#### Solved Examples and Worksheet for Problems on Multiplication and Division Involving Unknown Quantities

Q1Identify a situation that represents the equation.
7 × n = 84

A. Carol had n candies. She divided equally among 7 children. Each child got 84 candies.
B. James has n CDs and each of his CDs has 7 songs. The total number of songs in his collection is 84.
C. Smith purchased n lb of carrot and 7 lb of onions. Weight of both the vegetables is 84 lb.
D. Steve had 7 pencils and his friend had n pencils. Number of pencils both had is 84.

Step: 1
Steve had 7 pencils and his friend had n pencils. Number of pencils both had is 84 represents the equation "7 + n = 84".
Step: 2
James has n CDs and each of his CDs has 7 songs. The total number of songs in his collection is 84 represents the equation "7 × n = 84".
Step: 3
Smith purchased n lb of carrot and 7 lb of onions. Weight of both the vegetables is 84 lb represents the equation "n + 7 = 84".
Step: 4
Carol had n candies. She divided equally among 7 children. Each child got 84 candies represents the equation "n ÷ 7 = 84".
Step: 5
So, amongst the choices, the situation "James has n CDs and each of his CDs has 7 songs. The total number of songs in his collection is 84." represents correctly the given equation.
Correct Answer is :   James has n CDs and each of his CDs has 7 songs. The total number of songs in his collection is 84.
Q2Bryan had 20 pencils and he placed an equal number of pencils in 5 boxes. Which number sentence helps you find the number of pencils (n) he put in each box?
A. 5 + n = 20
B. n = 20 × 5
C. n = 20 + 5
D. n = 20 ÷ 5

Step: 1
Total number of pencils = number of pencils in each box × number of boxes
Step: 2
20 = n × 5
Step: 3
n = 20 ÷ 5.
Correct Answer is :   n = 20 ÷ 5
Q3Christina distributed 6 chocolates equally among 6 children. Which number sentence helps you find the number of chocolates each child would get?

A. n = 6 - 6
B. n = 6 + 6
C. n = 6 ÷ 6
D. n = 6 × 6

Step: 1
Let n be the number of chocolates that each child would get.
Step: 2
The number of chocolates that each child would get = total number of chocolates ÷ total number of children
[Christina distributed 6 chocolates equally among 6 children.]
Step: 3
n = 6 ÷ 6
[Substitute the values.]
Step: 4
So, n = 6 ÷ 6 is the number sentence that helps me find the number chocolates each child would get.
Correct Answer is :   n = 6 ÷ 6
Q4Andy had 21 marbles. He distributed the marbles equally among 3 friends. Which equation helps you find the number of marbles each friend has?
A. 21 + 3 =
B. 21 × 3 =
C. 21 - 3 =
D. 21 ÷ 3 =

Step: 1
Number of marbles Andy has = 21.
Step: 2
Number of friends he has = 3.
Step: 3
He distributed the marbles equally among 3 friends.
Step: 4
Then the number of marbles each friend would has = 21 ÷ 3
Step: 5
Amongst the given number sentences, '21 ÷ 3 =    ' represents correctly the given situation.
Correct Answer is :   21 ÷ 3 =
Q5William had 30 toys. He distributed them equally among 3 friends. Which number sentence helps you to find the number of toys each friend got?
A. 30 - 3 = 27
B. 30 ÷ 3 = 10
C. 30 × 3 = 90
D. 30 + 3 = 33

Step: 1
Number of toys William had = 30.
Step: 2
Number of friends = 3.
Step: 3
If William distribute the toys equally among them, then the numbe of toys each friend would get = number of toys ÷ number of friends
Step: 4
= 30 ÷ 3
Step: 5
= 10
Step: 6
So, from the given choices, the number sentence '30 ÷ 3 = 10' correctly represents the given situation.
Correct Answer is :   30 ÷ 3 = 10
Q6Henry distributed $40 equally among his 5 sons. Which equation helps you find the number of dollars each son got? A. - 5 =$35
B. 40 × 5 =
C. 40 ÷ 5 =
D. 40 +     = $45 Step: 1 Amount of money Henry has =$40.
Step: 2
Number of sons he has = 5.
Step: 3
He distributed the amount equally among 5 sons.
Step: 4
Then the amount of money each friend would get = 40 ÷ 5
Step: 5
Amongst the given number sentences, '40 ÷ 5 =    ' represents correctly the given situation.
Correct Answer is :   40 ÷ 5 =
Q7Bryan had 40 pencils and he placed an equal number of pencils in 8 boxes. Which number sentence helps you find the number of pencils (n) he put in each box?

