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Algebra · simplify before substitution

P6 · Algebra · PSLE Maths

Question

At a school funfair, Ali uses p to represent the price of each packet of stickers. Given that p = 6, find the values of 5p − 2p + 7 and (p + 4) × 3.

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Hint

First collect like terms or expand the brackets, then replace p with 6.

Show the answer and step-by-step explanation

Answer: Value of 5p − 2p + 7 25; Value of (p + 4) × 3 30

  1. Read carefully — We are given p = 6. We need to find the values of two expressions. A good habit is: simplify first, then substitute.
  2. Simplify A — Look at A: 5p − 2p are like terms, so we can combine them. 5 p-units minus 2 p-units leaves 3p; keep the +7.
  3. Simplify B — Look at B: (p + 4) × 3 means 3 equal groups of p + 4. So there are 3 p's and three 4's, giving 3p + 12.
  4. Substitute in A — Now substitute p = 6 into the simplified A. A = 3p + 7, so A = 3 × 6 + 7.
  5. Substitute in B — B is simplified to 3p + 12. Substitute p = 6: 3 × 6 + 12 = 30. 📌 Key idea: simplify the expression first, then substitute the value of the variable to avoid mistakes.

Method: When evaluating algebraic expressions, simplify first: collect like terms and multiply into brackets. Then substitute the given value of the variable.

Practice: 3 similar questions

  1. Given that n = 4, find the values of 6n − 2n + 5 and (n + 3) × 2.
    Answer

    21, 14 — 6n − 2n + 5 = 4n + 5. Substitute n = 4: 4 × 4 + 5 = 16 + 5 = 21. (n + 3) × 2 = 2n + 6. Substitute n = 4: 2 × 4 + 6 = 8 + 6 = 14.

  2. In a maths game, q = 8. Find the values of 7q − 3q − 6 and (q + 5) × 4.
    Answer

    26, 52 — 7q − 3q − 6 = 4q − 6. Substitute q = 8: 4 × 8 − 6 = 32 − 6 = 26. (q + 5) × 4 = 4q + 20. Substitute q = 8: 4 × 8 + 20 = 32 + 20 = 52.

  3. Given that y = 9, find the values of 3(2y + 1) − 4y and (y − 2) × 5 + 3y.
    Answer

    21, 62 — 3(2y + 1) − 4y = 6y + 3 − 4y = 2y + 3. Substitute y = 9: 2 × 9 + 3 = 18 + 3 = 21. (y − 2) × 5 + 3y = 5y − 10 + 3y = 8y − 10. Substitute y = 9: 8 × 9 − 10 = 72 − 10 = 62.

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