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00XP
← Unit 0 · Arithmetic survival kit

Lesson

Read the rule, then work each example: try the setup yourself, then tap to check one step at a time.

The rules

Rounding

Look at the NEXT digit: 5 or more → round up; 4 or less → leave it.

E-notation (calculator scientific notation)

E−k means × 10⁻ᵏ: move the decimal point k places LEFT and fill with zeros.

  1. Find the number after E (e.g. −4).
  2. Negative → move the decimal that many places LEFT; positive → RIGHT.
  3. Fill the empty places with zeros.
  4. A probability like 1.8E−7 is essentially 0.

Percents ↔ decimals

Percent → decimal: move 2 left and drop %. Decimal → percent: move 2 right and add %. Multiply percents as decimals.

  1. Adding or subtracting percents? Work with them directly: 28.8% − 12.6% + 35% = 51.2%.
  2. Multiplying percents? Change each to a decimal first, multiply, then change back.

Comparing decimals

Line up the decimal points and compare place by place from the left.

Fractions: reduce, 1 − a/b, add, multiply

Always reduce: divide top AND bottom by the same number.

  1. Ends in 0, 2, 4, 6, 8 → try ÷2.
  2. Ends in 0 or 5 → try ÷5.
  3. Digit sum divisible by 3 (or 9) → try ÷3 (or ÷9).
  4. Ends in 0 → ÷10.
  5. Multiplying? Cancel first: 3/4 × 16/9 = 4/3.

Divisibility tests

÷2: last digit even · ÷5: ends in 0 or 5 · ÷10: ends in 0 · ÷3 / ÷9: digit sum divisible by 3 / 9.

Complement of a set

The complement is everything in the box that is NOT listed in the event.

Traps and calculator keys are on the unit page →

Worked examples (25)

Example 1 · 0.rounding #Example 10/4

Round each number to the indicated decimal

2.5673 to 2 decimal places

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Example 2 · 0.rounding #Example 20/4

Round each number to the indicated decimal

10.147812 to the nearest whole number

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Example 3 · 0.enotation #Example 10/5

Convert each number from Scientific Notation to Standard Notation.

$9\,E^{-4}$

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Example 4 · 0.enotation #Example 20/5

Convert each number from Scientific Notation to Standard Notation.

$1.1390625\,E^{-5}$

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Example 5 · 0.percent-to-decimal #Example 10/5

Convert to decimals.

28%

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Example 6 · 0.percent-to-decimal #Example 20/3

Convert to decimals.

57.145%

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Example 7 · 0.decimal-to-percent #Example 10/5

Convert to percents.

0.25

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Example 8 · 0.decimal-to-percent #Example 20/3

Convert to percents.

0.05879

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Example 9 · 0.percent-add-sub #Example 10/4

Add and/or subtract as indicated. Use a calculator if needed.

50% + 20% – 10%

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Example 10 · 0.percent-add-sub #Example 20/4

Add and/or subtract as indicated. Use a calculator if needed.

27.3% + 35.5% – 5%

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Example 11 · 0.percent-multiply #Example 10/6

Multiply

(3%)(5%)

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Example 12 · 0.percent-multiply #Example 20/5

Multiply

23.3% x 52.12%

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Example 13 · 0.compare-decimals #Example 10/4

Insert < or > between each pair of numbers to form a true statement.

0.0045 ___ 0.014

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Example 14 · 0.fraction #Example 10/5

1. Reduce the fraction $\frac{105}{120}$ to its simplest form.

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Example 15 · 0.fraction #Example 10/4

Subtract mentally. Do not show work.

1. $1 - \frac{3}{5}$

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Example 16 · 0.fraction #Example 10/5

Add and/or subtract as indicated

1. $\frac{5}{8} + \frac{7}{8}$

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Example 17 · 0.fraction #Example 20/4

Add and/or subtract as indicated

2. $\frac{9}{52} + \frac{7}{52} - \frac{1}{52}$

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Example 18 · 0.fraction #Example 10/7

Multiply

1. $\frac{5}{8} \times \frac{3}{49} \times \frac{7}{45}$

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Example 19 · 0.complement #Example 10/5

Find the complement of

1. Red

Use the figure on the right to answer the questions.

[Figure: Rectangular box with a thick black border containing three colored words: "Red" (in red) at upper left, "Blue" (in blue) at upper right, "Green" (in green) at lower left.]

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Example 20 · 0.complement #Example 20/5

Find the complement of

2. Red and Green

Use the figure on the right to answer the questions.

[Figure: Rectangular box with a thick black border containing three colored words: "Red" (in red) at upper left, "Blue" (in blue) at upper right, "Green" (in green) at lower left.]

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Example 21 · 0.divisibility #Example 10/4

1. Find all numbers which are divisible by 2.
A number is divisible by 2 if it ends with 0, 2, 4, 6, or 8.

Given a set of numbers {378900, 62, 4571, 81465, 288, 41334}

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Example 22 · 0.divisibility #Example 20/4

2. Find all numbers which are divisible by 5.
A number is divisible by 5 if it ends with 0, or 5

Given a set of numbers {378900, 62, 4571, 81465, 288, 41334}

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Example 23 · 0.divisibility #Example 30/4

3. Find all numbers which are divisible by 10.
A number is divisible by 10 if it ends with 0.

Given a set of numbers {378900, 62, 4571, 81465, 288, 41334}

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Example 24 · 0.divisibility #Example 10/4

1. Find all numbers which are divisible by 3.
A number is divisible by 3 if the sum of its digits divided by 3 evenly

Given a set of numbers {378900, 62, 4571, 81465, 288, 41334}

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Example 25 · 0.divisibility #Example 20/4

2. Find all numbers which are divisible by 9.
A number is divisible by 9 if the sum of its digits divided by 9 evenly

Given a set of numbers {378900, 62, 4571, 81465, 288, 41334}

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