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Math  /  Numbers & Operations

QuestionFor problems 7−107-10, subtract.
7. −14−34-\frac{1}{4}-\frac{3}{4}
8. 38−(−78)\frac{3}{8}-\left(-\frac{7}{8}\right)
9. −35−(−45)-\frac{3}{5}-\left(-\frac{4}{5}\right)
10. −56−(−16)-\frac{5}{6}-\left(-\frac{1}{6}\right)

Studdy Solution

STEP 1

1. We are performing subtraction of fractions.
2. We will simplify the expressions where necessary.
3. We will assume that the fractions have common denominators where applicable.

STEP 2

1. Problem 7: Subtract fractions with a common denominator.
2. Problem 8: Subtract fractions with a common denominator and handle negative signs.
3. Problem 9: Subtract fractions with a common denominator and handle negative signs.
4. Problem 10: Subtract fractions with a common denominator and handle negative signs.

STEP 3

For problem 7, we have the expression −14−34-\frac{1}{4} - \frac{3}{4}.

STEP 4

Since the denominators are the same, subtract the numerators:
−14−34=−1−34=−44=−1-\frac{1}{4} - \frac{3}{4} = \frac{-1 - 3}{4} = \frac{-4}{4} = -1

STEP 5

For problem 8, we have the expression 38−(−78)\frac{3}{8} - \left(-\frac{7}{8}\right).

STEP 6

Subtracting a negative is the same as adding:
38−(−78)=38+78=3+78=108=54\frac{3}{8} - \left(-\frac{7}{8}\right) = \frac{3}{8} + \frac{7}{8} = \frac{3 + 7}{8} = \frac{10}{8} = \frac{5}{4}

STEP 7

For problem 9, we have the expression −35−(−45)-\frac{3}{5} - \left(-\frac{4}{5}\right).

STEP 8

Subtracting a negative is the same as adding:
−35−(−45)=−35+45=−3+45=15-\frac{3}{5} - \left(-\frac{4}{5}\right) = -\frac{3}{5} + \frac{4}{5} = \frac{-3 + 4}{5} = \frac{1}{5}

STEP 9

For problem 10, we have the expression −56−(−16)-\frac{5}{6} - \left(-\frac{1}{6}\right).

STEP 10

Subtracting a negative is the same as adding:
−56−(−16)=−56+16=−5+16=−46=−23-\frac{5}{6} - \left(-\frac{1}{6}\right) = -\frac{5}{6} + \frac{1}{6} = \frac{-5 + 1}{6} = \frac{-4}{6} = -\frac{2}{3}
The solutions to the problems are:
7. −1-1
8. 54\frac{5}{4}
9. 15\frac{1}{5}
10. −23-\frac{2}{3}

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