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This pdf covers the basics of substitution into algebraic expressions with examples for better understanding.

1.
MATHEMATICS

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Title: Substitution

Target: On completion of this worksheet you should be able to substitute

values into algebraic expressions and formulae and hence evaluate

unknowns.

When we replace a letter in an algebraic When we substitute negative numbers

expression by another term, that we know for letters we have to be careful. Using

has the same value, we are said to be brackets often helps.

substituting this letter.

Often we replace a letter by a number. E.g. If x = -5, y = -9 and z = 4 find

3x - 2y + z.

E.g. If x = 2 find 4x.

4 × 2 = 8. 3×(-5) - 2×(-9) + 4 = -15 – (-18) + 4

Remember 4x means 4 × x. = -15 + 18 + 4

= 7.

We need to remember that we must do

division and multiplication before addition See the number sheet on negative numbers if you have

and subtraction for more difficult difficulty with this.

Examples. Exercise.

1) If a = 4 and b = 6 find 3a + 2b.

If a=-4, b=6, c=-8, d=2 find the value of:

3 × 4 + 2 × 6 = 12 + 12 = 24. 1. b + a

2. b + 4a

2) If c = 3 and d =4 find 5(c + 2d). 3. 3c – b + 2a

4. 2 + 2a – 3b + c

5(3 + 2 × 4) = 5 × 11=55. 5. 6(2a - 3b)

Exercise. 6. 9(5c - d) - 4(a - 2b)

If a=2, b=4, c=7, d=1, e=0 find the value

of: (Answers: 2, -10, -38, -32,

1. 3+a -156, -314)

2. b+4a

3. a+3c+d

4. 2a+4b – 2c − 4e

5. 3(a+2b)

6. 2(a + b) − 3(2c − d)

(Answers: 5, 12, 24, 6, 30, -27)

C. Leech, Coventry University, June 2000. 1

SUPPORT CENTRE

Title: Substitution

Target: On completion of this worksheet you should be able to substitute

values into algebraic expressions and formulae and hence evaluate

unknowns.

When we replace a letter in an algebraic When we substitute negative numbers

expression by another term, that we know for letters we have to be careful. Using

has the same value, we are said to be brackets often helps.

substituting this letter.

Often we replace a letter by a number. E.g. If x = -5, y = -9 and z = 4 find

3x - 2y + z.

E.g. If x = 2 find 4x.

4 × 2 = 8. 3×(-5) - 2×(-9) + 4 = -15 – (-18) + 4

Remember 4x means 4 × x. = -15 + 18 + 4

= 7.

We need to remember that we must do

division and multiplication before addition See the number sheet on negative numbers if you have

and subtraction for more difficult difficulty with this.

Examples. Exercise.

1) If a = 4 and b = 6 find 3a + 2b.

If a=-4, b=6, c=-8, d=2 find the value of:

3 × 4 + 2 × 6 = 12 + 12 = 24. 1. b + a

2. b + 4a

2) If c = 3 and d =4 find 5(c + 2d). 3. 3c – b + 2a

4. 2 + 2a – 3b + c

5(3 + 2 × 4) = 5 × 11=55. 5. 6(2a - 3b)

Exercise. 6. 9(5c - d) - 4(a - 2b)

If a=2, b=4, c=7, d=1, e=0 find the value

of: (Answers: 2, -10, -38, -32,

1. 3+a -156, -314)

2. b+4a

3. a+3c+d

4. 2a+4b – 2c − 4e

5. 3(a+2b)

6. 2(a + b) − 3(2c − d)

(Answers: 5, 12, 24, 6, 30, -27)

C. Leech, Coventry University, June 2000. 1

2.
When letters are multiplied together or divided Substitution is frequently used with formulae. A

by each other the same principles apply. To formula expresses one variable in terms of other

avoid mistakes with minus signs we should variables.

again use brackets. E.g. V = IR, is a formula.

E.g. If a = 2, b = -6, and c=5 find the value of

We are often told the values of some of the

4ab + 7c 2 .

variables and asked to find the value of the others.

4 × 2 × (-6) + 7 × 5 2 = -48 + 175 E.g. If V = IR what is the value of V when I = 15

=127. when R = 16.

Remember 4ab means 4×a×b. V = 15×16 = 240.

Exercise.

If a = 5, b = -6, c = 2, d = -10 find the value of

1. If S = UV and U=5 and V=12 find S.

1. ac

b

2. ab - d 2 2. If H = and b=4 and c=8 find H.

3. 3(c - 4a) c

c rs

4. 3. If p= 2 and r = 4, s=12 and q=4 find p.

d q

ab (Answers: 60, 1 , 3)

5. 2

d −a

(Answers: 10, -130, -120, - 1 , 2)

5

C. Leech, Coventry University, June 2000. 2

by each other the same principles apply. To formula expresses one variable in terms of other

avoid mistakes with minus signs we should variables.

again use brackets. E.g. V = IR, is a formula.

E.g. If a = 2, b = -6, and c=5 find the value of

We are often told the values of some of the

4ab + 7c 2 .

variables and asked to find the value of the others.

4 × 2 × (-6) + 7 × 5 2 = -48 + 175 E.g. If V = IR what is the value of V when I = 15

=127. when R = 16.

Remember 4ab means 4×a×b. V = 15×16 = 240.

Exercise.

If a = 5, b = -6, c = 2, d = -10 find the value of

1. If S = UV and U=5 and V=12 find S.

1. ac

b

2. ab - d 2 2. If H = and b=4 and c=8 find H.

3. 3(c - 4a) c

c rs

4. 3. If p= 2 and r = 4, s=12 and q=4 find p.

d q

ab (Answers: 60, 1 , 3)

5. 2

d −a

(Answers: 10, -130, -120, - 1 , 2)

5

C. Leech, Coventry University, June 2000. 2