doing math

Learn

Short lessons to read before you play. Nothing here is timed. Each right try-one earns 1 XP, up to 10 XP a day per course; Learn pays no ✱ and doesn't count toward your streak.

quick techniques

Make ten · A sum crosses a ten, a hundred or a thousand.
  1. Top the bigger number up to the next ten.
  2. Take that much from the other number.
  3. Add what is left.

Example: 38 + 7

  1. 38 needs 2 to reach 40.
  2. 7 − 2 = 5 left.
  3. 40 + 5 = 45.

Answer: 45

used in: Small facts · Gaps & place value · Two-digit add & subtract

Doubles and near doubles · The two numbers are the same or close together.
  1. Double the smaller one.
  2. Add the difference.

Example: 25 + 26

  1. 25 + 25 = 50.
  2. One more: 50 + 1 = 51.

Answer: 51

used in: Small facts · Two-digit add & subtract

Count up to subtract · Subtracting, making change, or finding a gap.
  1. Start at the smaller number.
  2. Jump to the next round number, unless the bigger number comes first.
  3. Jump on to the bigger number.
  4. Add the jumps.

Example: 100 − 64

  1. 64 up to 70 is 6.
  2. 70 up to 100 is 30.
  3. 6 + 30 = 36.

Answer: 36

used in: Small facts · Gaps & place value · Two-digit add & subtract · Money & prices

Round, then adjust · A number sits just below a round one, like 29, 98 or $1.99.
  1. Use the round number instead.
  2. Work out the answer.
  3. Put back what the rounding changed. In a product, multiply the difference by the other number: 29 × 4 = 120 − 4.

Example: 83 − 29

  1. 83 − 30 = 53.
  2. You took away 1 too many, so add it back: 53 + 1 = 54.

Answer: 54

used in: Two-digit add & subtract · Bigger multiplication · Money & prices

Split and combine · Multiplying a two-digit number by a one-digit number.
  1. Split the bigger number into tens and ones.
  2. Multiply each part.
  3. Add the parts.

Example: 7 × 46

  1. 7 × 40 = 280.
  2. 7 × 6 = 42.
  3. 280 + 42 = 322.

Answer: 322

used in: Bigger multiplication · Division

Double and halve · One number is even and the other ends in 5.
  1. Halve the even number.
  2. Double the other one.
  3. Repeat until the product is easy.

Example: 16 × 25

  1. 16 × 25 = 8 × 50.
  2. 8 × 50 = 4 × 100.
  3. 4 × 100 = 400.

Answer: 400

used in: Times tables · Bigger multiplication

Shift for 10, 100 and 1,000 · Multiplying or dividing by 10, 100 or 1,000.
  1. Times 10 moves every digit one place to the left: 45 becomes 450.
  2. Dividing by 10 moves every digit one place to the right: 45 becomes 4.5.
  3. Count the zeros to know how many places to move.

Example: 3.2 × 100

  1. 100 has two zeros, so move two places left.
  2. 3.2 becomes 320.

Answer: 320

used in: Gaps & place value · Division · Decimals

Build from 10%, 5% and 1% · Finding any percent of an amount.
  1. 10% is the amount divided by 10.
  2. 5% is half of 10%.
  3. 1% is the amount divided by 100.
  4. Add the pieces you need: 15% = 10% + 5%.

Example: 15% of $80

  1. 10% of $80 is $8.
  2. 5% is half of that: $4.
  3. $8 + $4 = $12.

Answer: $12

used in: Percents · First Business Story · Percentages in Business

Know the equivalents · A percent is a simple fraction, or a fraction is a simple percent.
  1. Learn the anchors: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 1/10 = 10%.
  2. Eighths are half of quarters: 1/8 = 12.5%.
  3. 1/3 and 2/3 never end: 1/3 ≈ 33.3% and 2/3 ≈ 66.7%.

Example: 25% of 360

  1. 25% is 1/4.
  2. 360 ÷ 4 = 90.

Answer: 90

used in: Fraction basics · Percents · Division

Estimate first · Before a long calculation, and to check an answer.
  1. Round each number to its first digit.
  2. Do the easy calculation.
  3. Your exact answer should land near it. If it is 10 times off, a zero or a decimal point slipped.

Example: Round each number to its first digit, then multiply: 412 × 38

  1. 412 rounds to 400, and 38 rounds to 40.
  2. 400 × 40 = 16,000.
  3. The exact answer, 15,656, is close.

Answer: 16,000

used in: Grouping & estimating · Orders of magnitude · Fermi estimates

Work backward from a percent · You know the amount after a percent change and want the amount before it.
  1. Say what share of the original you have: 20% off leaves 80%.
  2. Divide by that share, written as a decimal.
  3. Never add the percent back on. That uses the wrong base.

Example: After 20% off, a coat costs $96. What was the original price?

  1. $96 is 80% of the original.
  2. $96 ÷ 0.8 = $120.
  3. Check: 20% of $120 is $24, and $120 − $24 = $96.

Answer: $120

used in: What percent? Work backward · Percentages in Business · Markup Is Not Margin · Invoices & Sales Tax

Pretend it is 100 · A percent question gives no amounts at all.
  1. Start with 100, or $100.
  2. Apply each change in order.
  3. Read the answer off your numbers: the gap from 100 is the percent change. A margin is profit ÷ price.

Example: A price goes up 10%, then down 10%. What is the overall change, in percent?

  1. 100 up 10% is 110.
  2. 110 down 10% is 99.
  3. 99 is 1 below 100: a 1% drop.

Answer: −1%

used in: Percentages in Business · Markup Is Not Margin · Money & prices

Keep the balance · Solving any equation.
  1. Whatever you do to one side, do to the other.
  2. Undo in reverse order: in 2x + 9, the 9 came last, so take it away first.
  3. Check by putting the answer back in.

Example: Solve for x: 2x + 9 = 25

  1. Take 9 from both sides: 2x = 16.
  2. Divide both sides by 2: x = 8.
  3. Check: 2 × 8 + 9 = 25.

Answer: 8

used in: Expressions & one-step equations · Linear equations · Solve for the Unknown

lessons · 0 of 131 done

Foundations

Mental Arithmetic

Fractions, Decimals & Percents

Business

Business Math

Accounting

Bookkeeping

Finance & Money

Growth & Marketing Math

Business Stats & Decisions

Thinking

Thinking

School math

Pre-Algebra

Geometry

Probability & Statistics

Counting & Discrete Math

Algebra

Number Theory

Trigonometry

College & beyond

Calculus

Linear Algebra

Beyond College