WRITING DIVISION EXPRESSIONS

The picture given below illustrates, how to write division expression for the given verbal phrase.  

Write division expression for each of the following verbal phrase :

Example 1 :

One fifth of sum of three times a number and 9

Answer :

Let x be the number.

Three times the number :

= 3x

Sum of three times the number and 9 :

= 3x + 9

One fifth of sum of three times the number and 9 :

= (1/5) of (3x + 9)

= (1/5) ⋅ (3x + 9)

= (3x + 9) / 5

Example 2 :

One seventh of 3 less than four times a number

Answer :

Let x be the number.

Four times the number :

= 4x

3 less than four times the number :

= 4x - 3

One seventh of 3 less than four times the number :

= (1/7) of (4x - 3)

= (1/7) ⋅ (4x - 3)

= (4x - 3)/7

Example 3 :

One fourth of three times the difference between a number and 6

Answer :

Let x be the number.

Difference between the number and 6 :

= x - 6

Three times the difference between the number and 6 :

= 3(x - 6)

One fourth of three times the difference between the number and 6 :

= (1/4) ⋅ 3(x - 6)

= (1/4) ⋅ (3x - 18)

= (3x - 18)/4

Example 4 :

Sum of five times a number and 3 is divided by 4

Answer :

Let x be the number.

Five times the number :

= 5x

Sum of five times the number and 3 :

= 5x + 3

Sum of five times the number and 3 is divided by 4 :

(5x + 3) / 4

Example 5 :

9 less than seven times a number is divided by 5

Answer :

Let x be the number.

Seven times the number :

= 7x

9 less than seven times the number

= 7x - 9

9 less than seven times the number is divided by 5 :

= (7x - 9)/5

Example 6 :

Jacob get x dollars salary and $500 incentive. He divides the total money to three of his friends evenly. Find the share of each friend.

Answer :

Total money received by Jacob :

= x + 500

He divides the total money to three of his friends evenly. 

Then, the share of each person is

= (x + 500)/3

Example 7 :

This year, David gets three times the profit of last year plus $2500 in his business. He divides the total profit of this year to his five children evenly. Find the share of each child. 

Answer :

Let x be the profit in the last year.

Total profit of this year :

= 3x + 2500

He divides the total profit to his 5 children evenly.

Then, the share of each child is

(3x + 2500) / 5

Example 8 :

Five friends share the cost of a dinner equally.

a. Write an expression for the cost per person.

b. Make up a total cost and test your expression. Is the result reasonable?

Answer :

Number of friends = 5

Cost of dinner = x

a) Cost per person = x/5

b) Let 250 is the total cost, dividing 250 by 5, we get 50.

Applying this in 5x, we get 5(50) which is 250.

Example 8 :

A television show has 19 episodes per season,.

a) Copy and complete the table

b)  Write an expression for the number of episodes in n seasons.

Answer :

a) Copy and complete the table

b)  Write an expression for the number of episodes in n seasons.

a) Number of episodes per season = 19

Let n be the number of seasons.

Number of episodes = 19n

When n = 1

Number of episodes in 1^st season = 19(1)

= 19

When n = 2

Number of episodes in 2 seasons = 19(2)

= 38

Number of episodes in 3 seasons = 19(3)

= 57

Number of episodes in 4 seasons = 19(4)

= 76

Number of episodes in 5 seasons = 19(5)

= 95

b) number of episodes in each season = 19n

Example 9 :

Write the phrase as an expression. Then evaluate when x = 5 and y = 20.

a)  3 less than the quotient of a number y and 4

b)  the sum of a number x and 4 all divided by 3.

c)  6 more than the product of 8 and a number x

d) the quotient of 40 and the difference of a number y and 16

Answer :

a)  3 less than the quotient of a number y and 4

= (y/4) - 3

Now applying the value of y as 20

= (20/4) - 3

= 5 - 3

= 2

b)  the sum of a number x and 4 all divided by 3.

= (x + 4)/3

applying the value of x as 5, we get

= (5 + 4)/3

= 9/3

= 3

c)  6 more than the product of 8 and a number x

= 8x + 6

applying x = 5

= 8(5) + 6

= 40 + 6

= 46

d) the quotient of 40 and the difference of a number y and 16

= 40 / (y - 16)

Applying y = 20

= 40/(20 - 16)

= 40/4

= 10

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