2.2 Adding And Subtracting Rational Numbers
EnglishSpanish2.2Adding and SubtractingRational NumbersHow does adding and subtracting rationalSSTATESTANDARDSnumbers compare with adding and subtracting integers?MA.7.A.3.21ACTIVITY: Adding and Subtracting Rational NumbersWork with a partner. Use a number line to find the sum or difference.a. Sample: 2.7 ( 3.4)Start at 0. Move 2.7units to the right. 3 2Then move 3.4 unitsleft to end at 0.7.Add 3.4.2.7 10123So, 2.7 ( 3.4) 0.7.310( )910610310b. — —c. — 1—d. 1.3 ( 3.4)e. 1.9 0.82ACTIVITY: Adding and Subtracting Rational NumbersWork with a partner. Write the numerical expression shown on the numberline. Then find the sum or difference.a.Start at 0. Move 1.5units to the right. 3b. 2Then move1.5 11unit20Subtractleft to end at 2. 356Chapter 2Then move 2.3 unitsleft to end at 0.8.Add 2.3.1Rational Numbers and Equations3Start at 0. Move1.2 1 22 1121 units to the left.120123
EnglishSpanish3ACTIVITY: Financial LiteracyWork with a partner. The table shows the balance ina checkbook. Black numbers are amounts added to the account. Red numbers are amounts taken from the account.DateCheck #––––Previous .0034.571/06/2009Check deposit1/11/2009ATM withdrawal40.00Electric company78.43Music store10.55Shoes47.211/14/20091251/17/20091/18/2009 Transaction1261/20/2009Check 12Cell phone59.99You can find the balance in the second row two different ways.100.00 34.57 65.43Subtract 34.57 from 100.00.100.00 ( 34.57) 65.43Add 34.57 to 100.00.a. Copy the table. Then complete the balance column.b. How did you find the balance in the tenth row?c. Use a different way to find the balance in part (b).4. IN YOUR OWN WORDS How does adding and subtracting rational numberscompare with adding and subtracting integers? Give an example.PUZZLE Find a path through the table so that the numbers add up to the sum.You can move horizontally or vertically.346. Sum: 0.075. Sum: —Start12—18 —23—57 —34 —13—StartEnd2.431.75 0.98 1.093.47 4.88EndUse what you learned about adding and subtracting rationalnumbers to complete Exercises 7–9 and 16 –18 on page 60.Section 2.2Adding and Subtracting Rational Numbers57
EnglishSpanishLesson2.2Lesson TutorialsAdding and Subtracting Rational NumbersTo add or subtract rational numbers, use the same rules forsigns as you used for integers.WordsNumbers4 1 4 1 3— — — —5 5551316 2616 2 16 1616 — — — — — — —EXAMPLE1Adding Rational Numbers83568356Find — —.Study Tip8356Rewrite using the LCD (least common denominator). 16 56how — is written as 83 166 — — — —In Example 1, notice83Estimate 3 1 2Write the sum of the numeratorsover the like denominator. — 166 — — —. 11656 —, or 1 —56The sum is 1 —.EXAMPLE2Simplify.56Reasonable? 1 — 2 Adding Rational NumbersFind 4.05 7.62. 7.62 4.05 . So, subtract 4.05 from 7.62 . 4.05 7.62 3.57Use the sign of 7.62.The sum is 3.57.Add.Exercises 4 –1258Chapter 2781413203( )721. — —2. 6 — —3.2 —4. 12.5 15.35. 8.15 ( 4.3)6.0.65 ( 2.75)Rational Numbers and Equations
EnglishSpanishEXAMPLE3Subtracting Rational Numbers17( ) ( ) 467Find 4 — — .17 4 —67—Estimate 4 ( 1) 31767Add the opposite of —.29767Write the mixed numberas an improper fraction.67— — — — 23727 —, or 3 —27Simplify.Reasonable? 3 — 3 131427The difference is 3 —.Subtract.13( )137. — —EXAMPLE48.56 3 — —9.124— 5—Real-Life ApplicationIn the water, the bottom of a boat is 2.1 feet below the surface and thetop of the boat is 8.7 feet above it. Towed on a trailer, the bottom of theboat is 1.3 feet above the ground. Can the boat and trailer pass underthe bridge?Step 1: Find the height h of the boat.Clearance: 11 ft 8 in.h 8.7 ( 2.1)Subtract the lowest point from the highest point. 8.7 2.1Add the opposite of 2.1. 10.8Add.Step 2: Find the height t of the boat and trailer.t 10.8 1.3 12.1Add the trailer height to the boat height.Add.Because 12.1 feet is greater than 11 feet 8 inches, the boat andtrailer cannot pass under the bridge.Exercises 13–2110. WHAT IF? In Example 4, the clearance is 12 feet 1 inch.Can the boat and trailer pass under the bridge?Section 2.2Adding and Subtracting Rational Numbers59
