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Algebra · combining like terms
P6 · Algebra · PSLE Maths
Question
Raju had 6a + 15 football cards. He gave 2a football cards to Siti and then bought 9 more football cards. If a = 8, how many football cards does Raju have now? Simplify the algebraic expression first, then evaluate it.
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Hint
Group the terms with a together, and group the number terms together. Remember to keep the sign in front of each term.
Show the answer and step-by-step explanation
Answer: Raju's cards now 56 cards
- Write the expression — Raju had 6a + 15 cards, gave away 2a cards, and bought 9 more cards. So the number of cards now is 6a + 15 - 2a + 9.
- Sort into groups — The blue cards are a-terms, and the yellow cards are number terms. Only like terms can be combined. Move each term together with its sign.
- Combine a-terms — Look at the blue a-terms first: 6a - 2a. 6 a's minus 2 a's leaves 4a.
- Combine numbers — Now look at the yellow number terms: 15 + 9 = 24. So the expression simplifies to 4a + 24.
- Substitute a = 8 — Now substitute a = 8 into the simplified expression. 4 × 8 + 24 = 56, so Raju has 56 football cards now. 📌 Key idea: simplify by combining like terms first, then substitute the value. This is faster and helps avoid mistakes.
Method: When combining like terms, terms with a are combined only with terms with a, and number terms are combined only with number terms. After simplifying, substitute the value of a.
Practice: 3 similar questions
- Siti had 5a + 6 stickers. She used a stickers and then received 14 more stickers. If a = 9, how many stickers does Siti have now? Simplify the algebraic expression first, then evaluate it.
Answer
56 stickers — Write the expression: 5a + 6 - a + 14. Combine like terms: 5a - a = 4a, and 6 + 14 = 20, so it simplifies to 4a + 20. Substitute a = 9: 4 × 9 + 20 = 36 + 20 = 56.
- Mei Ling saved $7a + $18. She spent $3a on lunch and then her mother gave her $12. If a = 5, how much money does Mei Ling have now? Simplify the algebraic expression first, then evaluate it.
Answer
50 $ — Write the expression: 7a + 18 - 3a + 12. Combine like terms: 7a - 3a = 4a, and 18 + 12 = 30, so it simplifies to 4a + 30. Substitute a = 5: 4 × 5 + 30 = 20 + 30 = 50, so she has $50 now.
- Ali had 3a + 10 coupons at the school funfair. He received 2a + 6 more coupons and then used a - 3 coupons. If a = 7, how many coupons did Ali have left? Simplify the algebraic expression first, then evaluate it.
Answer
47 coupons — Write the expression: 3a + 10 + 2a + 6 - (a - 3). Subtract each term in the bracket: -(a - 3) = -a + 3, so the expression becomes 3a + 10 + 2a + 6 - a + 3. Combine like terms: 3a + 2a - a = 4a, and 10 + 6 + 3 = 19, so it simplifies to 4a + 19. Substitute a = 7: 4 × 7 + 19 = 28 + 19 = 47.
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