# 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.

1. 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

2. 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

3. 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

4. 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

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

6. There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag?

7. Rewrite the expressions a × a × a - b × b using exponential.

8. 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.

9. 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?

10. A car travels 60 kilometers in one hour. At the same rate, what distance will be covered by this car in y hour?

11. Evaluate the expressions.
A) 2 3 + 3 2
B) 0.1 3
C) 6 × (2 / 3)

12. 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?

13. Solve the proportion : a / 3 = 5 / 18

14. 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)

15. List all factors of the following numbers.
A) 4
B) 12
C) 50

16. Find the greatest common factor to each pair of the given numbers.
A) 6 and 3
B) 18 and 24
C) 50 and 60

17. Write the number " Six hundred seventy-two million two hundred fifty-nine" using digits.

18. Which of the following expressions are equivalent?
A) 2(x + 3) - 2
B) 2x + 4
C) 3(x + 3) - x - 5

19. Find the lowest common multiple to each pair of the given numbers.
A) 2 and 3
B) 7 and 14
C) 25 and 15

20. Add and / or subtract and simplify
A) 1 / 3 + 2 / 3
B) 2/5 - 1 / 7

21. What is 2 / 3 of 21?

22. What is 40% of 1 / 4?

23. What is 20% of 50%?

24. How many seconds are there in one hour?

25. How many minutes are there in the month of January?

26. What is the location of each of the points: (-2 , 0) , (0 , 3) and (-2 , - 3) in a coordinate plane?

27. Order   7 / 5 , 12 / 10 , 21 / 20 and 111%   from the smallest to the largest.

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