Chapter 1: Positive and Negative Numbers

Positive and Negative Numbers

Addition

​Sum of two numbers with opposite sign

Process: Sum of the absolute value of the two numbers

Sign: Same as the two numbers

​Sum of two numbers with the same sign

Process: The difference when you subtract the smaller absolute value from the larger absolute value

Sign: Same sign as the number with the larger absolute value

Addition with positive and negative numbers is the same whether the are whole numbers, decimals, or fractions

Open Ended

Calculate: $$\left(+5.3\right)+\left(-2.3\right)$$

Open Ended

Calculate: $$\left(-0.4\right)+\left(-0.3\right)$$

Open Ended

Calculate: $$\left(-\frac{3}{7}\right)+\left(+\frac{2}{7}\right)$$

Open Ended

Calculate: $$\left(-\frac{4}{5}\right)+\left(-\frac{1}{5}\right)$$

Open Ended

Calculate: $$\left(-\frac{1}{3}\right)+\left(+\frac{1}{4}\right)$$

Open Ended

Calculate: $$\left(+\frac{1}{6}\right)+\left(-\frac{3}{10}\right)$$

​Laws of Addition

Example: 2+3 = 3+2

​Commutative Law: a+b = b+a

​Associative Law: (a+b)+c = a+(b+c)

Example: (2+3)+4 = 2+(3+4)

(5) + 4 = 2 + (7)

​These properties hold when negative numbers are involved as well.

Open Ended

Calculate and Compare the results of:

$$\left\{\left(+3\right)+\left(-4\right)\right\}+\left(-5\right)=?$$

and

$$\left(+3\right)+\left\{\left(-4\right)+\left(-5\right)\right\}=?$$

Open Ended

Calculate and Compare the results of:

$$\left\{\left(+3\right)+\left(-4\right)\right\}+\left(-5\right)=?$$

and

$$\left(-3\right)+\left\{\left(-4\right)+\left(-5\right)\right\}=?$$

​Subtraction

When subtracting with positive and negative numbers, you can ADD a number of the OPPOSITE SIGN instead of subtracting it.

Subtraction with positive and negative numbers is the same whether the are whole numbers, decimals, or fractions

Open Ended

Calculate:

$$\left(-1.6\right)-\left(+0.6\right)$$

Open Ended

Calculate:

$$\left(+3.5\right)-\left(-2.3\right)$$

Open Ended

Calculate:

$$\left(-\frac{1}{6}\right)-\left(-\frac{5}{6}\right)$$

Open Ended

Calculate:

$$\left(+\frac{1}{2}\right)-\left(-\frac{1}{3}\right)$$

Practice Problems p.27