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7RUNIT 2Rational NumbersName: ____________________Teacher: __________________Period: ______Lesson 1 – Introduction to DecimalsAim: I can round decimal numbers and identify place values.Warm up:1. In your own words, what is a rational number?2. Fill in the place value in the appropriate space:9 , 4 7 2 , 3 4 0 . 2 3 9 8A. Use the given decimal to answer the following questions: 743.12561. Which digit is in the hundreds place?__________2. Which digit is in the tens place? __________3. Which digit is in the ones place? __________4. Which digit is in the tenths place? __________5. Which digit is in the hundredths place? __________6. Which digit is in the thousandths place? __________7. Which digit is in the ten-thousandths place? __________Rounding Rules:1. Underline the place value you are rounding.2. Form a box around the place value you are rounding to and all numbers that come before that place value.2. Draw an arrow to the number after the place value you are rounding to.3. If the number after the place value you are rounding to is 5 or HIGHER, round UP.4. If the number after the place value you are rounding to is LESS THAN 5, the numbers stays the SAME.Rounding Rules:1. Underline the place value you are rounding.2. Form a box around the place value you are rounding to and all numbers that come before that place value.2. Draw an arrow to the number after the place value you are rounding to.3. If the number after the place value you are rounding to is 5 or HIGHER, round UP.4. If the number after the place value you are rounding to is LESS THAN 5, the numbers stays the SAME.Round to the nearest tenth. 2,453.27 = 2.453.3B. Guided Practice:Round the following decimals to the nearest tenth:1. 3.192. 4.9213. 5.9094. 89.9855. 12.487Round the following decimals to the nearest hundredth:6. 3.2977. 8.92948. 75.9899. 8.49510. 18.783Round the following decimals to the nearest thousandth:11. 3.297812. 2.423413. 52.009114. 18.123615. 21.7253C. Problem SetRound the following decimals to the nearest tenth:6. 5.4797. 72.1348. 41.2959. 9.98710. 1.05Round the following decimals to the nearest hundredth:6. 6.7547. 9.9878. 67.3339. 28.54510. 19.296Round the following decimals to the nearest thousandth:6. 0.00087. 8.06128. 14.11299. 63.986710. 7.0054Lesson 1 – Introduction to DecimalsHOMEWORKRound the following decimals to the nearest tenth:1. 2.682. 7.2343. 12.3574. 55.0215. 17.145Round the following decimals to the nearest hundredth:6. 5.2287. 30.1898. 78.9729. 24.29010. 7.895Round the following decimals to the nearest thousandth:11. 0.444412. 10.075713. 45.230514. 20.103315. 9.7001Round to the nearest whole number: 16. 5.542 17.33.27618. 107.89Lesson 2 – Adding, Subtracting, Multiplying, & Dividing DecimalsAim: I can add, subtract, multiply and divide decimal numbers.Warm up:Use the given decimal to answer the following questions:4,657.38921. Which digit is in the hundreds place?__________2. Which digit is in the tens place? __________3. Which digit is in the ones place? __________4. Which digit is in the tenths place? __________5. Which digit is in the hundredths place? __________6. Which digit is in the thousandths place? __________7. Which digit is in the ten-thousandths place? __________A. Vocabulary Review:Sum: ________________________________________________________________________________Difference: ___________________________________________________________________________Product: _____________________________________________________________________________Quotient: _____________________________________________________________________________ Rules for Adding and Subtracting Decimals1. Neatly line up the Decimals2. Add zeros as place markers, if necessary3. Add or SubtractB. Find the sum or difference.1) 2.132) 0.133) 6.575 + 0.4__ + 3.87 - 2.82 4) 195.62 – 35.15) 12.6 + 2.7 + 100.676) 9.001 – (-2.4)7) 16.2 + 24.98) 9.4 – 4.089) 3.8 + 10.5 + 1.2 + 710) A serving of popcorn contains 0.005 g of sodium. If butter adds .116 g of sodium and salt adds 0.5 g, how much sodium is in a serving of popcorn with butter and salt?Rules