Find the reciprocal of

a. - 1/10 (-4-7)

b. ½ / ¼
(hint: solve these first then find reciprocal of the answer)



Responses

- 1/10 (-4-7)

= 11/10
so the reciprocal is 10/11

for ½ / ¼
= 1/2 * 4/1
= 2

so the reciprocal is 1/2

3 1/3

To find the reciprocal of a fraction, you need to switch the numerator and the denominator.

a. Let's solve -1/10 * (-4-7) first.
To multiply a fraction by a whole number, you can multiply the numerator of the fraction by the whole number and keep the denominator the same.

-1/10 * (-4-7) = -1/10 * -11 = 11/10

Now, to find the reciprocal of 11/10, we switch the numerator and the denominator.
So, the reciprocal of 11/10 is 10/11.

b. Let's solve 1/2 ÷ 1/4 first.
To divide one fraction by another, you need to multiply the first fraction by the reciprocal of the second fraction.

1/2 ÷ 1/4 = 1/2 * 4/1 = 4/2 = 2

Now, to find the reciprocal of 2, we switch the numerator and the denominator.
So, the reciprocal of 2 is 1/2.

To summarize:
a. The reciprocal of -1/10 * (-4-7) is 10/11.
b. The reciprocal of 1/2 ÷ 1/4 is 1/2.