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Addition and Subtraction of Terms Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Addition and Subtraction of Terms Study Guide.

Addition and Subtraction of Terms Practice Questions

Practice 1

For each problem, combine pairs of signs and solve.

  1. 4 + (+10) =
  2. –3 – (+9) =
  3. 7 – (–1) =
  4. 0 + (–6) =
  5. 9 + (–8) – (–2) =
  6. 15 – (+2) + (–4) =
  7. –18 + (+20) – (–5) =

Practice 2

  1. 6a5 + 2a5 =
  2. –2p + 2p =
  3. 23q12 + (+11q12) =
  4. 3b2 +b2 + 10b2 =
  5. 10a3 – (–5a3) =
  6. –9t8 + 8t8 + (+13t8) =
  7. 15y4 + 12y4 – (–17y4) =

Practice 3

  1. 11g9 – 9g9 =
  2. 4j6 – 5j6 =
  3. 18n4 – (+13n4) =
  4. h2 + (–7h2) =
  5. –8z3z3z3 =
  6. 16t15 – 9t15 – (+t15) =
  7. 3r–2 – 4r–2 + (–7r–2) =

Practice 4

For each problem, decide if the terms can be combined or not.

  1. 10k2 – 10k
  2. n + 19n
  3. 8x–3 + (–8x3)
  4. –11y2 + (–15z2)
  5. a5b4c2 – (–2a5b4c2)

Solutions

Practice 1

  1. Combine the two plus signs into one plus sign and add: 4 + (+10) = 4 +10 = 14.
  2. Combine the minus sign and the plus sign into a minus sign and subtract: –3 – (+9) = –3 – 9 = –12.
  3. Combine the two minus signs into one plus sign and add: 7 – (–1) = 7 + 1 = 8.
  4. Combine the plus sign and the minus sign into a minus sign and subtract: 0 + (–6) = 0 – 6 = –6.
  5. Combine the first pair of signs into a minus sign, since the two signs are different: 9 + (–8) – (–2) = 9 – 8 – (–2). Combine the second pair of signs into a plus sign, because the two signs are the same: 9 – 8 – (–2) = 9 – 8 + 2 = 1 + 2 = 3.
  6. Combine the first pair of signs into a minus sign, since the two signs are different: 15 – (+2) + (–4) = 15 – 2 + (–4). Combine the second pair of signs into a minus sign, because the two signs are also different: 15 – 2 + (–4) = 15 – 2 – 4 = 13 – 4 = 9.
  7. Combine the first pair of signs into a plus sign, since the two signs are the same: –18 + (+20) – (–5) = –18 + 20 – (–5). Combine the second pair of signs into a plus sign, because the two signs are also the same: –18 + 20 + 5 = 2 + 5 = 7.

Practice 2

  1. Each term has a base of a and an exponent of 5, so the base and exponent of your answer is a5. Add the coefficients: 6 + 2 = 8, so 6a5 + 2a5 = 8a5.
  2. Each term has a base of p and an exponent of 1. Remember, if a base does not appear to have an exponent, then it has an exponent of 1. The base of your answer is p. Add the coefficients: –2 + 2 = 0, so –2p + 2p = 0p, or simply 0.
  3. Each term has a base of q and an exponent of 12, so the base and exponent of your answer is q12. Combine the two plus signs into one plus sign: 23q12 + (+11q12) = 23q12 + 11q12. Add the coefficients of each term: 23 + 11 = 34, so 23q12 + 11q12 = 34q12.
  4. Each term has a base of b and an exponent of 2, so the base and exponent of your answer is b2. Add the coefficients of each term. Remember, if there is no number before the base of a term, the coefficient of that term is 1: 3 + 1 + 10 = 14, so 3b2 + b2 + 10b2 = 14b2.
  5. Each term has a base of a and an exponent of 3, so the base and exponent of your answer is a3. Combine the two minus signs into one plus sign: 10a3 – (–5a3) = 10a3 + 5a3. Add the coefficients of each term: 10 + 5 = 15, so 10a3 + 5a3 = 15a3.
  6. Each term has a base of t and an exponent of 8, so the base and exponent of your answer is t8. Combine the two plus signs into one plus sign: –9t8 + 8t8 + (+13t8) = –9t8 + 8t8 + 13t8. Add the coefficients of each term: –9 + 8 + 13 = 12, so 9t8 + 8t8 + 13t8 = 12t8.
  7. Each term has a base of y and an exponent of 4, so the base and exponent of your answer is y4. Combine the two minus signs into one plus sign: 15y4 + 12y4 – (–17y4) = 15y4 + 12y4 + 17y4. Add the coefficients of each term: 15 + 12 + 17 = 44, so 15y4 + 12y4 + 17y4 = 44y4.
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