A. n = 40 ÷ 8
B. 8 + n = 40
C. n = 40 × 8
D. n = 40 + 8

Step: 1
Total number of pencils = number of pencils in each box × number of boxes
Step: 2
40 = n × 8
Step: 3
n = 40 ÷ 8.
Correct Answer is :   n = 40 ÷ 8
Q8Which of the expressions best represents the given statement?
'Cost of 4 shirts is $100' [Let$x denote the cost of 1 shirt.]

A. 4 + x = 115
B. 4 × 2x = 115
C. 5x = 115
D. 4x = 100

Step: 1
Cost of 4 shirts = Cost of one shirt × Number of shirts
= x × 4 = 100

Step: 2
Therefore, the expression that best suits the phrase 'Cost of 4 shirts is 100' is '4x = 100'.
Correct Answer is :   4x = 100
Q9Jim collected 4 stamps every day. Which number sentence helps you to find the number of stamps he would have collected in 12 days?
A. 12 ÷ 4 =
B.      - 4 = 4
C. 12 × 4 =
D. 12 +      = 20

Step: 1
Number of stamps Jim collected every day = 4.
Step: 2
Number of stamps Jim collected in 12 days = number of days × number of stamps Jim collected every day
Step: 3
So, from the choices, the number sentence '12 × 4 =    ' correctly represents the given situation.
Correct Answer is :   12 × 4 =
Q10Choose the algebraic expression for the statement.
The product of y and 3 is 63.

A. 3 + y = 63
B. 63 + 3 = y
C. 3y = 63
D. 63y = 3

Step: 1
The product of y and 3 is y × 3 = 3y
Step: 2
3y = 63
[The product of y and 3 is 63.]
Correct Answer is :   3y = 63
Q11Identify a situation that represents the equation.
x ÷ 7 = 50

A. Micheal purchased x lb of carrot and 7 lb of onions. Weight of both vegetables is 50 lb.
B. Carol has x candies. She divided equally among 8 children. Each child got 50 candies.
C. Mary has x chocolates. She divided them equally among 7 children. Each child got 50 chocolates.

Step: 1
Mary has x chocolates. She distributed them equally among 7 children. Each child got 50 chocolates, is represented by 'x ÷ 7 = 50'.
Step: 2
Micheal purchased x lb of carrot and 7 lb of onions. Weight of both vegetables is 50 lb, is represented by 'x + 7 = 50'.
Step: 3
Carol has x candies. She distributed equally among 8 children. Each child got 50 candies, is represented by 'x ÷ 8 = 50'.
Step: 4
So, the equation 'x ÷ 7 = 50' corresponds to the situation 'Mary has x chocolates. She distributed them equally among 7 children. Each child got 50 chocolates.'
Correct Answer is :   Mary has x chocolates. She divided them equally among 7 children. Each child got 50 chocolates.
Q12It takes 28 hours to paint 4 houses in a locality. Which number sentence gives the number of hours required to paint each house if it takes equal number of hours to paint each house?
A. 28 ÷ 4 =
B. 28 - 4 =
C. 28 + 4 =
D. 28 × 4 =

Step: 1
Separate 28 into 4 equal groups.
Step: 2
28 ÷ 4 gives the number of hours required to paint each house.
Step: 3
So, the number sentence that gives the number of hours required to paint each house is 28 ÷ 4 =    .
Correct Answer is :   28 ÷ 4 =
Q13Identify the situation for the following linear equation.
x4 = 20, given that x is the number of marbles shared equally among 4 pupils′

A. A number of marbles, x is shared equally among 20 pupils and each gets 4 marbles.
B. A number of marbles, x is shared equally among 2 pupils and each gets 20 marbles.
C. A number of marbles, x is shared equally among 4 pupils and each gets 10 marbles.
D. A number of marbles, x is shared equally among 4 pupils and each gets 20 marbles.

Step: 1
Number of marbles, x is shared equally among 4 pupils. Each pupil gets 20 marbles.
Correct Answer is :   A number of marbles, x is shared equally among 4 pupils and each gets 20 marbles.
Q14Marissa picked 55 flowers. She wants to put an equal number of flowers, m, in 5 vases. Which equation shows how many flowers are in each vase?

A. 55 - 5= m
B. 55 × 5= m
C. 55 ÷ 5= m
D. 55 + 5= m

Step: 1
Number of flowers Marissa has picked = 55.
Step: 2
Number of wases = 5.
Step: 3
But, Marissa wants to put an equal number of flowers, m, in 5 vases.
Step: 4
Number of flowers in each wase = 55 ÷ 5.
Step: 5
So, from the given choices, the equation '55 ÷ 5 = m' represents correctly the given situation.
Correct Answer is :   55 ÷ 5= m