `12/75 = 32/200`
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