Adding and Subtracting Integers and Rational Numbers: Grade 7 Math Test Answer Key – PDF Download

Question 1: Opposites (2 points)

1. The opposite of \(-13\) is \(13\).
2. Opposites add to zero, so \(-18.5 + 18.5 = \)\(0\).

Scoring: 1 point for each correct answer.

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

The jump is \(8\) units right from \(-5\) and ends at \(3\).

\(-5 + 8 = 3\)

Scoring: 1 point for the correct addends \(-5\) and \(8\), 1 point for the sum \(3\).

Question 3: Adding Integers (2 points)

1. \(14 – 9 = 5\), and \(-14\) has the larger absolute value, so \(-5\).
2. Same signs: \(8 + 6 = 14\), so \(-14\).

Scoring: 1 point for each correct sum.

Question 4: Subtracting Integers (2 points)

1. \(7 + (-15) = \)\(-8\).
2. \(-3 + 9 = \)\(6\).

Scoring: 1 point for each correct difference.

Question 5: Decimals and Fractions (2 points)

1. \(2.75 – 1.5 = 1.25\), with the sign of \(-2.75\): \(-1.25\).
2. \(-\frac{2}{4} + (-\frac{3}{4}) = \)\(-\frac{5}{4}\), or \(-1\frac{1}{4}\).

Scoring: 1 point for each correct value. Accept equivalent forms such as \(-1\frac{1}{4}\).

Question 6: Overnight Temperatures (2 points)

1. \(-8 + 15 = 7\), so \(7^{\circ}\text{F}\).
2. \(7 – 11 = -4\), so \(-4^{\circ}\text{F}\).

Scoring: 1 point for each correct temperature with the correct sign.

Question 7: Distance Between Points (3 points)

1. \(|-7.5 – 4| = |-11.5| = 11.5\). The distance is 11.5 units.
2. \(4 + 5.5 = \)\(9.5\).

Scoring: 2 points for part (a): 1 for a correct absolute value expression such as \(|-7.5 – 4|\), 1 for \(11.5\). 1 point for part (b).

Question 8: Account Balance (3 points)

1. \(-18.40 + 50 = 31.60\), so \(\$31.60\).
2. \(31.60 – 37.85 = -6.25\), so \(-\$6.25\).
3. The opposite of \(-6.25\) is \(6.25\), so he must deposit \(\$6.25\).

Scoring: 1 point for each part.

Question 9: Find the Error (2 points)

1. Liam subtracted \(2\) instead of subtracting \(-2\). Subtracting a negative number means adding its opposite, so the expression is \(-6 + 2\).
2. \(-6 + 2 = \)\(-4\).

Scoring: 1 point for a correct explanation (adding the opposite), 1 point for \(-4\).

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