1-6 real numbers and rational numbers miss battaglia – algebra 1 cp objective: compare and order...

1-6 R

EAL NUMBERS A

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NAL NUMBERS

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WARM UP

Evaluate 4n3 ÷ m for m = - 4, n = 3

PUT EXAMPLES IN THE VENN DIAGRAM

DEFINITIONS

A rational number is any number you can write in the form of a ratio, like or

An irrational number cannot be written as a ratio of two numbers, like or .

(Expressed in decimal form it is

a decimal that goes on forever

with no pattern).

DEFINITIONS

Integers are rational numbers because you can write them as ratios using 1 as the denominator.

Rational and irrational numbers make up the set of real numbers ( )

EXAMPLES (THINK & DISCUSS)

1)Write 3 numbers that are rational numbers but not integers.

2)Show that 0.75 is a rational number by writing it as a ratio.

3)Where have you used irrational numbers?

COMPARING

When you compare two real numbers, only one of these can be

true:

a < bor a = b or a > b less than equal to

greater than

EXAMPLE

Use a number line to compare and

Rewrite the answer

using the symbol for less than

EXAMPLE

Evaluate a + 2b where a = and b =

EXAMPLE

Use the expression (5/9)(F – 32) to change from the Fahrenheit scale to the Celsius scale. What is 10o F in Celsius?

DEFINITION

The reciprocal, or multiplicative inverse, of a rational number is .

Zero does not have a reciprocal because division by zero is undefined.

Ex: What is the reciprocal of ? What is the reciprocal of 3?

COMPLETE THE CHART

Number Reciprocal Product

3

.4

-1/2

What is the product of a number and its reciprocal?

EXAMPLE

Evaluate x/y for x = -3/4 and y = -5/2

𝑥𝑦

=𝑥÷ 𝑦

HOMEWORK

Pg 32–33 #2–26 even, 30, 35, 37, 41