A strip of wood 78 inches long is to be cut into pieces $[3 \frac{3}{4}]$ inches long. How many pieces can be cut?
A) 21
B) 20
C) 26
D) 12
Answer (1)
Convert the mixed fraction to an improper fraction: 3 4 3 = 4 15 .
Divide the total length by the length of each piece: 78 ÷ 4 15 = 78 × 15 4 = 15 312 = 5 104 = 20.8 .
Take the integer part of the result to find the number of whole pieces: ⌊ 20.8 ⌋ = 20 .
The number of pieces that can be cut is 20 .
Explanation
Understanding the Problem We are given a strip of wood that is 78 inches long and we want to cut it into pieces that are 3 4 3 inches long. Our goal is to find out how many such pieces we can cut from the strip.
Converting to Improper Fraction First, we need to convert the mixed fraction 3 4 3 into an improper fraction. To do this, we multiply the whole number (3) by the denominator (4) and add the numerator (3). This gives us 3 × 4 + 3 = 12 + 3 = 15 . So, the improper fraction is 4 15 . Therefore, each piece is 4 15 inches long.
Dividing the Lengths Now, we need to divide the total length of the strip (78 inches) by the length of each piece ( 4 15 inches). This will tell us how many pieces we can cut. So we perform the division:
78 ÷ 4 15 = 78 × 15 4 To simplify the calculation, we can first divide 78 by 3 and 15 by 3: 78 ÷ 3 = 26 and 15 ÷ 3 = 5 . So we have: 26 × 5 4 = 5 26 × 4 = 5 104 Now, we divide 104 by 5: 5 104 = 20.8
Finding the Number of Pieces Since we can only have whole pieces, we need to take the integer part of 20.8, which is 20. This means we can cut 20 whole pieces from the strip of wood.
Final Answer Therefore, the number of pieces that can be cut is 20.
Examples
Imagine you are a carpenter and you have a wooden plank that is 78 inches long. You need to cut this plank into smaller pieces, each 3 4 3 inches long, to build small decorative items. Knowing how many pieces you can get from the original plank helps you plan your project efficiently, minimizing waste and ensuring you have enough material for your needs. This is a practical application of division and fraction manipulation in everyday carpentry.
