A landscaper is combining two partial bags of fertilizer. The first bag contains \frac{3}{… — Armed Services Vocational Aptitude Battery (ASVAB)

A landscaper is combining two partial bags of fertilizer. The first bag contains $\frac{3}{4}$ of a pound, and the second bag contains $\frac{1}{6}$ of a pound. What is the total weight of the fertilizer when combined?

A
$\frac{2}{5}$
B
$\frac{1}{8}$
$\frac{11}{12}$ Answer
D
$\frac{1}{6}$

Answer

The total weight is

\frac{11}{12}

of a pound.

To add fractions with different denominators, a common denominator must first be found. The least common multiple of

4

and

6

12

. Converting both fractions to have a denominator of

12

yields

\frac{9}{12}

and

\frac{2}{12}

. Adding the numerators while keeping the denominator the same gives the correct sum of

\frac{11}{12}

Step-by-Step Solution

Find a common denominator for the fractions

\frac{3}{4}

and

\frac{1}{6}

The least common multiple of

4

and

6

12

Fractions must have the same denominator before they can be added or subtracted.

Convert both fractions to have the common denominator of

12

\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}

and

\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}

This creates equivalent fractions that represent the same values but share a denominator.

Add the numerators together while keeping the denominator the same.

\frac{9}{12} + \frac{2}{12} = \frac{9 + 2}{12} = \frac{11}{12}

Once denominators are equal, only the fractional parts (numerators) are combined.

Key Concept

Adding fractions with unlike denominators

Alternative Method

You can also use the cross-multiplication method:

\frac{(3 \times 6) + (1 \times 4)}{4 \times 6} = \frac{18 + 4}{24} = \frac{22}{24}

. Then, simplify the fraction by dividing both the numerator and denominator by

2

to get

\frac{11}{12}

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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