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

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 seventy-two million two hundred fifty-nine" 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

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