Order of Operations

Estimate Then Solve

Divide 45 by 5. First estimate: round 45 to 50, so 50 ÷ 5 = 10. Then find the exact answer: 45 ÷ 5 = 9. The estimate (10) is close to the exact answer (9), confirming the result.

Example

Estimate 45 ÷ 5 by rounding, then solve exactly.

highlighted = computed this step

Step 1 — Set up

Write the expression to solve.

45÷545 \div 5
Start with the exact problem 45 ÷ 5.problem45 ÷ 5estimate laneround--estimate--exact laneexact--comparewait for both answersfinal answer--

Step 2 — Estimate by rounding

Round 45 to 50 for an estimate.

45≈5045 \approx \hl{50}
Round 45 to the friendly estimate value 50.problem45 ÷ 5estimate laneround45 ≈ 50estimate--exact laneexact--comparewait for both answersfinal answer--

Step 3 — Estimate

Estimate: 50 ÷ 5 = 10.

50÷5=1050 \div 5 = \hl{10}
Estimate with the friendly value: 50 ÷ 5 = 10.problem45 ÷ 5estimate laneround45 ≈ 50estimate50 ÷ 5 = 10exact laneexact--comparewait for both answersfinal answer--

Step 4 — Exact answer

Solve exactly: 45 ÷ 5 = 9.

45÷5=945 \div 5 = \hl{9}
Solve the original problem exactly: 45 ÷ 5 = 9.problem45 ÷ 5estimate laneround45 ≈ 50estimate50 ÷ 5 = 10exact laneexact45 ÷ 5 = 9comparewait for both answersfinal answer--

Step 5 — Compare

Compare estimate 10 with exact answer 9.

10 vs 910 \ \mathrm{vs}\ \hl{9}
Compare estimate 10 with exact answer 9.problem45 ÷ 5estimate laneround45 ≈ 50estimate50 ÷ 5 = 10exact laneexact45 ÷ 5 = 9compare10 is near 9; estimate checks exactfinal answer--

Step 6 — Result

Read the final answer.

99
Final answer: 9.problem45 ÷ 5estimate laneround45 ≈ 50estimate50 ÷ 5 = 10exact laneexact45 ÷ 5 = 9compare10 is near 9; estimate checks exactfinal answer9
estimate-then-solve Estimating before solving helps you catch errors. Round the numbers to friendly values, compute a quick estimate, then solve exactly. Compare the two answers — if they are far apart, recheck your work.