#### Solved Examples and Worksheet for Understanding and Writing Algebraic Expressions

Q1What type of expression is 37 - 4x+ 5?

A. Numerical expression
B. Variable expression
C. None of the above

Step: 1
A variable expression is a group of numbers, variables and operations.
Step: 2
The expression 37 - 4x+ 5 has numerals, operation symbols and a variable.
Step: 3
It is a variable expression.
Correct Answer is :   Variable expression
Q2Which of the following is the coefficient in the expression 3x - 5?
A. 5
B. x
C. 3
D. None of the above

Step: 1
A co-efficient is the multiple of a variable.
Step: 2
In the expression, there is only one variable, x.
Step: 3
The co-efficient of x in the expression is 3.
Q3Which of the following is equivalent to sum of n and 6?
A. n ÷ 6
B. n + 6
C. n × 6
D. n - 6

Step: 1
The given expression is " Sum of n and 6".
Step: 2
Amongest the choices, the equivalent expression to "sum of n and 6 is n + 6.
Correct Answer is :   n + 6
Q4Choose the mathematical expression for the verbal description.
thrice as long as h

A. 3h
B. h3
C. h + 3
D. 3h

Step: 1
Amongest the choices equivalent expression to "thrice as long as h" is 3h.
Q5How many marbles are there in 10 rows, if each row has m marbles?
A. 10 + m
B. 10 × m
C. 10 ÷ m
D. 10 - m

Step: 1
Number of marbles in 10 rows = number of marbles in each row × number of rows
[Write an algebraic expression.]
Step: 2
= m × 10.
[Substitute the values.]
Step: 3
So, there are 10 × m marbles in 10 rows.
Correct Answer is :   10 × m
Q6How many bags of chips would each child get if 12 children share n bags of chips?
A. n × 12
B. n + 12
C. n ÷ 12
D. n - 12

Step: 1
Number of bags of chips each child gets = total number of bags of chips ÷ number of children
[Write an algebraic expression.]
Step: 2
= n ÷ 12
[Substitute the values.]
Step: 3
So, each child gets n ÷ 12 number of bags of chips.
Correct Answer is :   n ÷ 12
Q7Eric sells 55 milk cartons per day. He has sold 15 cartons. Write a number sentence to calculate the number of cartons still left to be sold.

A. 55 × n = 15
B. 15 + n = 55
C. 15 - n = 55
D. 15 × 55 = n

Step: 1
Let n be the number of milk cartons still left to be sold.
Step: 2
The number sentence can be given as, (Number of milk cartons already sold) + n = Number of milk cartons that Eric sells per day.
Step: 3
15 + n = 55
[Substitute the values.]
Step: 4
So, the number sentence used to calculate the number of milk cartons left to be sold is, 15 + n = 55.
Correct Answer is :   15 + n = 55
Q8Mark wants to buy a pencil and a calculator that costs $20. He has only$17. Identify the number sentence to calculate how much more money is required to buy them.

A. $20 +$17 = n
B. n + $20 =$17
C. $17 + n =$20
D. None of the above

Step: 1
Let n be the money required more to buy the pencil and the calculator.
Step: 2
The number sentence can be given as, (Money that Mark has) + n = Cost of a pencil and a calculator.
Step: 3
$17 + n =$20
[Substitute the values.]
Step: 4
So, the number sentence used to calculate the money required more to buy them is, $17 + n =$20.
Correct Answer is :   $17 + n =$20
Q9David makes $165 a week. He spent$54. Identify the number sentence to calculate the money left with David.

A. $165+ n =$54
B. n + $54 =$165
C. $165n =$54
D. $54$165 = n

Step: 1
Let n be the money left with David.
Step: 2
n + (Money spent) = (Money David makes in a week).
Step: 3
n + $54 =$165
[Substitute the values.]
Step: 4
So, the number sentence used to calculate the money left with David is, n + $54 =$165.
Correct Answer is :   n + $54 =$165
Q10There are 8 pieces of candy in a bag. 4 pieces are eaten. Identify the number sentence used to calculate the number of candies left in the bag.
A. 4 + 4 = n
B. 1 - n = 0
C. 8 + 1 = n
D. 8 = n + 4

Step: 1
Let n be the number of candies left in the bag.
Step: 2
The number sentence can be written as, (Number of candies in the bag) = n + (Number of candies eaten).
Step: 3
8 = n + 4
[Substitute the values.]
Step: 4
So, the number sentence used to calculate the number of candies left in the bag is, 8 = n + 4.
Correct Answer is :   8 = n + 4
Q11Identify the constant term in the polynomial - 12x3 + 7x2 + 5x - 17.

A. - 17
B. - 41
C. - 12
D. 17

Step: 1
- 12x3 + 7x2 + 5x - 17
[Original expression.]
Step: 2
A constant term is said to be the one which has no variables in it.
Step: 3
Therefore, - 17 is the constant term in the polynomial - 12x3 + 7x2 + 5x - 17.
Correct Answer is :   - 17
Q12Identify the constant term in the polynomial - 2x3 + 7x2 + 5x + 17.

A. - 12
B. - 41
C. 17
D. - 17

Step: 1
In an expression, for a term which has no literal factors is known as a constant term.
Step: 2
In - 2x3 + 7x2 + 5x + 17. the term 17 does not have any literal factors.
Step: 3
So, in the given polynomial 17 is a constant term.
Q13Determine the number of terms in the algebraic expression 4pq + 2p - 3pq2.
A. 4
B. 2
C. 3
D. 5

Step: 1
Each term in an algebraic expression are separated by plus (+) or minus (-) symbol.
Step: 2
So, there are 3 terms in the algebraic expression 4pq + 2p - 3pq2.
Q14Which of the following represent variable expression ?

A. 8 × 5
B. 3 + 2(2)
C. 10(4)
D. 6 - 2a

Step: 1
A variable expression is an expression that has numerals, operation symbols and variables.
Step: 2
Amongst the choices "6 - 2a" has numerals, operation symbols and variables .
Correct Answer is :   6 - 2a
Q15The like terms in the following algebraic terms - 5.7x2y, - 5.7xy2, 7.5xy and - 7.5x2y are ____________
A. 7.5xy and - 7.5x2y
B. - 5.7xy2 and 7.5xy
C. - 5.7x2y and - 7.5x2y
D. - 5.7x2y and - 5.7xy2

Step: 1
The terms which have the same algebraic factors are called like terms.
Step: 2
The factors of - 5.7x2y are - 5.7, x2 and y.
Step: 3
The factors of - 5.7xy2 are - 5.7, x and y2.
Step: 4
The factors of 7.5xy are 7.5, x and y.
Step: 5
The factors of - 7.5x2y are - 7.5, x2 and y.
Step: 6
Therefore - 5.7x2y and - 7.5x2y have same algebraic factors.
Step: 7
Hence - 5.7x2y and - 7.5x2y are like terms.
Correct Answer is :   - 5.7x2y and - 7.5x2y
• Variable