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. Work each one on the canvas under it (pen, eraser and clear are in the canvas toolbar; drag the handle below the canvas for more room). Enter your answer in the box (the keypad under it has fractions, exponents, square roots, pi, the degree sign and the symbols < > ≤ ≥ ≠). When a Unit row is shown, tap the unit for your answer. Then press Check. Write fraction answers as improper fractions in lowest terms. Write decimal answers as decimals. The eye at the right of the row shows or hides the worked solution.