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Question

Difficulty: EasyFraction Operations

A painter has 34\frac{3}{4} of a gallon of blue paint. If they use exactly 13\frac{1}{3} of this paint to complete a small project, how many gallons of paint did they use? (Express your answer as a decimal.)

Answer: 0.25 gallons

Answer

0.25
To find 13\frac{1}{3} of 34\frac{3}{4}, you must multiply the two fractions together. Calculating 34×13\frac{3}{4} \times \frac{1}{3} results in 312\frac{3}{12}. Simplifying by dividing the numerator and denominator by 3 gives 14\frac{1}{4}. Finally, converting 14\frac{1}{4} to a decimal yields 0.25.

Step-by-Step Solution

1
Identify the mathematical operation
Multiplication: 34×13\frac{3}{4} \times \frac{1}{3}
The phrase '13\frac{1}{3} of this paint' indicates finding a part of a part, which requires multiplication.
2
Multiply the fractions
312\frac{3}{12}
Multiply the numerators together (3×1=33 \times 1 = 3) and the denominators together (4×3=124 \times 3 = 12).
3
Simplify the resulting fraction
14\frac{1}{4}
Both 33 and 1212 share a greatest common factor of 33. Dividing both by 33 simplifies the fraction.
4
Convert the simplified fraction to a decimal
0.25
The question specifically requests the final answer to be expressed as a decimal.

Key Concept

Fraction multiplication and decimal conversion
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Topics

Fraction Operations

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