1-6 Real numbers and rational numbers Objective: Compare and order rational numbers; evaluate expressions with rational numbers. Mr. Pugh– algebra 1 A

Warm up Evaluate 4n3 ÷m for m=-4, n=3

Put examples in the venn diagram

(Expressed in decimal form it is definitions A rational number is any number you can write in the form of a ratio (or fraction). 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 All numbers on a number line

Examples (Think & Discuss) Write 3 numbers that are rational numbers but not integers. Show that 0.75 is a rational number by writing it as a ratio. Where have you used irrational numbers?

When you compare two real numbers, only one of these can be true: comparing When you compare two real numbers, only one of these can be true: a < b or a = b or a > b less than equal to greater than

Rewrite the answer using the symbol for less than Example Use a number line to compare − 1 8 and − 1 2 Rewrite the answer using the symbol for less than

example Evaluate a + 2b where a = 2 3 and b = − 5 8

example Use the expression 5/9(F - 32) = C to change from the Fahrenheit scale to the Celsius scale. What is 10 degrees in Celsius?

definition The reciprocal, or multiplicative inverse, of a rational number 𝑎 𝑏 is 𝑏 𝑎 . Zero does not have a reciprocal because division by zero is undefined. Ex: What is the reciprocal of 2 3 ? What is the reciprocal of 3?

Complete the chart Number Reciprocal Product 3 = _____ 5 - ½ What is the product of a number and its reciprocal?

𝑥 𝑦 =𝑥 ÷𝑦 example Evaluate 𝑥 𝑦 for x = − 3 4 and y = − 5 2

Pg 32–33 #1-19 odd, 25, 27, 36 No work? No credit! homework Pg 32–33 #1-19 odd, 25, 27, 36 No work? No credit!