Algebra Questions and Problems for Grade 6

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

• 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

• 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
• 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
• 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
• There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag?
• Rewrite the expressions a × a × a – b × b using exponential.
• 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.
• 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?
• A car travels 60 kilometers in one hour. At the same rate, what distance will be covered by this car in y hour?
• Evaluate the expressions.
A) 2 3 + 3 2
B) 0.1 3
C) 6 × (2 / 3)
• 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?
• Solve the proportion : a / 3 = 5 / 18
• 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)
• List all factors of the following numbers.
A) 4
B) 12
C) 50
• Find the greatest common factor to each pair of the given numbers.
A) 6 and 3
B) 18 and 24
C) 50 and 60
• Write the number ” Six hundred seventy-two million two hundred fifty-nine” using digits.
• Which of the following expressions are equivalent?
A) 2(x + 3) – 2
B) 2x + 4
C) 3(x + 3) – x – 5
• Find the lowest common multiple to each pair of the given numbers.
A) 2 and 3
B) 7 and 14
C) 25 and 15
• Add and / or subtract and simplify
A) 1 / 3 + 2 / 3
B) 2/5 – 1 / 7
• What is 2 / 3 of 21?
• What is 40% of 1 / 4?
• What is 20% of 50%?
• How many seconds are there in one hour?
• How many minutes are there in the month of January?
• What is the location of each of the points: (-2 , 0) , (0 , 3) and (-2 , – 3) in a coordinate plane?
• Order   7 / 5 , 12 / 10 , 21 / 20 and 111%   from the smallest to the largest.