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. 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.