Chapter 1: Concepts

What is a Whole Number?

A whole number is any of the numbers 0, 1, 2, 3, .... Whole numbers are not negative, and do not have fractions or decimals.

Example: 0, 7, and 25 are whole numbers. -3 and 2.5 are not.

What is Place Value?

Place value tells you the value of each digit based on its position in the number.
For example, in 3,582:

Example: In 4,105, the 1 is in the hundreds place, so it's worth 100.

What is a Fraction?

A fraction shows part of a whole. It is written as a/b, where a is the number of parts you have and b is the total number of equal parts.

Example: If you have a pizza cut into 8 slices and eat 3, you have 3/8 of the pizza left.

What is a Decimal?

A decimal is another way to show part of a whole, using a decimal point. For example, 0.5 means "five tenths," and is the same as the fraction 1/2.

Example: 0.25 is the same as 1/4 (one quarter).

What is Absolute Value?

The absolute value of a number is its distance from zero on the number line. It is always positive or zero. For any number a, absolute value is written |a|.

Example: |7| = 7, |-7| = 7, |0| = 0
Is it correct to say "absolute value is to throw away the sign"?
Almost! The absolute value is the distance from zero, so it is never negative. For positive numbers and zero, it stays the same. For negative numbers, it becomes positive. It's better to say: absolute value is the distance from zero, never negative.

What is Distance?

Distance is how far apart two numbers or points are. On a number line, the distance between a and b is |a - b| (the absolute value of their difference).

Example: The distance between 3 and 8 is |3 - 8| = 5.

Chapter 2: Examples & Exercises

Place Value

Example: In 6,382:
- 6 is in the thousands place (6 × 1000 = 6000)
- 3 is in the hundreds place (3 × 100 = 300)
- 8 is in the tens place (8 × 10 = 80)
- 2 is in the ones place (2 × 1 = 2)
Exercise 1: In the number 4,205, what is the value of 2?
Exercise 2: In 8,074, what is the place value of 7?

Adding Whole Numbers

Example: Add 246 + 135
Add the ones 6 + 5 = 11 plus carry carry 1 write 1
Add the tens 4 + 3 = 7 plus carry 7 + 1 = 8 write 8
Add the hundreds 2 + 1 = 3 plus carry - write 3
Final Answer: 381
Exercise 1: What is 527 + 168?
Exercise 2: What is 304 + 691?

Subtracting Whole Numbers

Example: Subtract 654 - 289 Final Answer: 365
Exercise 1: What is 832 - 457?
Exercise 2: What is 500 - 157?

Estimating Sums and Differences

Example: Estimate 478 + 125
  1. Round 478 to 500, 125 to 100.
  2. 500 + 100 = 600
Estimated sum: 600
Exercise 1: Estimate 671 + 249 (round to nearest hundred).
Exercise 2: Estimate 388 - 163 (round to nearest hundred).

Multiplying Whole Numbers

Example: Multiply 23 × 14
  1. 23 × 4 = 92
  2. 23 × 10 = 230
  3. 92 + 230 = 322
Final Answer: 322
Exercise 1: What is 34 × 12?
Exercise 2: What is 56 × 7?

Estimating Products

Example: Estimate 29 × 6
  1. 29 rounds to 30
  2. 30 × 6 = 180
Estimated product: 180
Exercise 1: Estimate 47 × 8 (round 47 to nearest ten).
Exercise 2: Estimate 63 × 9 (round 63 to nearest ten).

Dividing Whole Numbers

Example: Divide 156 ÷ 12
12 )156
Final Answer: 13
Exercise 1: What is 144 ÷ 12?
Exercise 2: What is 225 ÷ 15?

Chapter 3: Pre-Test

40 Multiple Choice Questions

Chapter 4: Remedial Practice (Based on Your Pre-Test)

Take the pre-test in Chapter 3. Any question you answer incorrectly will appear here for you to review and retry.