No-calculator fluency: the four operations, fraction/decimal/percent conversion, percentage shortcuts.
Apply order of operations: multiplication and division before addition and subtraction.
Calculate: 6 + 9 × 4
Answer: 42
Multiplication before addition: 9 × 4 = 36, then 6 + 36 = 42. The 60 foil works left to right ((6+9)×4) — ignoring order of operations.
Build the percentage from 10% (÷10) and 5% (half of 10%): e.g. 15% = 10% + 5%.
What is 15% of 80?
Answer: 12
15% = 10% + 5% = 8 + 4 = 12. The 8 foil stops at 10%; 16 uses 20%; 1.2 slips the decimal.
Convert everything to decimals (or percentages) before comparing.
Which of these is the largest? 0.6, 5/8, 62%, 0.59, 3/5
Answer: 5/8
Convert all to decimals: 0.6, 0.625, 0.62, 0.59, 0.6. The largest is 5/8 = 0.625. The 62% foil looks biggest as a percentage; 0.59 has the most digits but is smallest.
Round to one or two leading digits, compute, and match the order of magnitude.
Estimate 397 × 21. Which is closest?
Answer: 8,400
Round 397 to 400: 400 × 21 = 8,400 (actual 8,337). The 84,000 and 800 foils slip the magnitude by a factor of ten.
Divide numerator by denominator for the decimal; multiply by 100 for the percentage.
What is 3/8 as a percentage?
Answer: 37.5%
3 ÷ 8 = 0.375 = 37.5%. The 0.375% foil forgets to multiply by 100; 62.5% is the complement (5/8); the others invert the fraction.
Find the middle (median) value, then the option with the largest distance from it — not the largest value.
Which number is furthest from the middle value? 2, 18, 20, 21, 30
Answer: 2
The middle (median) value is 20. Distances: 2→18, 18→2, 21→1, 30→10. The furthest is 2 (gap 18). The 30 foil takes the maximum, not the furthest.
Try each operator between the numbers and keep the one that makes the equation true.
Which operator makes this true? 18 ? 6 = 12
Answer: −
18 − 6 = 12. (Deliberately 4 options — there are only four basic operators, a natural ceiling like the age problem.)
Look at the digit below the rounding place: 5 or more rounds up, less rounds down.
Round 6,847 to the nearest hundred.
Answer: 6,800
The tens/units are 47, below 50, so round down to 6,800. The 6,900 foil rounds the wrong way; the others round to the wrong place value.