WRITING AND EVALUATING EXPRESSIONS
About "Writing and Evaluating Expressions"
Writing and Evaluating Expressions :
In this section, we will learn, how to write a mathematical expression from a verbal description and evaluating expressions for the given values of the variables or unknowns.
Writing Expression from a Verbal Phrase
Let us see, how to write verbal phrase into expressions.
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 :
Plug x = 3 and y = 5 in the given expression
= 3(3) + 2(5)
= 9 + 10
= 19
Hence, the answer is 19.
Question 2 :
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 3 :
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 4 :
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 5 :
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 6 :
Evaluate the given expression for x = 3 and y = 5.
x² + y²
Answer :
Plug x = 3 and y = 5 in the given expression
= 3² + 5²
= 9 + 25
= 34
Hence, the answer is 34.
Question 7 :
Evaluate the given expression for m = 5 and n = 2.
5m² + 2m²n
Answer :
Plug m = 5 and n = 2 in the given expression
= 5(5)² + 2(5)²(2)
= 125 + 100
= 225
Hence, the answer is 225.
Question 8 :
Evaluate the given expression for s = 6.
s² -3s + 10
Answer :
Plug s = 6 in the given expression
= 6² - 3(6) + 10
= 36 - 18 + 10
= 28
Hence, the answer is 28.
Question 9 :
Evaluate the given expression for x = 2 and y = -5.
x² - 3y²
Answer :
Plug x = 2 and y = -5 in the given expression
= 2² + 3(-5)²
= 4 + 75
= 79
Hence, the answer is 79.
Question 10 :
Evaluate the given expression for m = 3.
(2m² + 5m - 7) / 2
Answer :
Plug m = 3 in the given expression
= [2(3)² + 5(3) - 7] / 2
= [18 + 15 - 7 ] / 2
= 26 / 2
= 13
Hence, the answer is 13.
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WORD PROBLEMS
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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
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Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
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Pythagorean theorem word problems
Percent of a number word problems
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Word problems on average speed
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OTHER TOPICS
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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
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
