2. Operations (N)
  3. Lesson 11: Order of Operations

Answers and Solutions



    1. \(\begin{align*} &3 \times 7 - 6 \div \dfrac{1}{3} & \text{Multiply} \\ = \ & 21 - 6 \div \dfrac{1}{3} & \text{Divide} \\ \end{align*}\)

      Solve the division problem.

      \(\begin{align*} 6 \div \dfrac{1}{3} &= 6 \times \dfrac{3}{1} \\ &= 18 \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ & 21 - 18 & \text{Subtract} \\ = \ & 3 \end{align*}\)


    2. \(\begin{align*} &\dfrac{1}{3} \times (2+4) + 7 & \text{Brackets} \\ = \ &\dfrac{1}{3} \times 6 + 7 & \text{Multiply} \\ \end{align*}\)

      Solve the multiplication problem.

      \(\begin{align*} \dfrac{1}{3} \times 6 &= \dfrac{1\times 6}{3} \\ &= \dfrac{6}{3} \\ &=2 \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ & 2 +7 & \text{Add} \\ = \ & 9 \end{align*}\)


    3. \(\begin{align*} &16 \times \left( \dfrac{3}{4} + \dfrac{1}{8} \right) \div 0.4 & \text{Brackets} \end{align*}\)

      Simplify the expression inside the brackets.

      \(\begin{align*} \dfrac{3}{4} + \dfrac{1}{8} &= \dfrac{6}{8} + \dfrac{1}{8} \\ &= \dfrac{7}{8} \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ & 16 \times \dfrac{7}{8} \div 0.4 & \text{Multiply} \end{align*}\)

      Solve the multiplication problem.

      \(\begin{align*} 16\times \dfrac{7}{8} &= \dfrac{16 \times 7}{8} \\ &= \dfrac{112}{8} \\ &= 14 \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ &14 \div 0.4 & \text{Division} \\ = \ & 140 \div 4 \\ = \ & 35 \end{align*}\)


    4. \(\begin{align*} &39 \div (0.9 + 0.4) - 2 \times (4+1) & \text{Brackets} \\ = \ & 39 \div 1.3 - 2 \times (4+1) & \text{Brackets} \\ = \ & 39 \div 1.3 - 2 \times 5 & \text{Divide} \end{align*}\)

      Solve the division problem.

      \(\begin{align*} 39 \div 1.3 &= 390 \div 13 \\ &= 30 \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ & 30 - 2 \times 5 & \text{Multiply} \\ = \ & 30 - 10 & \text{Subract} \\ = \ & 20 \end{align*}\)

    1. \(\begin{align*} 5 \times (8-3) &= 5\times 8 - 5\times 3 \\ &= 40 - 15 \\ &= 25 \end{align*}\)

    2. \(\begin{align*} (6+4) \div 2 &= 6\div 2 + 4 \div 2 \\ &= 3 - 2 \\ &= 5 \end{align*}\)

    3. \(\begin{align*} 4 \times (20 + 7) &= 4 \times 20 + 4 \times 7 \\ &= 80 + 28 \\ &= 108 \end{align*}\)
  3. Brian's solution is not correct because he did not find the reciprocal of the fraction when he changed the division to multiplication.  The correct solution is:\[\begin{align*} 998 \div 0.2 &= 998 \div \dfrac{2}{10} \\ &= (1000-2) \div \dfrac{2}{10} \\ &= (1000 -2) \times \dfrac{10}{2} \\ &= (1000-2) \times 5 \\ &= 1000 \times 5 - 2 \times 5 \\ &= 5000 - 10 \\ &= 4990 \end{align*}\]
    1. \(3\times 5 + \left( \dfrac{1}{2} + \dfrac{5}{2}\right) \times 2 = 21\)
    2. \((3+3\times3)\div 4 - (27-24)=0\)
    1. Answers will vary.
      1. There are \(3\) different answers that you can get.
      2. There are \(4\) different answers that you can get.

    1. \(\begin{align*} &\left( \dfrac{7}{8} -\dfrac{3}{4} \right) \times 3 + 4 & \text{Brackets} \end{align*}\)

      Simplify the expression inside the brackets.

      \(\begin{align*} \dfrac{7}{8} - \dfrac{3}{4} &= \dfrac{7}{8} - \dfrac{6}{8} \\ &= \dfrac{1}{8} \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ &\dfrac{1}{8} \times 3 + 4 & \text{Multiply} \end{align*}\)

      Solve the multiplication problem.

      \(\begin{align*} \dfrac{1}{8} \times 3 &= \dfrac{1\times 3}{8} \\ &= \dfrac{3}{8} \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ &\dfrac{3}{8} + 4 & \text{Add} \\ = \ & 4\dfrac{3}{8} \end{align*}\)


    2. \(\begin{align*} & (7 \div 0.56 + 5) \times 16 & \text{Brackets } \rightarrow \text{Divide} \end{align*}\)

      Solve the division problem.

      \(\begin{align*} 7 \div 0.56 &= 700 \div 56 \\ &= 12.5 \end{align*}\)

      Put this value back into the original problem.

       \(\begin{align*} = \ & (12.5 + 5) \times 16 & \text{Brackets} \\ = \ & 17.5 \times 16 & \text{Multiply} \\ = \ & \dfrac{175}{10} \times 16 \\ = \ & \dfrac{35}{2} \times 16 \\ = \ & \dfrac{16}{2} \times 35 \\ = \ & 8 \times 35 \\ = \ & 280 \end{align*}\)


    3. \(\begin{align*} &\Big(7 \div 0.25 + (-16)\Big) \times \Big((-3)-(-5)\Big) & \text{Brackets} \rightarrow \text{Divide} \end{align*}\)

      Solve the division problem.

      \(\begin{align*} 7 \div 0.25 &= 700 \div 25 \\ &= 28 \end{align*}\)

      Put this value back into the original problem.

      \(\begin{align*} = \ &\Big(28 + (-16)\Big) \times \Big((-3)-(-5)\Big) & \text{Brackets} \\ = \ & 12 \times \Big((-3)-(-5)\Big) & \text{Brackets} \\ = \ & 12 \times 2 & \text{Multiply} \\ = \ & 24 \end{align*}\)

    1. \((1+2-4)\times 3=(-3)\)
    2. \(4\times (3 + 2) -1 = 19\)
    3. \(1- (2 + 3)\times 4 = -19\)