WRITING AND EVALUATING EXPRESSIONS
In this section, you will learn how to write a mathematical expression from a verbal description and evaluate expressions for the given values of the variables or unknowns.
Writing Expression from a Verbal Phrase
Let us see, how to write a verbal phrase as an expression.
If there is any unknown value in the given verbal phrase, replace it by some English alphabet.
Example 1
Example 2
Example 3
Writing Expressions - Practice Questions
Question 1 :
Write the given verbal phrase into mathematical expression
"The sum of 5 times a number and 8"
Answer :
5x + 8
Question 2 :
Write the given verbal phrase into mathematical expression
"2 times the sum of 7 times a number and 4"
Answer :
2(7x + 4)
Question 3 :
Write the given verbal phrase into mathematical expression
"7 less than 4 times a number"
Answer :
4x - 7
Question 4 :
Write the given verbal phrase into mathematical expression
"One fifth of sum of 3 times a number and 9"
Answer :
(3x + 9) / 5
Question 5 :
Write the given verbal phrase into mathematical expression
"One seventh of 3 less than 4 times a number"
Answer :
(4x - 3) / 7
Question 6 :
Write the given verbal phrase into mathematical expression
"5 times of a number is decreased by 8"
Answer :
5x - 8
Question 7 :
Write the given verbal phrase into mathematical expression
"6 times of a number is increased by 15"
Answer :
6x + 15
Question 8 :
Write the given verbal phrase into mathematical expression
"7 less than 3 times the sum of a number and 6"
Answer :
3(x + 6) - 7
Question 9 :
Write the given verbal phrase into mathematical expression
"3 times the difference between a number and 8"
Answer :
3(x - 8)
Question 10 :
Write the given verbal phrase into mathematical expression
"One fourth of 3 times the difference between a number and 6"
Answer :
3(x - 6) / 4
Evaluating Expressions - Practice Questions
Question 1 :
Evaluate the given expression for x = 3 and y = 5.
3x + 2y
Answer :
Substitute 3 for x and 5 for y into the given expression.
3x + 2y = 3(3) + 2(5)
3x + 2y = 9 + 10
3x + 2y = 19
Question 2 :
Evaluate the given expression for m = 5 and n = 2.
m2 + 2mn2
Answer :
Substitute 5 for m and 2 for n into the given expression.
m2 + 2mn2 = 52 + 2(5)(2)2
m2 + 2mn2 = 25 + 40
m2 + 2mn2 = 65
Question 3 :
Evaluate the given expression for s = 5.
s2 + 7s - 2
Answer :
Substitute 5 for s into the given expression.
s2 + 7s - 2 = 52 + 7(5) - 2
s2 + 7s - 2 = 25 + 35 - 2
s2 + 7s - 2 = 58
Question 4 :
Evaluate the given expression for m = 1/3.
18m2 + 3m + 7
Answer :
Substitute 1/3 for m into the given expression.
18m2 + 3m + 7 = 18(1/3)2 + 3(1/3) + 7
18m2 + 3m + 7 = 2 + 1 + 7
18m2 + 3m + 7 = 10
Question 5 :
Evaluate the given expression for m = 13.
m2 + m - 54
Answer :
Substitute 13 for s into the given expression.
m2 + m - 54 = 132 + 13 -54
m2 + m - 54 = 169 + 13 - 54
m2 + m - 54 = 128
Question 6 :
Evaluate the given expression for x = 3 and y = 5.
x2 + y2
Answer :
Substitute 3 for x and 5 for y into the given expression.
x2 + y2 = 32 + 52
x2 + y2 = 9 + 25
x2 + y2 = 34
Question 7 :
Evaluate the given expression for m = 5 and n = 2.
5m2 + 2m2n
Answer :
Substitute 5 for m and 2 for n into the given expression.
5m2 + 2m2n = 5(5)2 + 2(5)2(2)
5m2 + 2m2n = 5(25) + 2(25)(2)
5m2 + 2m2n = 125 + 100
5m2 + 2m2n = 225
Question 8 :
Evaluate the given expression for s = 6.
s2 - 3s + 10
Answer :
Substitute 6 for s into the given expression.
s2 - 3s + 10 = 62 - 3(6) + 10
s2 - 3s + 10 = 36 - 18 + 10
s2 - 3s + 10 = 28
Question 9 :
Evaluate the given expression for x = 2 and y = -5.
x2 - 3y2
Answer :
Substitute 2 for x and -5 for y into the given expression.
x2 - 3y2 = 2(2)2 - 3(-5)2
x2 - 3y2 = 2(4) - 3(25)
x2 - 3y2 = 8 - 75
x2 - 3y2 = -77
Question 10 :
Evaluate the given expression for m = 3.
(2m2 + 5m - 7) / 2
Answer :
Substitute 3 for m into the given expression.
(2m2 + 5m - 7) / 2 = [2(3)2 + 5(3) - 7] / 2
(2m2 + 5m - 7) / 2 = [2(9) + 15 - 7 ] / 2
(2m2 + 5m - 7) / 2 = (18 + 15 - 7) / 2
(2m2 + 5m - 7) / 2 = 26 / 2
(2m2 + 5m - 7) / 2 = 13
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Using Reference Angles to Find Trig Values Worksheet
Apr 21, 21 10:43 PM
Using Reference Angles to Evaluate Trigonometric Functions Worksheet
-
Evaluating Trigonometric Functions for Any Angle
Apr 21, 21 10:29 PM
Evaluating Trigonometric Functions for Any Angle - Concept - Examples
-
How to Find the Roots of a Polynomial of Degree 4
Apr 21, 21 03:35 AM
How to Find the Roots of a Polynomial of Degree 4
