Substituting into expressions Substitution What does substitution mean
Substituting into expressions
Substitution What does substitution mean? In algebra, when we replace letters in an expression or equation with numbers we call it substitution.
Substitution How can 4 + 3 × be written as an algebraic expression? Using n for the variable we can write this as 4 + 3 n. We can evaluate the expression 4 + 3 n by substituting different values for n. When n = 5 4 + 3 n = 4 + 3 × 5 = 4 + 15 = 19 When n = 11 4 + 3 n = 4 + 3 × 11 = 4 + 33 = 37
Substitution 7× can be written as 7 n 2 2 7 n We can evaluate the expression by substituting 2 different values for n. When n = 4 7 n 2 = 7× 4÷ 2 = 28 ÷ 2 = 14 When n = 1. 1 7 n 2 = 7 × 1. 1 ÷ 2 = 7. 7 ÷ 2 = 3. 85
Substitution 2 +6 can be written as n 2 + 6 We can evaluate the expression n 2 + 6 by substituting different values for n. When n = 4 n 2 + 6 = 42 + 6 = 16 + 6 = 22 When n = 0. 6 n 2 + 6 = 0. 62 + 6 = 0. 36 + 6 = 6. 36
Substitution 2( + 8) can be written as 2(n + 8) We can evaluate the expression 2(n + 8) by substituting different values for n. When n = 6 2(n + 8) = 2 × (6 + 8) = 2 × 14 = 28 When n = 13 2(n + 8) = 2 × (13 + 8) = 2 × 21 = 42
Substitution exercise Here are five expressions. 1) a + b + c = 5 + 2 + – 1 = 6 2) 3 a + 2 c = 3 × 5 + 2 × – 1 = 15 + – 2 = 13 3) a(b + c) = 5 × (2 + – 1) = 5 × 1 = 5 4) abc = 5 × 2 × – 1= 10 × – 1 = – 10 b 2 – c 5) a = 22 – – 1 =5÷ 5=1 5 Evaluate these expressions when a = 5, b = 2 and c = – 1.
Now try these:
Answers: 11. 24 12. 13 13. 3 16. -9 17. 30 18. 10 14. -1 15. 17 19. 3 20. -3 21. 45 22. 23 23. 41 24. 9 25. 4 26. 8 27. 21 28. -12 32. 8 33. 9 29. 14 30. 27 31. -7 34. 25
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