6 2 Addition Subtraction and Estimation with Rational

6 -2 Addition, Subtraction, and Estimation with Rational Numbers Students will be able to understand explain • Addition of rational numbers with like and unlike denominators. • Rational numbers as mixed numbers. • Subtraction of rational numbers with like and unlike denominators. • Properties of addition and subtraction of rational numbers. • Addition properties of equality. • Estimation with rational numbers. ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 1

Addition of Rational Numbers (1 of 2) Area model ALWAYS LEARNING Copyright © 2020,

Addition of Rational Numbers (2 of 2) Number-line model ALWAYS LEARNING Copyright © 2020,

Addition of Rational Numbers with Like Denominators If are rational numbers, then ALWAYS LEARNING

Addition of Rational Numbers with Unlike Denominators If are rational numbers, then ALWAYS LEARNING

Example 6 (1 of 3) Find each of the following sums. a. b. ALWAYS

Example 6 (2 of 3) c. d. ALWAYS LEARNING Copyright © 2020, 2016, 2013

Example 6 (3 of 3) e. ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson

$Mixed Numbers that are made up of an integer and a fractional part of$

Mixed Numbers that are made up of an integer and a fractional part of an integer. A mixed number is a rational number, and therefore, it can always be written in the form ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 9

Example 7 Change each of the following mixed numbers to the form where a

Example 8 Change to a mixed number. ALWAYS LEARNING Copyright © 2020, 2016, 2013

Properties of Addition for Rational Numbers (1 of 3) Additive Inverse Property For any rational number there exists a unique called the additive inverse of such that ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 12

Properties of Addition for Rational Numbers (2 of 3) Properties of the additive inverse for rational numbers are analogous to those of the additive inverse for integers. ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 13

Properties of Addition for Rational Numbers (3 of 3) Addition Property of Equality If and are any rational numbers such that is any rational number, then ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 14

Subtraction of Rational Numbers If are any rational numbers, then is the unique rational

Subtraction of Rational Numbers If are any rational numbers, then ALWAYS LEARNING Copyright ©

Example 10 Find each difference. a. b. ALWAYS LEARNING Copyright © 2020, 2016, 2013

Example 11 Add or subtract, writing your answers in simplest form. a. b. ALWAYS

Estimation with Rational Numbers Many of the estimation and mental math techniques that are used with whole numbers also work with rational numbers. Estimation plays an important role in judging the reasonableness of computations. ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 19

Example 12 A sixth-grade class is collecting cans to take to the recycling center. Becky’s group brought the following amounts (in pounds). About how many pounds does her group have all together? Use front-end estimation and then adjust by using 0, and 1 as reference points. ALWAYS LEARNING Copyright © 2020, 2016, 2013 Pearson Education, Inc. 20