Algebra Questions and Problems for Grade 6
Grade 6 algebra questions and problems with detailed solutions are presented. Questions on expanding and simplifying expressions, solving linear equations, factoring expressions,....are included.
Questions and Problems

List all like terms included in each of the expressions given below.
A) 6 x + 5 + 12 x  6
B) 2 x^{ 2}  4 + 9 x^{ 2} + 9
C) x / 5 + x / 7 + 7
D) 0.2 x + 1.2 x + x / 2 + 5
E) 5 x  8 + 7 x  2 x^{ 2}  4 + 9 x^{ 2} + 4 x^{ 3}
F) 5 a + 8  7 a b
G) 5 a b+ 8 + 6 b a  a + 3 b
Solution 
Evaluate each of the expressions for the given value(s) of the variable(s).
A) 6 x + 5 for x = 2
B) 12 x^{ 2} + 5 x  2 for x = 1
C) 2( x + 7) + x for x = 0
D) 2 a + 3b  7 for a = 2 and b = 4
Solution 
Expand (if needed) and simplify each of the expressions below.
A) 3 x + 5 x
B) 2( x + 7) + x
C) 2(x + 3) + 3(x + 5) + 3
D) 2 (a + 1) + 5b + 3(a + b) + 3
Solution 
Factor each of the expressions below.
A) 3 x + 3
B) 8 x + 4
C) a x + 3 a
D) (x +1) y + 4 (x + 1)
E) x + 2 + b x + 2 b
Solution 
Solve each of the equations below and check your answer.
A) x + 5 = 8
B) 2 x = 4
C) x / 3 = 2
D) 0.2 x = 1
D) 3 x + 6 = 12
E) 3 (x + 2) + 2 = 8
Solution 
There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag?
Solution 
Rewrite the expressions a × a × a  b × b using exponents.
Solution 
The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectangle.
Solution 
Two thirds of students in a class study math and the remaining eight students do not study math. What is the total number of students in this class?
Solution 
A car travels 60 kilometers in one hour. At the same rate, what distance will be covered by this car in x hour?
Solution 
Evaluate the expressions.
A) 2^{ 3} + 3^{ 2}
B) 0.1 ^{ 3}
C) 6 × (2 / 3)
Solution 
A bag contains three red marbles; five blue marbles and seven green marbles. What is the ratio of blue marbles to the total number of marbles?
Solution 
Solve the proportion : a / 3 = 5 / 18
Solution 
Which of the following ordered pairs is a solution to the equation 2 x + 3 y = 8?
A) (0 , 0)
B) (4 , 0)
C) (1 , 2)
Solution 
List all factors of the following numbers.
A) 4
B) 12
C) 50
Solution 
Find the greatest common factor to each pair of the given numbers.
A) 6 and 3
B) 18 and 24
C) 50 and 60
Solution 
Write the number " Six hundred seventytwo million two hundred fiftynine" using the digits 0, 1, 2, ...9.
Solution 
Which of the following expressions are equivalent?
A) 2(x + 3)  2
B) 2x + 4
C) 3(x + 3)  x  5
Solution 
Find the lowest common multiple to each pair of the given numbers.
A) 2 and 3
B) 7 and 14
C) 25 and 15
Solution 
Add and / or subtract and simplify
A) 1 / 3 + 2 / 3
B) 2/5  1 / 7
Solution 
What is 2 / 3 of 21?
Solution 
What is 40% of 1 / 4?
Solution 
What is 20% of 50%?
Solution 
How many seconds are there in one hour?
Solution 
How many minutes are there in the month of January?
Solution 
What is the location of each of the points: (2 , 0) , (0 , 3) and (2 ,  3) in a coordinate plane?
Solution 
Order 7 / 5 , 12 / 10 , 21 / 20 and 111% from the smallest to the largest.
Solution
More References and links
Middle School Math (Grades 6, 7, 8, 9)  Free Questions and Problems With Answers
High School Math (Grades 10, 11 and 12)  Free Questions and Problems With Answers
Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers