Question

A mixture contains 1/16 pound sand and 7/8 pound compost. At that rate, what amount of sand is needed if the mixture contains 1 pound of compost?

A.

1/14

pound


B.

8/24

pound


C.

14 pounds


D.

15/16

pound

Answer 1

A. ¹/₁₄ lb

Explanation:

¹/₁₆ lb sand goes with ⅞ lb compost.

For 1 lb compost, the mass of sand needed is:

1 lb compost × (¹/₁₆ lb sand)/(⅞ lb compost).

We must evaluate the fraction (¹/₁₆)/(⅞).

Invert the denominator and multiply

(¹/₁₆)/(⅞) = ¹/₁₆ × ⁸/₇ Cancel the 8s

= ½ × ⅐ Multiply numerators and denominators

= ¹/₁₄

For 1 lb of compost, the mass of sand needed is ¹/₁₄ lb.