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Zorluk: OrtaFraction Addition and Subtraction in Context

A Navy Seabee is framing a new barracks and starts with a wooden board that is 163816 \frac{3}{8} feet long. For the first section of the frame, a piece measuring 4344 \frac{3}{4} feet is cut from the board. For the second section, another piece measuring 5565 \frac{5}{6} feet is cut. Assuming there is no waste from the saw cuts, what is the remaining length of the wooden board?

  1. A
    623406 \frac{23}{40}
  2. 519245 \frac{19}{24}Cevap
  3. C
    1071210 \frac{7}{12}
  4. D
    65246 \frac{5}{24}

Cevap

The remaining length of the wooden board is 519245 \frac{19}{24} feet.
To find the remaining length, the lengths of the two cut pieces must first be added together. Finding a common denominator of 24, the cuts are 418244 \frac{18}{24} and 520245 \frac{20}{24}. Their sum is 938249 \frac{38}{24}, which regroups to 10142410 \frac{14}{24}. Next, subtract this total from the original board length: 16924−10142416 \frac{9}{24} - 10 \frac{14}{24}. Since 924\frac{9}{24} is smaller than 1424\frac{14}{24}, borrowing from the whole number is required: 153324−101424=5192415 \frac{33}{24} - 10 \frac{14}{24} = 5 \frac{19}{24}.

Adım Adım Çözüm

1
Calculate the total length of the wooden board that was cut off.
434+556=41824+52024=93824=1014244 \frac{3}{4} + 5 \frac{5}{6} = 4 \frac{18}{24} + 5 \frac{20}{24} = 9 \frac{38}{24} = 10 \frac{14}{24} feet.
Adding the removed sections determines the total amount to subtract from the original board.
2
Set up the subtraction of the total cut length from the original length.
1638−101424=16924−10142416 \frac{3}{8} - 10 \frac{14}{24} = 16 \frac{9}{24} - 10 \frac{14}{24}
A common denominator is needed to subtract the fractions.
3
Borrow from the whole number to subtract the fractions.
153324−101424=5192415 \frac{33}{24} - 10 \frac{14}{24} = 5 \frac{19}{24} feet.
Since 924\frac{9}{24} is less than 1424\frac{14}{24}, borrowing 11 (or 2424\frac{24}{24}) from the whole number 1616 makes the subtraction possible.

Anahtar Kavram

Adding and subtracting mixed numbers with unlike denominators, including regrouping (borrowing).
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Konular

Fraction Addition and Subtraction in Context

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