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

Problem 1: Opposites and Zero

The opposite of a number is the same distance from \(0\) on the other side.

1. \(-9\)
2. \(15\)
3. \(-2.5\)
4. \(0\)

Since \(-23 + 23 = 0\), the missing number is \(23\).

Problem 2: Opposites in real life

1. \(+15\). The opposite is \(-15\): \(15\text{ ft}\) below sea level.
2. \(-9\). The opposite is \(9\): gaining \(\$9\).
3. \(-6\). The opposite is \(6\): the temperature rises \(6^{\circ}\text{F}\).

Opposites are the same distance from \(0\) on opposite sides.

(a) \(15\) and \(-15\). (b) \(-9\) and \(9\). (c) \(-6\) and \(6\).

Problem 3: Adding on a Number Line

Move right for a positive number and left for a negative number.

1. \(-4 + 7 = 3\)
2. \(-4 + (-3) = -7\)
3. \(-4 + 4 = 0\)
4. \(-4 + (-6) = -10\)

Answers: 3, \(-7\), 0, \(-10\).

Problem 4: Jumping from three

Adding a negative number moves left. Subtracting a positive number moves left. Subtracting a negative number moves right.

1. \(3 + (-8) = -5\)
2. \(3 – 6 = 3 + (-6) = -3\)
3. \(3 – (-4) = 3 + 4 = 7\)

(a) \(-5\). (b) \(-3\). (c) \(7\).

Problem 5: Adding Integers

1. Different signs: \(9 – 4 = 5\), keep the negative sign. \(-9 + 4 = -5\).
2. \(11 – 6 = 5\), keep the negative sign. \(6 + (-11) = -5\).
3. Same signs: \(7 + 5 = 12\), negative. \(-7 + (-5) = -12\).
4. Opposites: \(15 + (-15) = 0\).
5. \(35 – 20 = 15\), positive. \(-20 + 35 = 15\).

Answers: \(-5\), \(-5\), \(-12\), 0, 15.

Problem 6: More sums of integers

1. Same signs: \(13 + 8 = 21\), so the sum is negative. \(-13 + (-8) = -21\).
2. Different signs: \(17 – 6 = 11\), and \(17\) is larger, so the sum is positive. \(17 + (-6) = 11\).
3. \(25 – 9 = 16\), and \(-25\) is farther from \(0\), so the sum is negative. \(-25 + 9 = -16\).
4. Same signs: \(4 + 19 = 23\). \(-4 + (-19) = -23\).
5. \(50 – 31 = 19\), and \(50\) is larger, so the sum is positive. \(-31 + 50 = 19\).

\(-21\), \(11\), \(-16\), \(-23\), \(19\)

Problem 7: Subtracting Integers

1. \(9 + (-14) = -5\)
2. \(-6 + (-8) = -14\)
3. \(5 + 7 = 12\)
4. \(-10 + 4 = -6\)
5. \(0 + 13 = 13\)

Answers: \(-5\), \(-14\), 12, \(-6\), 13.

Problem 8: More differences

1. \(8 + (-15) = -7\)
2. \(-12 + (-5) = -17\)
3. \(7 + 9 = 16\)
4. \(-14 + 14 = 0\)
5. \(-20 + 35 = 15\)

\(-7\), \(-17\), \(16\), \(0\), \(15\)

Problem 9: Subtracting on a Number Line

1. Subtracting \(9\) moves \(9\) units left: \(2 – 9 = -7\).
2. Subtracting \(-5\) is adding \(5\): \(2 – (-5) = 7\).
3. \(2 – 9 = 2 + (-9) = -7\).

Answers: \(-7\), 7, \(2 + (-9)\).

Problem 10: Three terms

1. \(-8 + 15 = 7\). Then \(7 + (-12) = -5\).
2. \(6 – (-4) = 6 + 4 = 10\). Then \(10 – 13 = -3\).
3. \(-7 – (-9) = -7 + 9 = 2\). Then \(2 + (-3) = -1\).

(a) \(-5\). (b) \(-3\). (c) \(-1\).

Problem 11: Distance on a Number Line

1. \(|-8 – 3| = |-11| = 11\) units.
2. \(|-5 – (-12)| = |7| = 7\) units.
3. \(|-4.5 – 2.5| = |-7| = 7\) units.
4. \(|-8 – 3| = |-11| = 11\) and \(|3 – (-8)| = |11| = 11\), so they are equal.

Answers: 11, 7, 7, and both expressions equal 11.

