Question

On a number line, which fraction is between 1/4 and 1/5?

Answer 1

7/32

Explanation:

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To find a fraction between 1/4 and 1/5:

1. Make common denominators with both fractions. The larger the common denominator, the more you will find.

2. Choose any fraction between 1/4 and 1/5. That fraction will be in between 1/4 and 1/5.

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`(1)/(4)\ \text{and }(1)/(5) \ \rightarrow \ (1 * 40)/(4 * 40) \ \text{and} \ (1 * 32)/(5 * 32) \ \rightarrow \ (40)/(160) \ \text{and} \ (32)/(160)`

Now, you may choose any fraction between 40/160 and 32/160.

My chosen fraction is 35/160, which when simplified, gives 7/32.

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Answer 2

`(9)/(40)`

Explanation:

Subtract 1/5 from 1/4, divide by 2, then add to 1/5:

`\implies (\frac14-\frac15)/(2)+\frac15`

`\implies ((5)/(20)-(4)/(20))/(2)+\frac15`

`\implies ((1)/(20))/(2)+\frac15`

`\implies (1)/(20) * \frac12+\frac15`

`\implies (1)/(40)+\frac15`

`\implies (1)/(40)+(8)/(40)`

`\implies (9)/(40)`