Test Prep Thursday: Order of Operations - Part 2

Welcome to part 2 of our Test Prep session on Order of Operations! How did you do last week? Let’s find out!

1. -2(3-1) + 4 x 3 – 2 = 6
2. (40 – 18 x 2)³ ÷ 2 – 5 = 27
3. 20 + 3[8² + 5(200 x 4 - 2⁵) – 11] = 11,699

Great job! If you need some more explanation, let’s break each of these problems down, step-by-step, according to PEMDAS.

1. Since parentheses is first up in the order, we need to calculate the parenthetical expression. 3-1 = 2, so then we go from there.
   1. -2(3-1) + 4 x 3 – 2
   2. -2(2) + 4 x 3 – 2
   3. -4 + 12 – 2 = 6
2. This problem also has parenthesis, but we also must follow order of operations within the parentheses.
   1. (40 – 18 x 2)³ ÷ 2 – 5
   2. (40 – 36)³ ÷ 2 – 5
   3. (4)³ ÷ 2 – 5
   4. 64 ÷ 2 – 5
   5. 32 – 5 = 27
3. This problem may seem long and daunting, but as long as we take it step-by-step and follow PEMDAS, we should be just fine!
   1. 20 + 3[8² + 5(200 x 4 - 2⁵) – 11]
   2. 20 + 3[64 + 5(200 x 4 - 32) – 11]
   3. 20 + 3[64 + 5(800 - 32) – 11]
   4. 20 + 3[64 + 5(764) – 11]
   5. 20 + 3[64 + 3840 – 11]
   6. 20 + 3[3893]
   7. 20 + 11,679 = 11,699

Well done! Hopefully now you feel better equipped to tackle these tricky equations and score high on your ACT and SAT. Make sure to check back every week for more Test Prep, as well as important Mathnasium updates!