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Stage 19 of 20

Mixed Operations & Order

Apply parentheses, exponents, multiplication, division, addition, and subtraction in the correct order using checks and clear mental checkpoints.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Apply parentheses and exponents before the four basic operations
  • Treat multiplication and division as equal-priority operations from left to right
  • Treat addition and subtraction as equal-priority operations from left to right
  • Estimate and use inverse operations to detect order or calculation errors

Why This Matters

Science formulas, spreadsheets, code, finance, and measurement depend on operation order. Parentheses communicate which quantities belong together, while left-to-right rules resolve equal-priority operations.

Understanding Mixed Operations & Order

A shared convention gives mixed expressions one value. Evaluate grouping symbols, then exponents, multiplication/division left to right, and addition/subtraction left to right. Stages 1–18 supplied the operations; this stage controls their sequence.

PEMDAS does not create six ranks. Multiplication and division tie: 24 ÷ 6 × 3 becomes 4 × 3 = 12. Addition and subtraction also tie, so 18 − 5 + 2 becomes 13 + 2 = 15.

Parentheses change structure. Compare 6 + 3 × 4 = 18 with (6 + 3) × 4 = 36. A grouped expression behaves as one quantity, and nested grouping proceeds from the inside outward.

A square is repeated multiplication: 5² = 5 × 5 = 25, not 5 × 2. Evaluate it before addition in 4 + 5² = 29. Stage 20 develops squares further.

Replace one completed part at a time: 30 − 18 ÷ 3 + 4 becomes 30 − 6 + 4, then 24 + 4, then 28. An estimate can expose misplaced grouping or skipped priority.

Worked Examples: Think It Through

Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.

Multiply before adding

7 + 6 × 4

  1. 1 Multiplication has priority over the ungrouped addition.
  2. 2 Calculate 6 × 4 = 24.
  3. 3 Add 7 + 24 = 31.

7 + 6 × 4 = 31

Your turn — try it on new numbers

(12 + 6) × 2 = ?

Let parentheses lead

(18 − 6) ÷ 3 + 5

  1. 1 Evaluate the parentheses: 18 − 6 = 12.
  2. 2 Divide next: 12 ÷ 3 = 4.
  3. 3 Finish with addition: 4 + 5 = 9.

(18 − 6) ÷ 3 + 5 = 9

Your turn — try it on new numbers

(3 − 1) × 3 = ?

Respect equal priority

48 ÷ 8 × 3

  1. 1 Division and multiplication have equal priority, so work left to right.
  2. 2 First calculate 48 ÷ 8 = 6.
  3. 3 Then calculate 6 × 3 = 18.

48 ÷ 8 × 3 = 18

Your turn — try it on new numbers

23 + 3 × 3 = ?

Evaluate a square first

3 × 4² − 10

  1. 1 Evaluate the exponent: 4² = 4 × 4 = 16.
  2. 2 Multiply: 3 × 16 = 48.
  3. 3 Subtract: 48 − 10 = 38.

3 × 4² − 10 = 38

Your turn — try it on new numbers

17 + 5 × 5 = ?

Common Mistakes and How to Fix Them

Reading strictly from left to right

For 3 + 4 × 2, adding first gives 14 but ignores priority. Mark the multiplication, calculate 8, then add 3 to get 11.

Putting multiplication ahead of earlier division

In 36 ÷ 6 × 2, do not multiply 6 × 2 first. Multiplication and division tie, so work left to right: 6 × 2 = 12.

Reading a square as times two

The small 2 counts equal factors. Replace 7² with 7 × 7 = 49, never 7 × 2 = 14.

Mixed Operations & Order in Everyday Life

A club charges a £12 entry fee plus £4 for each of 3 activities. The total is 12 + 4 × 3 = £24. Parentheses would model a different deal: (12 + 4) × 3 charges both amounts three times.

Pro Tips

  • • Rewrite only the part completed at each checkpoint and carry every untouched term forward.
  • • Remember the two ties: multiply/divide left to right; add/subtract left to right.
  • • Translate every square into repeated multiplication before using it.
  • • Estimate the expression’s size to catch impossible signs or magnitudes.

Practice Exercises

Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.

  1. 1. 3 + 4 × 2 = ?
  2. 2. (3 + 4) × 2 = ?
  3. 3. 20 − 12 ÷ 3 = ?
  4. 4. 24 ÷ 6 × 3 = ?
  5. 5. 18 − 5 + 2 = ?
  6. 6. 5 + 3² = ?
  7. 7. 2 × 5² − 6 = ?
  8. 8. (16 − 4) ÷ 2 = ?
  9. 9. 30 − 18 ÷ 3 + 4 = ?
  10. 10. 8 + 24 ÷ 6 × 2 = ?
  11. 11. 6 × (7 − 3) + 5 = ?
  12. 12. 64 ÷ 8 + 7 × 2 = ?
  13. 13. 4² + 3² = ?
  14. 14. 50 − (6 × 7) = ?
  15. 15. 72 ÷ (3 × 4) = ?
  16. 16. 100 ÷ 10 ÷ 2 = ?
  17. 17. 9 + 2 × (11 − 6) = ?
  18. 18. (8 + 4)² ÷ 12 = ?

Drill Stage 19 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses mixed expressions that follow the order of operations. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

2 + 3 × 4 = ?

Stage 19 Questions

Does PEMDAS mean multiplication always comes before division?

No. Multiplication and division share priority and are evaluated from left to right. The same shared-priority rule applies to addition and subtraction.

What happens when parentheses are nested?

Evaluate the innermost pair first, replace it with its value, and then move outward one layer at a time.

Why not simply add parentheses everywhere?

Useful parentheses clarify intended grouping, but arbitrary ones can change the value. Standard precedence already defines ungrouped expressions.