) Tim has a cedar plank that is ππ π feet long. If he cuts four identical sections off the end of the plank, each
π
π π feet long, and no wood is wasted, how long will the remaining piece be? Write one expression that π
represents this situation and evaluate it to find the answer.
The remaining length of the plank can be found by subtracting the length of the four identical sections from the original length of the plank.
Expression: 11 7/8 - (4 * 8 1/3)
To simplify this expression, we need to convert the mixed fractions into improper fractions:
Expression: 11 7/8 - (4 * 25/3)
To multiply fractions, we multiply the numerators and then multiply the denominators:
Expression: 11 7/8 - (100/3)
To subtract fractions, we need a common denominator:
Expression: 11 7/8 - (100/3 * 8/8)
Now, we can multiply and subtract:
Expression: 11 7/8 - (800/24)
To subtract mixed fractions, we subtract the whole numbers separately and then subtract the fractions:
Expression: (11 - 800/24) + (7/8)
To simplify further, we convert the mixed fraction 11 to an improper fraction:
Expression: (264/24 - 800/24) + (7/8)
Now, we can subtract the fractions:
Expression: -536/24 + (7/8)
To add fractions, we need a common denominator:
Expression: (-536/24 * 8/8) + (7/8)
Expression: (-4288/24 + 7/8)
To add fractions, we add the numerators and keep the common denominator:
Expression: (-4288 + 21)/24
Expression: -4267/24
Therefore, the remaining piece of the plank will be 4267/24 feet long.
To find the length of the remaining piece, we need to subtract the total length of the four identical sections from the initial length of the plank.
The total length of the four identical sections is 4 * (8 1/3) = 33 1/3 feet.
Therefore, the length of the remaining piece is 117 - 33 1/3 = 83 2/3 feet.
The expression that represents this situation is:
117 - 4 * (8 1/3)
or simplified as:
117 - 33 1/3 = 83 2/3.