ALGEBRAIC AND NUMERIC EXPRESSIONS

Expressions are mathematical statements. There are two types of expressions - ones that contain only numbers, and ones that contain both numbers and variables (unknown values). 

Solved Problems

Problems 1-5 : Calculate the value of the numerical expression.

Problem 1 :

12.45 + 4.76

Solution :

= 12.45 + 4.76

= 17.21

Problem 2 :

3 ⋅ 3.75

Solution :

= 3 ⋅ 3.75

= 11.25

Problem 3 :

6.25 ÷ 0.25

Solution :

= 6.25 ÷ 0.25

= 25

Problem 4 :

2 ⋅ 1.25 + 5

Solution :

= 2 ⋅ 1.25 + 5

Use PEMDAS Rule.

= 2.5 + 5

= 7.5

Problem 5 :

3 ⋅ 5 - 10 ÷ 2

Solution :

= 3 ⋅ 5 - 10 ÷ 2

Use PEMDAS Rule.

= 15 - 10 ÷ 2

= 15 - 5

= 10

Problem 6 :

The length of a desk is x inches. How long is this in centimeters?

Solution :

1 in. = 2.54 cm.

To convert inches to centimeters, you have to multiply the given inches by 2.54.

x in. = 2.54 ⋅ x cm.

x in. = 2.54 cm.

Note :

2.54x is called an algebraic expression, as it contains an unknown quantity. The variable x represents the unknown quantity - the number of inches to be converted to centimeters. An algebraic expression always contains at least one variable (and very often it contains numbers as well).

Problem 7 :

The cost of an item is $3.25 plus sales tax of $1.30 per item. If you buy x number of items, write an algebraic expression which represents the total cost.

Solution :

= 3.25x + 1.30x

= 4.55x

Problem 8 :

A cab service costs a fixed charge of $5 and $2 per mile. If you travel x miles, write an algebraic expression which represents the total cost.

Solution :

= 5 + 2x

Problem 9 :

Three more than 4 times of a number. If the number is y, write an algebraic expression which represents the above situation.

Solution :

= 4x + 3

Problem 10 :

Five less than 7 times of a number. If the number is y, write an algebraic expression which represents the above situation.

Solution :

= 7y - 5

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