Question

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

Answer 1

Answer:

$\dfrac{9}{40}$

Step-by-step explanation:

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

$\implies \dfrac{\frac14-\frac15}{2}+\dfrac15$

$\implies \dfrac{\frac{5}{20}-\frac{4}{20}}{2}+\dfrac15$

$\implies \dfrac{\frac{1}{20}}{2}+\dfrac15$

$\implies \dfrac{1}{20} \times \dfrac12+\dfrac15$

$\implies \dfrac{1}{40}+\dfrac15$

$\implies \dfrac{1}{40}+\dfrac{8}{40}$

$\implies \dfrac{9}{40}$

Answer 2

Answer:

7/32

Step-by-step explanation:

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

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.

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

$\dfrac{1}{4}\ \text{and }\dfrac{1}{5} \ \rightarrow \ \dfrac{1 \times 40}{4 \times 40} \ \text{and} \ \dfrac{1 \times 32}{5 \times 32} \ \rightarrow \ \dfrac{40}{160} \ \text{and} \ \dfrac{32}{160}$

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

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

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