WRITING ALGEBRAIC EXPRESSIONS WORKSHEET

Write algebraic expression for the given verbal phrase.

1) The sum of 7 and x.

2) The quotient of z and 3.

3) The product of 11 and x.

4) y less than 8.

5) The sum of 5 times a number and 8.

6) 7 less than 4 times a number.

7) One fifth of sum of 3 times a number and 9.

8) 5 times of a number is decreased by 8.

9) One seventh of 3 less than 4 times a number.

10) One fourth of 3 times the difference between a number and 6.

11) 7 less than 4 times the sum of x and y.

12) 4 times x less than sum of y and 6.

13) 18 is taken away from 8 times of a number.

14) The denominator of a fraction exceeds the numerator by 5.

15) If thrice of A's age 6 years ago be subtracted from twice his present age.

16) Alan is y years old and has 8 sisters. Write an expression for how old each sister is.

(a) Beth is 3 years old than Alan.

(b) Clara is 2 years younger than Alan.

(c) Donna is three times Alan’s age.

(d) Emma is half Alan’s age.

(e) Fiona is two years younger than Donna.

(f) Georgia is twice Beth’s age.

(g) Hannah is 4 years older than Fiona.

(h) Isabelle is three times Clara’s age.

17)  Guy, Eric and Luke go Christmas shopping. Write an expression for how much money each man has left after shopping.

(a) Guy had £20 and spends £y on presents.

(b) Eric had £m and spends £12 on presents.

(c) Luke had £a and spends £b on presents.

18)  TV costs £x. A DVD player costs £45 less than the TV. Write an expression for the total cost of the TV and DVD player.

19) A plumber charges £15 per hour plus a £y initial callout charge. Write an expression for the total cost of:

(a) A job lasting 3 hours

(b) A job lasting 8 hours

(c) A job lasting n hours

20)  Write an expression for the perimeter of each shape below.

1. Answer :

The sum of 7 and x :

7 + x

2. Answer :

The quotient of z and 3 :

z/3

3. Answer :

The product of 11 and x :

11x

4. Answer :

y less than 8 :

8 - y

5. Answer :

The sum of 5 times a number and 8.

Let 'x' be the number.

5x + 8

6. Answer :

7 less than 4 times a number :

Let 'x' be the number.

4x - 7

7. Answer :

One fifth of sum of 3 times a number and 9.

Let 'x' be the number.

(3x + 9)/5

8. Answer :

5 times of a number is decreased by 8.

Let 'x' be the number.

5x - 8

9. Answer :

One seventh of 3 less than 4 times a number.

Let 'x' be the number.

(4x - 3)/7

10. Answer :

One fourth of 3 times the difference between a number and 6.

Let 'x' be the number.

3(x - 6)/4

11. Answer :

7 less than 4 times the sum of x and y :

4(x + y) - 7

12. Answer :

4 times x less than sum of y and 6 :

(y + 6) - 4x

13. Answer :

18 is taken away from 8 times of a number.

Let x be the number.

8x -18

14. Answer :

The denominator of a fraction exceeds the numerator by 5.

Let x be the numerator.

x/(x + 5)

15. Answer :

If thrice of A's age 6 years ago be subtracted from twice his present age.

Let x be the present age of A.

Then, A's age 6 years ago = x - 6.

2x - 3(x - 6)

16. Answer :

Alan is y years old and has 8 sisters. Write an expression for how old each sister is.

(a) Beth is 3 years old than Alan.

• Alan's age = y
• Beth's age = y + 3

(b) Clara is 2 years younger than Alan.

• Alan's age = y
• Clara's age = y - 2

(c) Donna is three times Alan’s age.

• Alan's age = y
• Donna's age = 3y

(d) Emma is half Alan’s age.

• Alan's age = y
• Emma's age = y/2

(e) Fiona is two years younger than Donna.

• Donna's age = 3y
• Fiona's age = 3y - 2

(f) Georgia is twice Beth’s age.

• Beth's age = y + 3
• Georgia's age = 2(y + 3)

(g) Hannah is 4 years older than Fiona.

• Fiona's age = 3y - 2
• Hanna's age = 3y - 2 + 4
• = 3y + 2

(h) Isabelle is three times Clara’s age.

• Clara's age = y - 2
• ISabelle's age = 3(y - 2)

17. Answer :

Guy, Eric and Luke go Christmas shopping. Write an expression for how much money each man has left after shopping.

(a) Guy had £20 and spends £y on presents.

Amount he has = 20

amount he spends = y

Amount he left after shopping = 20 - y

(b) Eric had £m and spends £12 on presents.

Amount Eric has = m

Amount he spends = 12

Amount he left = m - 12

(c) Luke had £a and spends £b on presents.

amount Luke had = a

Amount he spens = b

Amount he has as left over = a - b

18. Answer :

Cost of TV = £x

Cost of a DVD player = £45 less than the TV

= x - 45

Total cost of TV and DVD player = x + x - 45

2x - 45

So, the required total cost is 2x - 45.

19. Answer :

initial callout charge = £y

Charge per hour = £15

(a) Number of hour = 3 hours

Required amount = 3(15) + y

= 45 + y

(b) A job lasting 8 hours

Required amount = 8(15) + y

= 120 + y

(c) A job lasting n hours

Required amount = n(15) + y

= 15n + y

20. Answer :

Perimeter of square which has the side length m.

Perimeter = m + m + m + m 

= 4m

Perimeter of rectangle which has the length as d and width as c.

Perimeter of rectangle = 2(length + width)

= 2(d + c)

Perimeter of isosceles triangle = f +f + g

= 2f + g

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