Writing Algebraic Equations From Word Problems Worksheet

WRITING ALGEBRAIC EXPRESSIONS FROM WORD PROBLEMS WORKSHEET

The following table will help you to learn some of the words (phrases) that can be used to indicate mathematical operations :

Addition

The sum of
increased by
plus
added to
more than

Multiplication

the product of
multiplied by
times

Subtraction

the difference of
decreased by
minus
subtracted from
less than

Division

the quotient of
divided by
the ratio of

Question 1 :

Write the algebraic expressions for the following :

Sum of x and twice y

Question 2 :

Write the algebraic expressions for the following :

Subtraction of z from y

Question 3 :

Write the algebraic expressions for the following :

Twice the sum of m and n

Question 4 :

Write the algebraic expressions for the following :

b is decreased by twice a

Question 5 :

Write the algebraic expressions for the following :

Sum of x squared and y squared

Question 6 :

Write the algebraic expressions for the following :

Two times the product of a and b divided by 5

Question 7 :

Write the algebraic expressions for the following :

Product of p and q added to 7

Question 8 :

Write the algebraic expressions for the following :

x more than two-third of y

Question 9 :

Write the algebraic expressions for the following :

Half a number x decreased by 3

Question 10 :

Write the algebraic expressions for the following :

Sum of numbers m and n decreased by their product

Question 11 :

Write the algebraic expressions for the following :

4 times x less than sum of y and 6

Question 12 :

Write the algebraic expressions for the following :

Double the sum of one third of a and m

Detailed Answer Key

Question 1 :

Write the algebraic expressions for the following :

Sum of x and twice y

Solution :

Twice y = multiply 'y' be 2 -----> 2y

Sum of x and twice y :

x + 2y

Question 2 :

Write the algebraic expressions for the following :

Subtraction of z from y

Solution :

Subtraction of z from y :

y - z

Question 3 :

Write the algebraic expressions for the following :

Twice the sum of m and n

Solution :

Sum of m and n = m + n

Twice = multiply by 2

Twice the sum of m and n :

2(m + n)

Question 4 :

Write the algebraic expressions for the following :

b is decreased by twice a

Solution :

Twice a = multiply 'a' by 2 -----> 2a

b is decreased by twice a :

b - 2a

Question 5 :

Write the algebraic expressions for the following :

Sum of x squared and y squared

Solution :

Square of x = x²

Square of y = y²

Sum of x squared and y squared :

x² + y²

Question 6 :

Write the algebraic expressions for the following :

Two times the product of a and b divided by 5

Solution :

Two times the product of a and b = 2ab

Two times the product of a and b divided by 5 :

2ab / 5

Question 7 :

Write the algebraic expressions for the following :

Product of p and q added to 7

Solution :

Product of p and q = pq

Product of p and q added to 7 :

pq + 7

Question 8 :

Write the algebraic expressions for the following :

x more than two-thirds of y

Solution :

Two-thirds of y = (2/3)y

x more than two-thirds of y :

x + (2/3)y

Question 9 :

Write the algebraic expressions for the following :

Half a number x decreased by 3

Solution :

Half a number x = (1/2) x

Decreased by 3 = - 3

Half a number x decreased by 3 :

(x/2) - 3

Question 10 :

Write the algebraic expressions for the following :

Sum of numbers m and n decreased by their product

Solution :

Sum of numbers m and n = m + n

Decreased by their product = -mn

Sum of numbers m and n decreased by their product :

(m + n) - mn

Question 11 :

Write the algebraic expressions for the following :

4 times x less than sum of y and 6

Solution :

4 times x = 4x

Sum of y and 6 = y + 6

4 times x less than sum of y and 6 :

4x - (y + 6)

Question 12 :

Write the algebraic expressions for the following :

Double the sum of one third of a and m.

Solution :

One third of a and m = (1/3)a + m

Double = multiply by 2

Double the sum of one third of a and m :

2[ (1/3)a + m]

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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