Algebraic Expressions  Grade 6
Grade 6 examples and questions on algebraic expressions with detailed solutions and explanations are presented.

Which of the following is an algebraic expression?
 2x + 2
 x + 2 & 8
 x / 2 + 6  x
 5  3 # x
 (x + 3) / 2
  x / 8

What is the coefficient of the term in x in the following algebraic expressions?
 2x  7
 x/2  10
  x + 7
 x + 7
  x / 4

What is the value of 2x + 7 for the given values of x?
 x =  1
 x =  4
 x = 0
 x = 5

What is the value of the expression x / 3  9 for the given values of x?
 x = 0
 x = 3
 x = 9
 x =  12

What is the value of the expression ( x + 2) / 2 + 1 for the given values of x?
 x = 0
 x = 2
 x =  2
 x =  12

What is the value of the expression 12 x  3 for the given values of x?
 x = 1/2
 x = 1/6
 x =  3/4
 x =  1 / 4

What is the value of the expression  0.1 x + 2.5 for the given values of x?
 x = 1
 x =  1
 x = 2
 x =  2

Which of the following expressions has the largest value for x =  3?
 x + 10
  x + 10
 x / 3 + 10
  x / 3 + 10

Which of the following shows the commutativity property of the addition?
 a + b = b  a
 a + b = b a
 a + b = a / b
 a + b = b + a

Which of the following shows the associatitivity property of the addition?
 a + b = b + a
 (a + b) + c = c + (a + b)
 a + ( b + c ) = (a + b) + c
 a + ( b + c ) = (a + b)  c

Which of the following expressions is equivalent to the algebraic expression 3x + 2  x + 4?
 6
 4x + 6
 2x + 6

3x^{2} +6

Which of the following algebraic expression is a mathematical representation to the statement "2 times x plus 20".
 2 + x + 20
 2 x + 20
 2  x + 20
 2 ÷ x + 20

Which of the following algebraic expression is a mathematical representation to the statement "Three times x subtracted from 17".
 3x  17
 17  3x
 3x + 17
 17+3x

Jo has has x cards. Janette has 10 cards more that Jo. Write an algebraic expression that indicates how many cards Janette has.
 10 x
 x  10
 x + 10
 x / 10

Carla had 20 toy cars. She lost x toy cars lately. Write an algebraic expression that indicates how many toy cars Carla has now.
 10 x
 x  10
 x + 10
 x / 10

Chris had $200. He spent $20 on food and he bought a book at the price of a dollars. Write an algebraic expression that indicates how much money chris has left.
 200 + 20  a
 200  20  a
 20 + a  200
 200 + a + 20

Nathan had x cards and he gave half to Tanya and Tanya gave a third of her card to Salma. Write an algebraic expression that indicates the number of cards Tanya has.
Solutions to the Above Problems

Solution
Algebraic expressions contain real numbers, variables and one or many of the the 4 mathematics operators (+ ,  , × , ÷ or /). Hence the following are algebraic expressions:
2x + 2 , x / 2 + 6  x , (x + 3) / 2 ,  x / 8
Note: 2x means 2 × x
The following are not algebraic expressions.
x + 2 & 8 : it contains the character & which is not a number, neither a variable nor a mathematical operator.
5  3 # x : it contains the character # which is not a number, neither a variable nor a mathematical operator.

Solution
To find the coefficient of a term in x (or any other variable), isolate the term in x and write it as a multiplication and the real number involved in the multiplication is the coefficient of the term.
expression  term in x  write as a multiplication  find coefficient 
2x  7  2x  2×x  2 
x/2  10  x / 2  (1/2)×x  1 / 2 
 x + 7   x  (1)×x   1 
x + 7  x  (1)×x  1 
 x/4   x / 4  (1/4)×x   1 / 4 

Solution
To evaluate an algebraic expression for a given numerical value of x, substitute x in the expression by its numerical value and evaluate the expression.
expression  value of x  substitute x in expression by its value using brackets  evaluate 
2x + 7  1  2(1)+7=  2 + 7 = 5 
2x + 7   4  2(4)+7=   8 + 7 =  1 
2x + 7  0  2(0)+7=  0 + 7 = 7 
2x + 7  5  2(5)+7=  10 + 7 = 17 

Solution
To evaluate an algebraic expression for a given numerical value of x, substitute x in the expression by its numerical value and evaluate the expression.
expression  value of x  substitute x in expression by its value using brackets  evaluate 
x / 3  9  0  (0) / 3  9=  0  9 =  9 
x / 3  9  3  (3) / 3  9 =  1  9 =  8 
x / 3  9  9  (9) / 3  9 =  3  9 =  6 
x / 3  9   12  (12) / 3  9 =   4  9 =  13 

