doing math

courses › Mental Arithmetic

Bigger multiplication

level 10 course

Multiply two-digit numbers in your head with friendly shortcuts.

Best in your head · no pen, no calculator why?

Learn first (about 3 minutes)

Opens at level 10.

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Builds on: Times tables (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Multiplying bigger numbers in your head means turning one hard product into a few facts you already know.

Three moves do most of the work. Split a number into tens and ones, and multiply each part. Round a factor like 19 up to 20, then take away the extra copy: 19 × 24 is 20 copies of 24, minus one. Or make a round factor: 5, 25 and 50 are pieces of 10 and 100, and halving one factor while doubling the other keeps the product the same.

Techniques

Split and combine

A two-digit number times a one-digit number.

  1. Split the two-digit number into tens and ones.
  2. Multiply each part by the one-digit number.
  3. Add the two products.
worked example

Example: 27 × 6

  1. 20 × 6 = 120.
  2. 7 × 6 = 42.
  3. 120 + 42 = 162.

Answer: 162

Round, then fix by one copy

One factor is one away from a round number, like 19, 51 or 99.

  1. Round that factor: 19 becomes 20.
  2. Multiply the other number by the round one.
  3. 19 is one copy short of 20, so take one copy away. For 51, add one copy.
  4. A copy is the whole other number, never 1.
worked example

Example: 29 × 14

  1. 30 × 14 = 420.
  2. That is one copy of 14 too many.
  3. 420 − 14 = 406.

Answer: 406

Make a round factor

One factor is 5, 25 or 50, or ends in 5 and the other is even.

  1. × 5 is × 10, then halve. × 50 is × 100, then halve.
  2. × 25 is × 100, then ÷ 4, because four 25s make 100.
  3. With 15, 35 or 45, halve the even factor and double the other: 16 × 35 is 8 × 70.
  4. Halving one factor and doubling the other keeps the product the same.
worked example

Example: 25 × 36

  1. × 25 is × 100, then ÷ 4.
  2. 36 × 100 = 3,600.
  3. 3,600 ÷ 4 = 900.

Answer: 900

Tips by skill

  • TipTwo-digit × one-digit: Split the bigger number into tens and ones, multiply each part, then add the two results.
  • Tip× 5, × 25, × 50: × 5 and × 50: multiply by 10 or 100, then halve. × 25: multiply by 100, then divide by 4.
  • TipNear round numbers: Round the factor one away from a round number, like 19 or 51. Multiply, then add or take away one whole copy of the other.
  • TipDouble and halve: Double the factor ending in 5 or 50 so it becomes round, and halve the other. The product doesn't change.

Watch out for

  • Adding the ones instead of multiplying them. 18 × 7 is 70 plus 8 × 7, which is 126, not 70 plus 15.
  • Taking away 1 instead of one whole copy. 19 × 24 is 480 minus 24, which is 456, not 479.
  • Halving one factor and forgetting to double the other. That halves the whole answer.
  • Losing a zero. 25 × 48 is close to 25 × 50, which is 1,250, so 120 is far too small.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

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