EXPRESSIONS AND EQUATIONS WORKSHEETS

About "Expressions and equations worksheets"

Expressions and equations worksheets : 

Worksheet on expressions and equations is much useful to the students who would like to practice solving  real world problems using expressions and equations. 

Expressions and equations worksheets - Problems

Write each verbal phrase as mathematical expression :

1.  The sum of 7 and 3 times of a number. 

2.  Three less than four times of a number.

3.  One fourth of 3 times of a number. 

4.  One fifth of sum of 3 times a number and 9

5.  7 less than 3 times the sum of a number and 6

Evaluating expressions : 

6.  Evaluate the given expression for x = 3  and y = 5. 

3x + 2y

7.  Evaluate the given expression for m = 5  and n = 2. 

m² + 2mn²

8.  Evaluate the given expression for s = 5. 

s² + 7s - 2

9.  Evaluate the given expression for m = 1/3. 

18m² + 3m + 7

10.  Evaluate the given expression for m = 13. 

m² + m - 54

Word problems :

11.  The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool ? 

12.  Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

13.  Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers ?

14.  Three consecutive integers add up to 51. What are these integers ?

15.  The sum of three consecutive multiples of 8 is 888. Find the multiples.

Expressions and equations worksheets - Solution

Question 1 :

Write the given verbal phrase as mathematical expression

"The sum of 7 and 3 times of a number"

Answer :

Question 2 :

Write the given verbal phrase as mathematical expression

"Three less than four times of a number"

Answer :

Question 3 :

Write the given verbal phrase as mathematical expression

"One fourth of 3 times of a number"

Answer :

Question 4 :

Write the given verbal phrase as mathematical expression

"One fifth of sum of 3 times a number and 9"

Answer :

( 3x + 9 ) / 5

Question 5 :

Write the given verbal phrase as mathematical expression

"7 less than 3 times the sum of a number and 6"

Answer :

3(x + 6) - 7

Question 6 :

Evaluate the given expression for x = 3  and y = 5. 

3x + 2y

Answer :

Plug x = 3 and y = 5 in the given expression

3(3) + 2(5)  =  9 + 10  =  19

Hence, the answer is 19

Question 7 :

Evaluate the given expression for m = 5  and n = 2. 

m² + 2mn²

Answer :

Plug m = 5 and n = 2 in the given expression

5² + 2(5)(2)²  =  25 + 40  =  65

Hence, the answer is 65

Question 8 :

Evaluate the given expression for s = 5. 

s² + 7s - 2

Answer :

Plug s = 5 in the given expression

5² + 7(5) - 2  =  25 + 35 - 2  =  58

Hence, the answer is 58

Question 9 :

Evaluate the given expression for m = 1/3. 

18m² + 3m + 7

Answer :

Plug m = 1/3 in the given expression

18(1/3)² + 3(1/3) + 7  =  2 + 1 + 7  =  10

Hence, the answer is 10.

Question 10 :

Evaluate the given expression for m = 13. 

m² + m - 54

Answer :

Plug m = 13 in the given expression

13² + 13 -54  =  169 + 13 - 54  =  128

Hence, the answer is 128

Question 11 :

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool ? 

Answer :

Let the breadth be x m.

The length will be (2x + 2) m.

Perimeter of swimming pool = 2(l + b) = 154 m

2(2x + 2 + x) = 154

2(3x + 2) = 154

Dividing both sides by 2,

3x + 2 = 77

Subtracting 2 on both sides, we get

3x + 2 - 2 = 77 - 2

3x = 75

On dividing 3 on both sides

 x = 25

2x + 2 = 2 × 25 + 2 = 52

Hence, the breadth and length of the pool are 25 m and 52 m respectively.  

Question 12 :

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Solution :

Let one number be x.

Therefore, the other number will be x+ 15.

According to the question,

x + x + 15 = 95

2x + 15 = 95

Subtract 15 on both sides

2x = 95 - 15

2x = 80

Divide by 2 on both sides

x = 40

x + 15 = 40 + 15 = 55

Hence, the numbers are 40 and 55.

Question 13 :

Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

Solution :

Let the common ratio between these numbers be x. Therefore, the numbers will be 5x and 3x respectively.

Difference between these numbers = 18

5x - 3x= 18

2x= 18

Divide by 2 on both sides

x = 9

First number = 5x= 5 × 9 = 45

Second number = 3x= 3 × 9 = 27

Hence the required numbers are 27, 45.

Question 14 :

Three consecutive integers add up to 51. What are these integers?

Solution :

Let three consecutive integers be x, x + 1, and x+ 2.

Sum of these numbers = x + x + 1 + x + 2 = 51

3x+ 3 = 51

Subtract by 3 on both sides

3x = 51 - 3

3x = 48

Divide by 3 on both sides

x = 16

x + 1 = 17

x + 2 = 18

Hence, the consecutive integers are 16, 17, and 18. 

Question 15 :

The sum of three consecutive multiples of 8 is 888. Find the multiples.

Solution :

Let the three consecutive multiples of 8 be 8x, 8(x + 1), 8(x + 2).

Sum of these numbers = 8x + 8(x+ 1) + 8(x+ 2) = 888

8(x + x + 1 +x + 2) = 888

8 (3x + 3) = 888

Dividing by 8 both sides 

3x+ 3 = 111

Subtract 3 on both sides

3x + 3 - 3 = 111 - 3

3x= 108

Divide by 3 on both sides 

x = 36

First multiple = 8x = 8 × 36 = 288

Second multiple = 8(x + 1) = 8 × (36 + 1) = 8 × 37 = 296

Third multiple = 8(x + 2) = 8 × (36 + 2) = 8 × 38 = 304

Hence, the required numbers are 288, 296, and 304.

We hope that the students would have understood the stuff given on "Expressions and equations worksheets"

Apart from the stuff given on "Expressions and equations worksheets", if you want to know more about "Expressions and equations worksheets", please click here.

For your doubts and clarifications on "Expressions and equations worksheets", please mail us : v4formath@gmail.com

Apart from "Expressions and equations worksheets", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6