Question

Solve.

6 1/3 + k +3 5/6 + 5 1/2 =26 1/6

What fraction is k?

1. 9 1/2
2.10 1/6
3.10 1/2
4.11 1/2

Answer 1

The answer is C:
`10\text{ }^1/_2`. Here are the details:


`\text{Equation:}\\ 6\text{ }^1/_3+10\text{ }^1/_2\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Start with the integers.}\\ 6+10=16\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{...then with the fractions, but rewrite them first to make it easier.}\\ ^1/_3+\text{ }^1/_2\stackrel{\text{rewrite}}{\to}\text{ }^2/_6+\text{ }^3/_6=\text{ }^5/_6\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Add 'em up!}\\ 16\text{ }^5/_6`


`\text{Equation:}\\ 16\text{ }^5/_6+3\text{ }^5/_6\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Start with the integers.}\\ 16+3=19\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{...then with the fractions, but rewrite them first to make it easier.}\\ ^5/_6+\text{ }^5/_6=\text{ }^(10)/_6\stackrel{\text{rewrite}}{\to}\text{ }^5/_3\stackrel{\text{rewrite}}{\to}1\text{ }^2/_3\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Add 'em up!}\\ 20\text{ }^2/_3`


`\text{Last equation:}\\ 20\text{ }^2/_3+5\text{ }^1/_2\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Start with the integers.}\\ 20+5=25\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{...then with the fractions, but rewrite them first to make it easier.}\\ ^2/_3+\text{ }^1/_2\stackrel{\text{rewrite}}{\to}\text{ }^4/_6+\text{ }^3/_6=\text{ }^7/_6\stackrel{\text{rewrite}}{\to}1\text{ }^1/_6\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Add the integer and fraction together.}\\ 25+1\text{ }^1/_6\stackrel{?}{=}26\text{ }^1/_6`


`26\text{ }^1/_6\stackrel{\checkmark}{=}26\text{ }^1/_6`