**Divisibility Tests**

A number is divisible by:

2 if the last digit is 0, 2, 4, 6, or 8.

3 if the sum of the digits is divisible by 3.

5 if the last digit is 5 or 0.

6 if it is divisible by both 2 and 3.

10 if it ends with 0.**How to find the prime factorization of a composite number.**- Step 1. Find two factors whose product is the given number, and use these numbers to create two branches.
- Step 2. If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.
- Step 3. If a factor is not prime, write it as the product of two factors and continue the process.
- Step 4. Write the composite number as the product of all the circled primes.

**How To Find the least common multiple using the prime factors method.**- Step 1. Write each number as a product of primes.
- Step 2. List the primes of each number. Match primes vertically when possible.
- Step 3. Bring down the columns.
- Step 4. Multiply the factors.

**Equality Symbol**

a=ba=b is read “*a*is equal to*b*.”

The symbol “=” is called the equal sign.

**Inequality****Inequality Symbols**

**G**

anan means multiply*a*by itself,*n*times.

The expression anan is read*a*to the nthnth power.**Simplify an Expression**

To simplify an expression, do all operations in the expression.**How to use the order of operations.**- Step 1. Parentheses and Other Grouping Symbols
- Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.

- Step 2. Exponents
- Simplify all expressions with exponents.

- Step 3. Multiplication and Division
- Perform all multiplication and division in order from left to right. These operations have equal priority.

- Step 4. Addition and Subtraction
- Perform all addition and subtraction in order from left to right. These operations have equal priority.

- Step 1. Parentheses and Other Grouping Symbols
**How to combine like terms.**- Step 1. Identify like terms.
- Step 2. Rearrange the expression so like terms are together.
- Step 3. Add or subtract the coefficients and keep the same variable for each group of like terms.

**Figure 1.9**

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