Solve the following word problem and enter your final answer. You may use a mixed number, … — Armed Services Vocational Aptitude Battery (ASVAB)

Solve the following word problem and enter your final answer. You may use a mixed number, improper fraction, or decimal format.

Answer:A Navy seaman is painting the exterior of a ship. He uses

3 \frac{1}{2}

gallons of gray paint on the port side and

2 \frac{1}{4}

gallons on the starboard side. In total, he used 【5 3/4】 gallons of paint.

5 3/4

To find the total amount of paint used, the two quantities must be added together. By finding a common denominator of 4, the fraction

\frac{1}{2}

is converted to

\frac{2}{4}

. Adding the fractions

\frac{2}{4}

and

\frac{1}{4}

yields

\frac{3}{4}

. Adding the whole numbers 3 and 2 gives 5. The combined total is

5 \frac{3}{4}

gallons.

Set up the addition problem to combine the two quantities of paint.

3 \frac{1}{2} + 2 \frac{1}{4}

The total amount of paint used is the sum of the paint used on both sides of the ship.

Find a common denominator for the fractional parts (2 and 4).

The least common multiple of 2 and 4 is 4.

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

Convert the first fraction to an equivalent fraction with a denominator of 4.

3 \frac{1}{2} = 3 \frac{2}{4}

This allows the fractional parts to be added seamlessly.

Add the whole numbers and the fractions.

Whole numbers:

3 + 2 = 5

. Fractions:

\frac{2}{4} + \frac{1}{4} = \frac{3}{4}

. Final total:

5 \frac{3}{4}

Combining the separate sums gives the total value of the mixed numbers.

Adding mixed numbers with unlike denominators

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