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

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

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Lesson Notes

Multiplying fractions: multiply the tops, multiply the bottoms, then simplify. Dividing by a fraction: multiply by its reciprocal.

$\tfrac{a}{b} \times \tfrac{c}{d} = \tfrac{ac}{bd}$$\tfrac{a}{b} \div \tfrac{c}{d} = \tfrac{a}{b} \times \tfrac{d}{c}$

Worked example 1: dividing by a decimal

$4.8 \div 0.6$: move the decimal point one place in both numbers, so it becomes $48 \div 6$.

$48 \div 6 = 8$

Worked example 2: order of operations

$6 - 2 \times \tfrac{3}{4}$: multiply first, then subtract.

$6 - \tfrac{3}{2} = \tfrac{12}{2} - \tfrac{3}{2} = \tfrac{9}{2}$

Signs

Same signs give a positive answer. Different signs give a negative answer.
Order of operations: grouping first, then multiply and divide left to right, then add and subtract left to right.

Counting decimal places: when you multiply decimals, the product has as many decimal places as both factors together.

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.