A landscaper lays down \frac{1}{2} of a ton of gravel in the front yard and \frac{3}{8} of… — Armed Services Vocational Aptitude Battery (ASVAB)

A landscaper lays down $\frac{1}{2}$ of a ton of gravel in the front yard and $\frac{3}{8}$ of a ton of gravel in the backyard. What is the total amount of gravel used?

$\frac{7}{8}$ tonCevap
B
$\frac{2}{5}$ ton
C
$\frac{1}{8}$ ton
D
$\frac{1}{2}$ ton

Cevap

\frac{7}{8}

ton

The correct answer is found by identifying that finding the total amount requires addition. Converting the

\frac{1}{2}

ton to an equivalent fraction of

\frac{4}{8}

allows it to be added directly to the

\frac{3}{8}

of a ton, resulting in a total of

\frac{7}{8}

ton.

Adım Adım Çözüm

Identify the operation needed.

The problem asks for the 'total amount', which means adding

\frac{1}{2}

and

\frac{3}{8}

To find the combined weight of gravel used in both yards, the two quantities must be added together.

Find a common denominator for the fractions.

The least common multiple of 2 and 8 is 8.

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

Convert

\frac{1}{2}

to an equivalent fraction with a denominator of 8.

Multiply both the numerator and denominator by 4:

\frac{1 \times 4}{2 \times 4} = \frac{4}{8}

This creates an equivalent fraction that can be directly added to

\frac{3}{8}

Add the numerators and keep the common denominator.

\frac{4}{8} + \frac{3}{8} = \frac{4 + 3}{8} = \frac{7}{8}

Once denominators are the same, only the parts (numerators) are added.

Anahtar Kavram

Adding fractions with unlike denominators requires converting them to equivalent fractions with a common denominator first.

Soru

Cevap

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