Solution
To evaluate an algebraic expression for a given numerical value of x, substitute x in the expression by its numerical value and evaluate the expression.
expression  value of x  substitute x in expression by its value using brackets  evaluate 
( x + 2) / 2 + 1  0  ( (0) + 2) / 2 + 1 =  = (0 +2) / 2 + 1 = 2 / 2 + 1 = 1 + 1 = 2 
( x + 2) / 2 + 1  2  ((2) + 2) / 2 + 1 =  (2 + 2) / 2 + 1 = 0 / 2 + 1 = 0 + 1 = 1 
( x + 2) / 2 + 1  2  ( ( 2) + 2) / 2 + 1 =  (2 + 2 ) / 2 + 1 = 4/2 + 1 = 2 + 1 = 3 
( x + 2) / 2 + 1   12  ( (12) + 2) / 2 + 1 =  (12 + 2) / 2 + 1 = 14/2 + 1 = 7 + 1 = 8 

Solution
expression  value of x  substitute x in expression by its value using brackets  evaluate 
12 x  3  1/2  12 (1/2)  3 =  = 12 / 2  3 = 4  3 = 1 
12 x  3  1/6  12 (1/6)  3 =  = 12 / 6  3 = 2  3 =  1 
12 x  3  3/4  12(  3/4)  3 =  =  36 / 4  3 =  9  3 =  12 
12 x  3  1/4  12 (1/4)  3 =  = 12 / 2  3 =  6  3 =  9 

Solution
expression  value of x  substitute x in expression by its value using brackets  evaluate 
 0.1 x + 2.5  1   0.1 (1) + 2.5 =  = 0.1 + 2.5 = 2.4 
 0.1 x + 2.5   1   0.1 (  1) + 2.5 =  = 0.1 + 2.5 = 2.6 
 0.1 x + 2.5  2   0.1 (2) + 2.5 =  = 0.2 + 2.5 = 2.3 
 0.1 x + 2.5   2   0.1 (2) + 2.5 =  = 0.2 + 2.5 = 2.7 

Solution
expression  value of x  substitute x in expression by its value using brackets  evaluate 
x + 10   3  (3) + 10 =  =  3 + 10 = 7 
 x + 10   3   (3) + 10 =  = 3 + 10 = 13 
x / 3 + 10   3  (3) / 3 + 10 =  =  1 + 10 = 9 
 x / 3 + 10   3   (3) / 3 + 10 =  = 3 / 3 + 10 = 1 + 10 = 11 
The algebraic expression  x + 10 has the largest value 13 for x =  3.

Solution
The commutative property of the addition is given by:
a + b = b + a

Solution
The associative property of the addition is given by:
a + ( b + c ) = (a + b) + c

Solution
All the expressions are in simplified form and therefore we first need to simplify the given expression by grouping like terms.
3x + 2  x + 4 = 3x  x + 2 + 4 = 2 x + 6
Expression 3x + 2  x + 4 is equivalent to 2 x + 6.

Solution
We convert ""2 times x plus 20". " to a mathematical expression by steps.
"2 times x " is mathematically represented by : 2 × x = 2 x
"2 times x plus 20" is mathematically represented by : 2 x + 20

Solution
We convert "Three times x subtracted from 17" to a mathematical expression by steps.
"Three times x " is mathematically represented by : 3 × x = 3 x
"Three times x subtracted from 17" is mathematically represented by : 17  3x

Solution
Jo has x cards.
Jo : x
"Janette has 10 cards more that Jo" is mathematically represented by :
x + 10

Solution
Carle starts with 20 toy cars.
Carla : 20
What is lost is subtracted from the total number of toys. Hence since she lost x toys,
20  x car toys are left.

Solution
Chris starts with $200.
Chris : $200
He spent $20 on food and therefore we need to subtract it from the total
Chris : $200  $20 after bying the food
He spent a dollars on books and therefore we need to subtract it from 200  20
Chris : $200  $20  a , the money that Chris has after bying food and a book.

Solution
Nathan has x cards
Nathan : x
Nathan gave half of his cards to Tanya and so Tanya has
Nathan to Tanya : (1/2) x
If Tanya gave 1/3 of her cards to Salma, she is left with 2/3 of the cards given to her by Nathan. Hence Tanya has
(2/3)((1/2) x) = ( 2/6) x cards


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