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Math  /  Numbers & Operations

QuestionUse the number line to find the difference of 312−83 \frac{1}{2}-8 A. −312-3 \frac{1}{2} B. −412-4 \frac{1}{2} C. 5125 \frac{1}{2} D. −512-5 \frac{1}{2}

Studdy Solution

STEP 1

1. The problem involves subtracting a whole number from a mixed number.
2. The subtraction will result in a negative number because the whole number being subtracted is larger than the mixed number.
3. The final answer should be simplified to a mixed number form.

STEP 2

1. Convert the mixed number to an improper fraction.
2. Perform the subtraction of the improper fraction and the whole number.
3. Convert the resulting improper fraction back to a mixed number.
4. Simplify the result to match one of the given choices.

STEP 3

Convert 3123 \frac{1}{2} to an improper fraction.
312=3+12=62+12=72 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}

STEP 4

Subtract 88 from 72\frac{7}{2}. First, express 88 as a fraction with the same denominator.
8=8×21×2=162 8 = \frac{8 \times 2}{1 \times 2} = \frac{16}{2}
Now perform the subtraction:
72−162=7−162=−92 \frac{7}{2} - \frac{16}{2} = \frac{7 - 16}{2} = \frac{-9}{2}

STEP 5

Convert the improper fraction −92\frac{-9}{2} back to a mixed number.
Since −92\frac{-9}{2} means −9-9 divided by 22, we get:
−9÷2=−4 with a remainder of −1 -9 \div 2 = -4 \text{ with a remainder of } -1 So, −92=−412 \frac{-9}{2} = -4 \frac{1}{2}

STEP 6

Simplify the result to match one of the given choices.
The result is:
−412 -4 \frac{1}{2}
Which matches choice B.

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