Multiplying and Dividing Integers and Rational Numbers: Grade 7 Math Test Answer Key – PDF Download

Question 1: Products (2 points)

1. Different signs: \(-63\).
2. Same signs: \(66\).

Scoring: 1 point for each correct product.

Question 2: Product from a Number Line (2 points)

Three jumps, each \(4\) units to the left.

\(3 \times (-4) = -12\)

Scoring: 1 point for the correct multiplication \(3 \times (-4)\), 1 point for \(-12\).

Question 3: Quotients (2 points)

1. Different signs: \(-9\).
2. Same signs: \(8\).

Scoring: 1 point for each correct quotient.

Question 4: Zero in Division (2 points)

1. \(0 : (-9) = \)\(0\), since \((-9) \cdot 0 = 0\).
2. \(6 : 0 = r\) would require \(0 \cdot r = 6\). No number multiplied by \(0\) gives \(6\), so the quotient is undefined.

Scoring: 1 point for part (a). 1 point for part (b) for explaining that no number \(r\) satisfies \(0 \cdot r = 6\).

Question 5: Decimals and Fractions (2 points)

1. \(0.5 \times 8.4 = 4.2\), negative: \(-4.2\).
2. \(\frac{18}{30} = \)\(\frac{3}{5}\), positive because both factors are negative.

Scoring: 1 point for each correct product. Accept \(0.6\) for part (b).

Question 6: A Pattern of Products (3 points)

1. \((-5)(-1) = 5\) and \((-5)(-2) = 10\).
2. Each product increases by \(5\).
3. The products continue upward past \(0\) into positive values, so a negative times a negative is positive.

Scoring: 1 point for each part.

Question 7: Falling Temperature (3 points)

1. \(6 \times (-4) = -24\), so \(-24^{\circ}\text{F}\).
2. \(10 + (-24) = -14\), so \(-14^{\circ}\text{F}\).
3. \(-24 : 6 = \)\(-4^{\circ}\text{F}\) per hour.

Scoring: 1 point for each part.

Question 8: Equivalent Forms (2 points)

1. All three equal \(-3\).
2. \(\frac{15}{-3} = \frac{-15}{3} = \)\(-5\).

Scoring: 1 point for part (a) with all three values correct. 1 point for part (b), giving the equivalent form and the value.

Question 9: Three Factors (2 points)

\((-2)(-5) = 10\). Then \(10 \cdot (-3) = -30\). Finally \(-30 : 6 = \)\(-5\).

Scoring: 1 point for a correct partial product (\(10\) or \(-30\)), 1 point for the final answer \(-5\).

⬇ Download the Grade 7 Multiplying and Dividing Integers and Rational Numbers test answer key (PDF, 97 KB)

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