Multiply, Divide, and Order of Operations, Challenge Answer Key

Grade 7 rational numbers: multiplying and dividing rational numbers, dividing by decimals, and the order of operations. Tuesday practice at the challenge level.

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Lesson Notes

Plan before you calculate: find the grouping, decide the order, and decide whether fractions or decimals are the cleaner form.

Worked example

$\tfrac{5}{6} - \tfrac{1}{2} \div \left(-\tfrac{3}{4}\right)$: divide first.

$\tfrac{1}{2} \times \left(-\tfrac{4}{3}\right) = -\tfrac{2}{3}$, so $\tfrac{5}{6} + \tfrac{2}{3} = \tfrac{5}{6} + \tfrac{4}{6} = \tfrac{3}{2}$

To write a fraction as a decimal, divide the numerator by the denominator with long division. A remainder that repeats means the decimal repeats.
Subtracting a negative result adds a positive.

Check by estimating. A rough answer from friendly numbers catches most sign and decimal-place errors.

25 problems. Show your work in the space under each problem, then put a box around your answer. Write fraction answers as improper fractions in lowest terms. Write decimal answers as decimals. On screen, the eye at the right of each problem shows or hides the worked solution.