Problem 12: Distances between points

1. \(|-7 – (-2)| = |-5| = 5\) units.
2. \(|-2 – 4.5| = |-6.5| = 6.5\) units.
3. \(|-7 – 4.5| = |-11.5| = 11.5\) units. Check: \(5 + 6.5 = 11.5\).
4. \(-7 – 3.5 = -10.5\).

(a) 5 units. (b) 6.5 units. (c) 11.5 units. (d) \(-10.5\).

Problem 13: Mixed number types

1. \(-1.25 + 3.5 = 2.25\). Then \(2.25 – (-2.75) = 2.25 + 2.75 = 5\).
2. Use sixths: \(-\frac{5}{6} – \frac{2}{6} = -\frac{7}{6}\). Then \(-\frac{7}{6} + \frac{3}{6} = -\frac{4}{6} = -\frac{2}{3}\).
3. \(1\frac{1}{2} = \frac{3}{2} = \frac{9}{6}\) and \(-\frac{2}{3} = -\frac{4}{6}\). Distance: \(\frac{9}{6} – (-\frac{4}{6}) = \frac{13}{6} = 2\frac{1}{6}\).

(a) \(5\). (b) \(-\frac{2}{3}\). (c) \(2\frac{1}{6}\).

Problem 14: Fractions and Decimals

1. \(-\frac{3}{4} + \frac{2}{4} = -\frac{1}{4}\). Then \(-\frac{1}{4} + \frac{5}{4} = \frac{4}{4} = 1\).
2. \(-2.6 + 5.4 = 2.8\). Then \(2.8 + (-1.8) = 1\).
3. \(\frac{3}{2} = 1.5\), so the distance is \(|-2.5 – 1.5| = |-4| = 4\).

Answers: 1, 1, 4.

Problem 15: Temperature Change

1. \(-5 + 12 = 7\), so noon was \(7^{\circ}\text{F}\).
2. \(7 – 9 = -2\), so 6 p.m. was \(-2^{\circ}\text{F}\).
3. Change = final minus start: \(-11 – (-2) = -11 + 2 = -9\). The temperature changed by \(-9^{\circ}\text{F}\), a drop of \(9^{\circ}\text{F}\).

Problem 16: Golf scores

1. Highest: \(5\) (Diego). Lowest: \(-4\) (Priya). \(5 – (-4) = 5 + 4 = 9\).
2. Ethan: \(3\). Aisha: \(-1\). \(3 – (-1) = 3 + 1 = 4\).
3. \(-1 – 4 = -1 + (-4) = -5\).

(a) 9 strokes. (b) 4 strokes. (c) \(-5\) (5 strokes under par).

Problem 17: Yards gained and lost

1. Gains are positive and losses are negative: \(7 + (-12) + 5 + (-9)\). \(7 + (-12) = -5\), then \(-5 + 5 = 0\), then \(0 + (-9) = -9\). The net yardage is \(-9\) yards.
2. The team needs to go from \(-9\) to \(10\). \(10 – (-9) = 10 + 9 = 19\).

Check: \(-9 + 19 = 10\).

(a) \(-9\) yards (a net loss of 9 yards). (b) 19 yards.

Problem 18: Elevation Differences

1. \(35 – (-48) = 83\), so \(83\text{ ft}\).
2. \(120 – (-48) = 168\), so \(168\text{ ft}\).
3. \(-48 + 30 = -18\), so \(-18\text{ ft}\).
4. \(35 – (-18) = 53\), so the diver is \(53\text{ ft}\) below the bird.

Problem 19: Scuba dive

1. Up \(12\): \(-35 + 12 = -23\). Down \(20\): \(-23 – 20 = -43\). Up \(15\): \(-43 + 15 = -28\).
2. The final elevation is \(-28\text{ ft}\), which is \(28\text{ ft}\) below the surface.
3. \(|-28 – (-35)| = |7| = 7\), so the distance is \(7\text{ ft}\).

(a) \(-23\text{ ft}\), \(-43\text{ ft}\), \(-28\text{ ft}\). (b) \(28\text{ ft}\). (c) \(7\text{ ft}\).

Problem 20: Bank Balance

1. After the check: \(45.50 – 72.25 = -26.75\). After the deposit: \(-26.75 + 30 = 3.25\). After the fee: \(3.25 – 5.75 = -2.50\). Balances: \(-\$26.75\), \(\$3.25\), \(-\$2.50\).
2. Add the opposite of \(-2.50\): \(\$2.50\).

See every chapter on the Grade 7 math page.