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Algebra and Negative Numbers
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Algebra and Negative Numbers
🔢 Part 1: Negative Numbers
1. Calculate: -7 + 4 = _____
2. Work out: -6 - (-3) = _____
3. Calculate: -5 × 3 = _____
4. Find: -8 ÷ (-2) = _____
5. Simplify: -2 + (-9) = _____
6. Circle the correct rule for multiplying negative numbers:
Negative × Negative = Negative
Negative × Negative = Positive
Negative × Positive = Positive
📝 Part 2: Simplifying Algebraic Expressions
7. Simplify: 5a - 3a + 6
8. Simplify: 2y + 7 - y + 4
9. Simplify: 9b - 4b - 2b + 1
10. Simplify: 3m + 2n - m + 5
11. Simplify: -2x + 8 - x - 3
12. Which of these are like terms? (Check all that apply)
3x and -5x
2y and 4z
7a and 9a
5 and -3
📖 Part 3: Expanding Single Brackets
13. Expand: 2(y + 5)
14. Expand: -4(x - 3)
15. Expand: 5(a + 2b)
16. Expand: -3(2x + 1)
17. Expand: 6(m - 4)
18. Match each expression with its expanded form:
1. 3(x + 2)
2. -2(y - 4)
3. 4(2a + 1)
A. 8a + 4
B. 3x + 6
C. -2y + 8
🔧 Part 4: Factorising Single Brackets
19. Factorise: 4y + 12
20. Factorise: 10a - 15
21. Factorise: 9m + 3n
22. Factorise: -8x - 20
23. Factorise: 14p + 7
24. Circle the highest common factor (HCF) of 12x and 18:
2
3
6
12
🌟 Part 5: Challenge Questions
25. Temperature Challenge: The temperature in Manchester was -3°C in the morning. It rose by 8°C during the day, then dropped by 5°C in the evening. What was the final temperature?
26. Simplify and then expand: 2(3x - 1) + 4(x + 2)
27. Fill in the missing number: 3(x + ____) = 3x + 15
28. Explain in your own words what it means to "factorise" an expression:
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