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Difficulty: EasyFraction Multiplication and Division in Context

A carpentry team is preparing materials for a project. They have a wooden beam that is 1212 feet long. They need to cut the beam into smaller support blocks that are each 34\frac{3}{4} of a foot long. How many support blocks can they cut from the beam?

  1. A
    44
  2. B
    99
  3. 1616Answer
  4. D
    33

Answer

The team can cut 1616 support blocks from the beam.
The correct answer is 1616. To find how many smaller pieces can be cut from a larger piece, you must divide the total length by the length of one piece. Dividing 1212 by 34\frac{3}{4} is the same as multiplying 1212 by 43\frac{4}{3}, which results in 1616.

Step-by-Step Solution

1
Identify the total length of the beam and the length of each required block.
The total length is 1212 feet, and each block is 34\frac{3}{4} of a foot long.
These values are needed to determine how many times the smaller length fits into the total length.
2
Set up a division equation.
12÷3412 \div \frac{3}{4}
To find how many equal pieces can be made from a total amount, division is required.
3
Convert the division problem into a multiplication problem by using the reciprocal of the fraction.
12×4312 \times \frac{4}{3}
Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.
4
Multiply the whole number by the numerator and divide by the denominator.
12×43=483=16\frac{12 \times 4}{3} = \frac{48}{3} = 16
This completes the calculation, showing the total number of blocks.

Key Concept

Fraction Division in Context
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Topics

Fraction Multiplication and Division in Context

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