How can you use what you know about adding integers to add rational numbers? ACTIVITY: Adding Rational Numbers

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1 . How can you use what you know about adding integers to add rational numbers? ACTIVITY: Work with a partner. Use a number line to find the sum. a.. +.) Start at 0. Move. units to the right. Add... Then move. units left to end at So,. +.) =. b.. +.) c d. + e ) ACTIVITY: COMMON CORE Rational Numbers In this lesson, you will add rational numbers. solve real-life problems. Learning Standards.NS.a.NS.b.NS.d.NS. Work with a partner. Use a number line to find the sum. a. + ) Then move unit left to end at. Add. So, + ) =. Start at 0. Move units to the left. 0 b ) c. + d ) e ) ) 0 Chapter Rational Numbers

2 ACTIVITY: Writing Expressions Math Practice Use Operations What operation is represented in each number line? How does this help you write an expression? Work with a partner. Write the addition expression shown. Then find the sum. a. b. Then move units 0 right to end at. Start at 0. Move. units to the right. 0 Add. 0 Add... Then move. units left to end at Start at 0. Move 0 units to the left. 0 c. Then move 0. unit left to end at. Add 0... Start at 0. Move. units to the left. 0. IN YOUR OWN WORDS How can you use what you know about adding integers to add rational numbers? PUZZLE Find a path through the table so that the numbers add up to the sum. You can move horizontally or vertically.. Sum:. Sum: 0.0 Start Start End End Use what you learned about adding rational numbers to complete Exercises on page. Section.

3 . Lesson Lesson Tutorials Words To add rational numbers, use the same rules for signs as you used for integers. Numbers + = + = + = = Study Tip EXAMPLE In Example, notice how 8 is written as 8 = 8 =. Find 8 +. Estimate + = 8 + = + = + = = Rewrite using the LCD least common denominator). Write the sum of the numerators over the common denominator. Add. Write the improper fraction as a mixed number. The sum is. Reasonable? EXAMPLE Find =.. >.0. So, subtract.0 from.. Use the sign of.. The sum is.. Exercises Add ) ) ) Chapter Rational Numbers

4 EXAMPLE Evaluating Expressions Evaluate x + y when x = and y =. x + y = ) + ) Substitute for x and for y. = + ) Multiply. = + ) = Simplify. Write the sum of the numerators over the common denominator. EXAMPLE Year Profit billions of dollars) Real-Life Application The table shows the annual profits in billions of dollars) of a financial company from 008 to 0. Positive numbers represent gains, and negative numbers represent losses. Which statement describes the profit over the five-year period? A gain of $0. billion B gain of $0 million C loss of $ million D loss of $00 million To determine whether there was a gain or a loss, find the sum of the profits. five-year profit =. +.) Write the sum. = ) Comm. Prop. of Add. = 0 +.) Additive Inv. Prop. = Add. Prop. of Zero =.9 +. Add. and 0.8. = 0. Add.9 and.. The five-year profit is $0. billion. So, the company has a five-year loss of $0. billion, or $00 million. The correct answer is D. Exercises Evaluate the expression when a = and b =.. b + a 8. a + b 9. WHAT IF? In Example, the 0 profit is $.0 billion. State the company s gain or loss over the six-year period in millions of dollars. Section.

5 . Exercises Help with Homework. WRITING Explain how to find the sum OPEN-ENDED Write an addition expression using fractions that equals.. DIFFERENT WORDS, SAME QUESTION Which is different? Find both answers. Add. and.. What is the distance between. and.? What is. increased by.? Find the sum of. and.. 9+-)= +-)= +-9)= 9+-)= Add. Write fractions in simplest form.. + ) ) ) 9. + ) ) ) ) ERROR ANALYSIS Describe and correct the error in finding the sum ) = + 8 = 8 = 0. Evaluate the expression when x = and y =.. x + y. x + y. x + y 8. BANKING Your bank account balance is $0.8. You deposit $.0. What is your new balance? 9. HOT DOGS You eat of a pack of hot dogs. 0 Your friend eats of the pack of hot dogs. What fraction of the pack of hot dogs do you and your friend eat? Chapter Rational Numbers

6 Add. Write fractions in simplest form ) + 8). + + ) ) +.. NUMBER SENSE When is the sum of two negative mixed numbers an integer?. WRITING You are adding two rational numbers with different signs. How can you tell if the sum will be positive, negative, or zero? June July August 8 9. RESERVOIR The table at the left shows the water level in inches) of a reservoir for three months compared to the yearly average. Is the water level for the three-month period greater than or less than the yearly average? Explain.. BREAK EVEN The table at the right shows the annual profits in thousands of dollars) of a county fair from 008 to 0. What must the 0 profit be in hundreds of dollars) to break even over the five-year period?. REASONING Is a + b = a + b for all rational numbers a and b? Explain. Year Profit thousands of dollars) ? 8. Repeated Reasoning Evaluate the expression ) ) ) ) + 0 Identify the property. Then simplify. Skills Review Handbook) ) + = ) 0.. 9) =.) ) = + ) + 8. =. MULTIPLE CHOICE The regular price of a photo album is $8. You have a coupon for % off. How much is the discount? Skills Review Handbook) A $.0 B $ C $ D $.0 Section.