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