Evaluate 3 + 4 × 2.
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Answer
11
Multiplication comes before addition: 4 × 2 = 8, then 3 + 8 = 11. 14 is what you get working left to right.
Arithmetic Workout
Order of operations, fractions, percents and mental math, with worked steps
Arithmetic Workout is a Bertopia flashcard pack of 62 cards: order of operations, fractions, percents and mental math, with worked steps. It covers order of operations; negative numbers; factors, primes and divisibility; fractions; decimals; percentages; ratios and proportion; rates and units; mental math; powers and roots; estimation and averages.
Sample cards
Evaluate 8 − (−3).
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Answer
11
Subtracting a negative is adding its opposite: 8 + 3 = 11.
What is the greatest common divisor of 84 and 126?
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Answer
42
84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. Take the lowest power of each shared prime: 2 × 3 × 7 = 42.
Compute .
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Answer
19/12
Common denominator 12: 9/12 + 10/12 = 19/12. Adding tops and bottoms (8/10) is the classic mistake.
Compute 1.2 × 1.5.
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Answer
1.8
12 × 15 = 180, and the factors have two decimal places in total, so 1.80 = 1.8.
What is 15% of 240?
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Answer
36
10% of 240 is 24 and 5% is 12, so 15% is 36.
Sources
2 sources
- OpenStax, Prealgebra 2e, OpenStax, Rice University
- OpenStax, Elementary Algebra 2e, OpenStax, Rice University
