# Basic Algebra/Introduction to Basic Algebra Ideas/Working With Negative Numbers

Positive
Negative

## Lesson

### Negative Numbers

A positive number is a number more than zero.

A negative number is a number less than zero. You make a negative number by doing the negative operation on a positive number. You use the " – " sign for the negative operation. This sign is the same you use for subtracting.

Adding a negative number is the same as subtracting a positive number.

• $7 + (-4) = 7 - 4$
• $x + (-y) = x - y$

Subtracting a negative number is the same as adding a positive number.

• $7 - (-4) = 7 + 4$
• $x - (-y) = x + y$

### Multiplying and Dividing

Multiplying a negative number by a positive number, or a positive number by a negative number makes the answer negative.

• $-2 \times 3 = -6$
• $2 \times -3 = -6$

Multiplying a negative number by a negative number makes the answer positive.

• $-2 \times -3 = 6$

You do the same for dividing.

• $-6 \div 3 = -2$
• $6 \div -3 = -2$
• $-6 \div -3 = 2$

### Exponentiating

Exponentiating a negative number to an even (a number you can divide by two) power makes a positive answer.

• $(-3)^2 = 9$
• $(-x)^2 = x \times x = x^2$

Exponentiating a negative number to an odd (a number you can not divide by two) power makes a negative answer.

• $(-2)^3 = -8$
• $(-x)^3 = -x \times -x \times -x = x^2 \times -x = -x^3$

### Order of Operations

The negative operation has the same precedence as multiplying and dividing.

• $3 + 8 \div 4 = 3 + 2 = 5$
• $-3^2 = -(3 \times 3) = -9$
• $(-3)^2 = -3 \times -3 = 9$

## Example Problems

1. $4 + (-4) = 0$
2. $4 + (-7) = -3$
3. $0 + (-2) = -2$
4. $-5 + 7 - 2 \times (-4) = 10$

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## Practice Problems

1. $6 + (-3) =$
2. $3 + (-9) =$
3. $-4 \times 4 =$
4. $4 \times (-9) =$
5. $-2 \times (-4) =$
6. $\frac{-25}{5^2} =$
7. $-4 \div 2=$
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