Lesson 1: Arithmetic with Whole Numbers and Money

New Concept

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division. Each operation has specific vocabulary for the parts of an equation.

• Addition:
  $$\text{addend} + \text{addend} = \text{sum}$$
• Subtraction:
  $$\text{minuend} - \text{subtrahend} = \text{difference}$$
• Multiplication:
  $$\text{factor} \times \text{factor} = \text{product}$$
• Division:
  $$\frac{\text{dividend}}{\text{divisor}} = \text{quotient}$$

What’s next

Next, you'll apply these operations in worked examples with whole numbers and money. We will also begin evaluating expressions by substituting variables with numbers.

Property

A sequence is a list of terms arranged according to a certain rule.

Examples

The sequence $1, 3, 6, 10, ...$ increases by one more each time. The next term is $10 + 5 = 15$.
In the sequence $40, 35, 30, 25, ...$, the rule is to subtract 5. The next term is $25 - 5 = 20$.
The sequence $2, 6, 18, 54, ...$ follows the rule of multiplying by 3. The next term is $54 \times 3 = 162$.

Explanation

Imagine you are a detective cracking a code! A sequence is just a line of numbers following a secret rule. Your job is to figure out that pattern. Is it adding 2 each time, or maybe something trickier?

Property

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division.

Examples

In $12 + 8 = 20$, the addends are $12$ and $8$, and the sum is $20$.
In $25 - 10 = 15$, the minuend is $25$, the subtrahend is $10$, and the difference is $15$.
In $7 \times 6 = 42$, the factors are $7$ and $6$, and the product is $42$.

Explanation

Meet the fantastic four of math: Addition, Subtraction, Multiplication, and Division! Each one has its own special vocabulary. Addition builds things up (sum), subtraction takes things away (difference), multiplication is like super-fast adding (product), and division splits things into equal parts (quotient).

Property

In mathematics, letters are often used to represent numbers—in formulas and expressions, for example. The letters are called variables because their values are not constant; rather, they vary. We evaluate an expression by calculating its value when the variables are assigned specific numbers.

Examples

Evaluate $a + b$ for $a = 15$ and $b = 10$. We substitute to get $15 + 10 = 25$.
Evaluate $xy$ for $x = 8$ and $y = 5$. We substitute to get $8 \times 5 = 40$.
Evaluate $\frac{m}{n}$ for $m = 24$ and $n = 4$. We substitute to get $\frac{24}{4} = 6$.

Explanation

Variables are like secret agents in math, often represented by letters like x or y. They can stand for any number! To 'evaluate' an expression means you are given the secret code—the value for each variable. You just substitute the numbers in for the letters and solve the puzzle. It is like unlocking a secret message with the right key!