Question

Carl has a rock collection. Of the rocks, 3/8 are quartz and 1/3 are granite. What fraction of Carl's rocks are quartz or granite

Answer 1

`(17)/(24)` of Carl's rocks are quartz or granite

Explanation:

Proportions and Fractions

A proportion is expressed as a fraction a/b, where a and b are compared by division. If a=b, the proportion (or ratio) equals 1, if a<b, the ratio is less than 1, and if a>b, the ratio is greater than 1. The proportion of elements of a set to the total number of elements of the set is less than one, and the sum of all them equals 1.

We know 3/8 of Carl's rock collection are quartz and 1/3 are granite. If both subsets of rocks are mutually exclusive or disjoint (cannot happen simultaneously), then the proportion of both is the sum of the fractions.

`\displaystyle (3)/(8)+(1)/(3)=(9+8)/(24)=(17)/(24)`