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Question 4: Divide the following directed numbers. a) (-300) / (-6) b) (-1/2) / (1/4) c) (0.5) / (-0.25) / (-0.2) d) 200 / (1/4) - 0.2

Mathematics

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Answers

4 parts
a
50
b
-2
c
10
d
799.8

Step-by-step solution

10 steps

Part 4

Divide the following directed numbers

Part a50

  1. Divide the absolute values.

    300÷6=50300 \div 6 = 50
  2. Determine the sign.

    A negative number divided by a negative number results in a positive number.

    (−300)÷(−6)=50(-300) \div (-6) = 50

    The solution is 50\boxed{50}.

Part b-2

  1. Rewrite the division as multiplication by the reciprocal of the second fraction.

    (−12)÷(14)=(−12)×(41)\left(-\frac{1}{2}\right) \div \left(\frac{1}{4}\right) = \left(-\frac{1}{2}\right) \times \left(\frac{4}{1}\right)
  2. Multiply the fractions.

    −1×42×1=−42-\frac{1 \times 4}{2 \times 1} = -\frac{4}{2}
  3. Simplify the fraction.

    −42=−2-\frac{4}{2} = -2

    The solution is −2\boxed{-2}.

Part c10

  1. Perform the first division

    (0.5)÷(−0.25)(0.5) \div (-0.25).

    0.5÷(−0.25)=0.5−0.25=−20.5 \div (-0.25) = \frac{0.5}{-0.25} = -2
  2. Perform the second division with the result from Step 1

    (−2)÷(−0.2)(-2) \div (-0.2).

    (−2)÷(−0.2)=−2−0.2=10(-2) \div (-0.2) = \frac{-2}{-0.2} = 10

    The solution is 10\boxed{10}.

Part d799.8

  1. Perform the division first according to the order of operations.

    (200)÷(14)=200×4(200) \div \left(\frac{1}{4}\right) = 200 \times 4 200×4=800200 \times 4 = 800
  2. Perform the subtraction.

    800−(0.2)800 - (0.2)
  3. Simplify the expression.

    800−0.2=799.8800 - 0.2 = 799.8

    The solution is 799.8\boxed{799.8}.

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