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Question
Fill in the blank using ‘>’, ‘<’ or ‘=’ :
`11/16` ______ `14/15`
Options
>
<
=
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Solution
`11/16 underlinebb(<) 14/15`
Explanation:
In order to compare fractions with different denominators, we will convert them to like fractions.
LCM of 16 and 15
| 2 | 16, 15 |
| 2 | 8, 15 |
| 2 | 4, 15 |
| 2 | 2, 15 |
| 3 | 1, 15 |
| 5 | 1, 5 |
| 1, 1 |
∴ LCM of 16 and 15 = 2 × 2 × 2 × 2 × 3 × 5 = 240
Now, converting each of the given fractions to an equivalent fractions with denominators 240.
`(11 xx 15)/(16 xx 15) = 165/240` and `(14 xx 16)/(15 xx 16) = 224/240`
Clearly, `224/240 > 165/240`
∴ `11/16 < 14/15`
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