EnglishSpanishExercises2.2Help with Homework1. WRITING Explain how to find the sum 8.46 5.31.122. OPEN-ENDED Write an addition expression using fractions that equals —.3. DIFFERENT WORDS, SAME QUESTION Which is different? Find “both” answers.Add 4.8 and 3.9.What is 3.9 less than 4.8?What is 4.8 increased by 3.9?Find the sum of 4.8 and 3.9.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Add. Write fractions in simplest form.12( )( )1112914561547125. — —8158. 4 1 —4. — —27( )237. 2 — —10. 3.1 ( 0.35)( )136. — 4 —9. 4.2 3.311. 12.48 ( 10.636)12. 20.25 ( 15.711)Subtract. Write fractions in simplest form.3( )5814784 13. — —11161214. — —5338( )5915. — —1616. 5 —17. 8 — 10 —18. 1 2.519. 5.5 8.120. 7.34 ( 5.51)21. 6.673 ( 8.29)22. ERROR ANALYSIS Describe and correctthe error in finding the difference. 34923 94 2 62— — — — 35623. SPORTS DRINK Your sports drink bottle is — full. After practice the bottle is38— full. Write the difference of the amounts after practice and before practice.24. BANKING Your bank account balance is 20.85. You deposit 15.50.What is your new balance?Evaluate.16( ) ( )837925. 2 — — 4 —60Chapter 226. 6.3 ( 7.8) ( 2.41)Rational Numbers and Equations125 136 ( )2327. — — 3 —
EnglishSpanish28. REASONING When is the difference of two decimals an integer? Explain.233429. RECIPE A cook has 2 — cups of flour. A recipe calls for 2 — cups of flour. Doesthe cook have enough flour? If not, how much more flour is needed?Springville30. ROADWAY A new road that connects Uniontown to13Springville is 4 — miles long. What is the change innew road3mi.8distance when using the new road instead of thedirt roads?Uniontown35mi.6RAINFALL In Exercises 31– 33, the bar graph shows the differences in rainfallfrom the historical average in Pensacola, Florida.31. What is the difference inrainfall between the wettestand driest months?Pensacola Monthly Rainfall4.0Rainfall (inches)232. Find the sum of the differencesfor the year.33. What does the sum in Exercise 32tell you about the rainfall forthe year?3.0Historical Average2.362.00.941.00.831.390.350 1.0 0.45 0.88 2.0 3.0 0.90 1.35 1.39 0.96 1.67Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonthALGEBRA Add or subtract. Write the answer in simplest form.3n85b8a336. 4a —38.2n8n835. — — —34. 4x 8x 6x( )2b337. — —Fill in the blanks to make the solution correct.5.Evaluate.4 (.8) 3.61SKILLS REVIEW HANDBOOK39. 5.2 6.940. 7.2 2.4231441. 2 — 3 —451242. 9 — 3 —43. MULTIPLE CHOICE A sports store has 116 soccer balls. Over 6 months, it sellseight soccer balls per month. How many soccer balls are in inventory at theend of the 6 months?SECTION 1.4SECTION 1.3A 48 B 48 Section 2.2C 68 D 108 Adding and Subtracting Rational Numbers61
2.2 Lesson 58 Chapter 2 Rational Numbers and Equations Adding and Subtracting Rational Numbers Words To add or subtract rational numbers, use the same rules for signs as you used for integers. Numbers 4 — 5 1 — 5 4 1 — 5 3 — 5 1 — 3 1 — — 6 2
Adding and Subtracting Fractions Objective 1: Adding or subtracting fractions with common denominators When adding or subtracting fractions, all you need to do is add or subtract the numerators if the denominators are the same. Example: Add or subtract. Remember to leave all fractions in lowe
Virginia Department of Education 2018 1 Mathematics Instructional Plan – Algebra I Adding and Subtracting Polynomials Using Algebra Tiles Strand: Expressions and Operations Topic: Adding and subtracting polynomials Primary SOL: A.2 The student will perform operations on polynomials, including b) adding, subtracting, multipl
Adding and Subtracting Rational Expressions Return to Table of Contents Slide 51 / 179 Just as in multiplication and division, when adding or subtracting rationals, use the same rules as basic fractions. Recall: When adding and subtracting fractions, you MUST use common denominators. Adding and
Adding and Subtracting Rational Expressions Add or subtract. Identify any x-values for which the expression is undefined. Example 1A: Adding and Subtracting Rational Expressions with Like Denominators Add the numerators. The expression is undefined at x –4 because this value makes
So adjust answer by adding 1. Answer is 81. 76 40 can be rounded to 80 40 40. 76 is 4 less than 80. So adjust answer by subtracting 4. Answer is 36. Regrouping is another mental math strategy for adding and subtracting numbers. Regroup numbers into 5s or 10s to make calculations
Adding Fractions with Unlike Denominators . 32 Adding Mixed Numbers with Like Denominators .34 Adding Mixed Numbers with Unlike Denominators .36 Subtracting Fractions with Like Denominators .38 Subtracting Fractions with Unlike Denominators .40 Subtracting Fractions from Whole Numbers .
Step 4: Since our fraction part now has equal sized slices, we can subtract their numerators. Subtracting their numerators we have, of a whole. Step 5: Combining our whole number and fraction parts we get, . Exercise 5: Subtract the fractions, Step 1: Subtracting the whole number part, we get Step 2: Subtra
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