Algebra Questions and Problems for Grade 6

Grade 6 algebra questions and problems with detailed solutions. Topics include expanding and simplifying expressions, solving linear equations, factoring expressions, and more.

Questions and Problems

  1. List all like terms included in each of the expressions given below.

    A) \(6x + 5 + 12x - 6\)
    B) \(2x^2 - 4 + 9x^2 + 9\)
    C) \( \dfrac{x}{5} + \dfrac{x}{7} + 7 \)
    D) \(0.2x + 1.2x + \dfrac{x}{2} + 5\)
    E) \(5x - 8 + 7x - 2x^2 - 4 + 9x^2 + 4x^3\)
    F) \(5a + 8 - 7ab\)
    G) \(5ab + 8 + 6ba - a + 3b\)
    Solution

  2. Evaluate each of the expressions for the given value(s) of the variable(s).

    A) \(6x + 5\) for \(x = 2\)
    B) \(12x^2 + 5x - 2\) for \(x = 1\)
    C) \(2(x + 7) + x\) for \(x = 0\)
    D) \(2a + 3b - 7\) for \(a = 2\) and \(b = 4\)
    Solution

  3. Expand (if needed) and simplify each of the expressions below.

    A) \(3x + 5x\)
    B) \(2(x + 7) + x\)
    C) \(2(x + 3) + 3(x + 5) + 3\)
    D) \(2(a + 1) + 5b + 3(a + b) + 3\)
    Solution

  4. Factor each of the expressions below.

    A) \(3x + 3\)
    B) \(8x + 4\)
    C) \(ax + 3a\)
    D) \((x + 1)y + 4(x + 1)\)
    E) \(x + 2 + bx + 2b\)
    Solution

  5. Solve each of the equations below and check your answer.

    A) \(x + 5 = 8\)
    B) \(2x = 4\)
    C) \(\dfrac{x}{3} = 2\)
    D) \(0.2x = 1\)
    E) \(3x + 6 = 12\)
    F) \(3(x + 2) + 2 = 8\)
    Solution

  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?

    Solution

  7. Rewrite the expressions \(a \times a \times a - b \times b\) using exponents.

    Solution

  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.

    Solution

  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?

    Solution

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

    Solution

  11. Evaluate the expressions.

    A) \(2^3 + 3^2\)
    B) \(0.1^3\)
    C) \(6 \times \dfrac{2}{3}\)
    Solution

  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?

    Solution

  13. Solve the proportion: \(\dfrac{a}{3} = \dfrac{5}{18}\)

    Solution

  14. Which of the following ordered pairs is a solution to the equation \(2x + 3y = 8\)?

    A) (0, 0)
    B) (4, 0)
    C) (1, 2)
    Solution

  15. List all factors of the following numbers.

    A) 4
    B) 12
    C) 50
    Solution

  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
    Solution

  17. Write the number "Six hundred seventy-two million two hundred fifty-nine" using the digits 0, 1, 2, ...9.

    Solution

  18. Which of the following expressions are equivalent?

    A) \(2(x + 3) - 2\)
    B) \(2x + 4\)
    C) \(3(x + 3) - x - 5\)
    Solution

  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
    Solution

  20. Add and/or subtract and simplify

    A) \(\dfrac{1}{3} + \dfrac{2}{3}\)
    B) \(\dfrac{2}{5} - \dfrac{1}{7}\)
    Solution

  21. What is \(\dfrac{2}{3}\) of 21?

    Solution

  22. What is 40% of \(\dfrac{1}{4}\)?

    Solution

  23. What is 20% of 50%?

    Solution

  24. How many seconds are there in one hour?

    Solution

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

    Solution

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

    Solution

  27. Order \(\dfrac{7}{5}, \dfrac{12}{10}, \dfrac{21}{20}\) and 111% from the smallest to the largest.

    Solution

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