Add the ones. Carry the ten.
Every zetamac addition is two numbers from 2 to 100. Start with the ones digits, because they decide whether anything carries into the tens.
Zetamac range (2–100) + (2–100)
The method 47 + 38
- 1Add the ones digits.
Look only at the last digit of each number. For 47 + 38 that’s 7 + 8 = 15.
- 2Past 10? Keep the ones digit and carry the 1.
15 is 10 or more, so the answer ends in 5 and a 1 carries into the tens. Under 10 there’s nothing to carry: 42 + 35 simply ends in 7.
- 3Add the tens, plus the carry.
4 + 3 + 1 = 8, so the answer is 85.
TypingYou work right to left but type left to right. Hold the 5, type the 8, then the 5. Zetamac takes the answer the moment it’s right, so there’s no Enter to wait for.
Subtract the ones. Borrow when you can’t.
Zetamac’s subtraction is its addition run backwards, so the answer is always from 2 to 100. Check the ones digits first. If the top one is at least as big as the bottom one, nothing borrows. If it’s smaller, as in 62 – 17, you borrow, and there are two good ways to do it.
Zetamac range addition problems in reverse
Without borrowing 68 – 23
- 1Subtract the ones.
8 – 3 = 5.
- 2Subtract the tens.
6 – 2 = 4. The answer is 45.
Borrowing, way 1: count up 62 – 17
Instead of taking away, picture how far it is from the smaller number up to the bigger one.
- 1Jump to the next ten.
From 17 up to 20 is 3.
- 2Jump to the top number.
From 20 up to 62 is 42.
- 3Add the two jumps.
3 + 42 = 45. That’s the answer.
Borrowing, way 2: take it from ten 62 – 17
Keep working digit by digit, but let the ones run the other way.
- 1Subtract the ones the other way round.
The bottom ones digit is the bigger one, so take the top one from it: 7 – 2 = 5. That’s what’s left over.
- 2Take the leftover from 10.
10 – 5 = 5. That’s the answer’s ones digit.
- 3Subtract the tens, and 1 more for the borrow.
6 – 1 – 1 = 4. The answer is 45.
Which wayBoth give the same answer, so use whichever feels quicker. Counting up tends to suit numbers that sit close together, like 83 – 78. The Practice game drills borrowing and non-borrowing problems separately.
Split the big number. Multiply twice, then add.
Zetamac multiplies a number from 2 to 12 by one from 2 to 100. Unless the small number is 11, the quickest route is to break the big number into its tens and its ones.
Zetamac range (2–12) × (2–100)
Every case except 11 7 × 43
- 1Multiply the small number by the tens.
7 × 40 = 280. Hold 280 in your head.
- 2Multiply it by the ones.
7 × 3 = 21.
- 3Add the two.
280 + 21 = 301. That’s the answer.
Skip the splitA round number like 7 × 40, or a single digit like 7 × 8, is already one times-table fact.
Times 11 11 × 43
Any two-digit number times 11 has a shortcut.
- 1Spread the digits apart with a 0 between them.
43 becomes 403.
- 2Add the two digits and put the sum under the 0.
4 + 3 = 7, so 403 becomes 473. That’s the answer.
- 3If the sum is 10 or more, carry the 1 into the hundreds.
For 11 × 58: spread to 508, and 5 + 8 = 13. The 3 goes under the 0 and the 1 carries: 508 + 130 = 638.
Edge cases11 times a single digit is that digit written twice (11 × 7 = 77), and 11 × 100 = 1100.
Find the multiple underneath. Divide what’s left.
Zetamac’s division is its multiplication run backwards: a number from 2 to 12 goes into the one shown, and the answer is from 2 to 100. Every step leans on the times table, so it has its own tab.
Zetamac range multiplication problems in reverse
The method 434 ÷ 7
- 1Know the divisor’s times table.
You need 7 × 1 up to 7 × 9 without thinking, because the next three steps are built from them. The tab drills them.
- 2Find the biggest round multiple underneath.
Which of 7 × 10, 7 × 20, 7 × 30 … sits just under 434? 7 × 60 = 420. Hold the 60.
- 3Take the difference.
434 – 420 = 14.
- 4Divide the difference, and add.
14 ÷ 7 = 2, and 60 + 2 = 62. That’s the answer.
ShortcutsUnder 10 times the divisor (56 ÷ 7), there’s nothing to take off: it’s one times-table fact. If the difference is 0 (420 ÷ 7), the round multiple is the answer.
Know the table cold.
Division and the split method both come down to 2–12 × 2–12. Study the grid, hide it to test yourself, then drill the facts one at a time until each one comes without thinking.
Count the places. Build from ten percent.
The quant tests add decimals, percentages, fractions, number sequences and estimates to the four operations. Each one has a quick way in, and every method below turns it back into whole-number arithmetic you already know.
Tests 80 in 8 · sequences · fractions · estimation
Decimals times decimals 3.4 × 2.5
- 1Drop the points and multiply.
34 × 25 = 850, as whole numbers.
- 2Count the decimal places in the question.
3.4 has one and 2.5 has one: 2 places.
- 3Put that many back.
850 with two places is 8.50, so type 8.5.
DividingMove both points the same way until the divisor is whole: 7.2 ÷ 0.8 is 72 ÷ 8 = 9. Adding and subtracting: line the points up, and fill a missing place with 0 (12.75 + 6.50).
Percentages 12% of 850
- 1Find 10%: move the point one place left.
10% of 850 is 85.
- 2Build the rest from 10%, 5% and 1%.
5% is half of 10%, and 1% is a tenth of it. Here 12% is 10% and two 1%s: 2% = 17.
- 3Add the pieces.
85 + 17 = 102.
Swap themx% of y is y% of x, so pick the easier one: 8% of 25 is 25% of 8, which is 2. And 12.5% is an eighth, 2.5% a fortieth.
Fractions to decimals 7/16
- 1Know the one-part fraction.
1/16 is 0.0625. The ones worth learning: 1/8 = 0.125, 1/16 = 0.0625, 1/20 = 0.05, 1/25 = 0.04, 1/40 = 0.025.
- 2Multiply by the top number.
7 × 0.0625 = 0.4375: think 7 × 625 = 4375, then four places.
EighthsLearn them as a row: 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875. A percent is the decimal × 100 (3/8 = 37.5%), and “eighths in 0.375” runs it backwards: 0.375 ÷ 0.125 = 3.
Number sequences 3, 7, 15, 31
- 1Write the gaps between terms.
3, 7, 15, 31 has gaps 4, 8, 16. Same gap every time: add it once more.
- 2Gaps growing? Look at them as their own sequence.
4, 8, 16 doubles, so the next gap is 32: 31 + 32 = 63. Gaps that grow by the same amount (2, 4, 6) mean the next grows by it too.
- 3Nothing yet? Try ratios, squares, and two sequences at once.
× 2 or × 3 each time, × 2 then + 1, squares or cubes plus a constant, each term the sum of the two before, or odd and even places running separately (2, 37, 8, 51, 14 is 2, 8, 14 and 37, 51).
Estimation 48.7 × 21.3
- 1Round each number to two figures.
49 × 21. Rounding one up and one down keeps the error small.
- 2Multiply the round numbers.
49 × 21 = 1029 (50 × 21 = 1050, less 21).
- 3Stop there: within 5% counts.
The exact answer is 1037.31, and 1029 is under 1% off. For a square root, find the squares either side: √5,200 sits just over 72 (72² = 5,184).