for Multiplying Decimals1. Ignore the decimals 2. Multiply the given numbers as if they were whole numbers3. Count the amount of places after the decimal in each number4. Move the decimal the number of places you counted from the right C. Find the product.1) 1.02 × 3.62) -58 ×2.63) -4.15( -2.1)4) (2.6)(0.45) 5) (2.15)(1.5)6) (0.91)(2.7)Rules for Dividing Decimals1. Rewrite each problem as long division2. Change the outside number to a whole number3. Move the inside decimal the same amount of places as the outside number4. Divide the two numbers as whole numbers to find the quotient5. Write the decimal UP into the answerD. Find the quotient.1) 3.12 ÷ 2.62) 19.2 ÷ -3.23) -10.8 ÷ -2.74) 300755) 3007.56) 3000.75Lesson 2 – Adding, Subtracting, Multiplying, & Dividing DecimalsHOMEWORKFind the sum or difference.1) 4.6 + 8.79 2) - 8.7 – 2.03 3) 14.8 + 29.07 4) 14.5 – 8.3 5) 8.9 + 2.14 + 7.1 6) 5.002 – -4.3Find the product.7) 4.6 × 3.98) (-1.8)(0.7)9) (2.1)(3.1)Find the quotient.10) 4.85 ÷ 0.111) 57.4 ÷0.712) -4.74-0.06Apply what you’ve learned to a real-world scenario.13) An apple costs $.60. How much will it cost to purchase a dozen apples?14) Nina and three friends ate lunch at the cafe. They decided to split the bill evenly. The total bill was $17.84. How much was each person's share?15) Alicia paid $1.32 for a bag of potato chips. The potato chips cost $0.55 per pound. How much does the bag of potato chips weigh?Lesson 3 – Introduction to FractionsAim: I can simplify and determine equivalent fractions.Warm up: Label the fraction parts:25463503810______________________________________________A. Equivalent fractions (multiply by “1”)5(2)8(2) = 1016Find the missing numbers.1) 23= 102) 710= 1003) 67= 544) 330= 605) 09= 366) 712= 427) 19= 98) 821= 639) 45= 10010) 28= 36B. Simplify fractions (divide the numerator and denominator by the GCF). 12 ÷(4)20 ÷(4) = 35Simplify each fraction.1) 915= 32) 832= 43) 1720= 174) 5664= 85) 1248= 16) 1525= 37) 612= 28) 1232= 89) 25100= 110) 1317= 17C. Problem SetWrite two equivalent fractions to each given fraction (Multiply or Divide): 1) 24= 2) 68= 3) 1248= 4) 915= 5) 17= 6) 1620= Compare these fractions using <, >, or =.Rules:1. Write each fraction with a common denominator2. Compare the numerators1) 6 7 47 2) 4 8 16323) 2 3 344) 19 32 2132 5) 45 910 6) 1 4 15Apply what you’ve learned to a real-world scenario.1) John has 40 bolts in his toolbox. 12 of them are brass. What fraction of the bolts are brass? Write the answer as a simplified fraction.2) There are 60 washers in John's toolbox. 48 of them are zinc-plated. What fraction of the washers are zinc-plated? Write the answer as a simplified fraction.3) John owns a bolt that has a length of 34 in. Give 3 equal measures for the length of the bolt.Lesson 3 – Introduction to FractionsHOMEWORKFind the missing numbers:1) 27= 122) 610= 503) 2025= 1004) 39= 215) 07= 566) 46= 327) 111= 1218) 77= 709) 1220= 4010) 59= 36Simplify each fraction:11) 336= 112) 710= 1013) 1624= 214) 1535= 715) 10100= 1016) 1420= 717) 80100= 5 18) 1248= 119) 3640= 1020) 19= 9Write three equivalent fractions to each given fraction:21) 2025= 22) 18= 23) 79=24) 45= 25) 816= 26) 512=Compare these fractions using <, >, or = :27) 4 9 59 28) 1 2 13 29) 2 3 81230) 16 17 1717 31) 11 12 5560 32) 13 14 67Lesson 4 – Adding and Subtracting FractionsAim: I can add and subtract fractions.Warm up: Order the following fractions from least to greatest: 25 , 14 , 310Rules for Adding and Subtracting Fractions1. Write each fraction with a common denominator2. Add or Subtract the numerators3. Keep the common denominator4. If possible, simply the answer into lowest termsA. Guided Practice.Add.1) 512 + 1122) 25 + 353) 516 + 5164) 34 + 1205) 35 + 171) 39 + 292) 18 + 1103) 19 + 234) 14 + 585) 512 + 815Subtract.1) 35- 252) 712- 1123) 510- 5104) 23- 145) 78- 3161) 58- 382) 12- 133) 49- 164) 89- 495) 35- 17Rules for Converting Improper Fractions to Mixed Numbers1: Divide the numerator by the denominator. 2: The number of times your numerator can be divided into equally becomes your whole number.3: Your remainder becomes your new numerator and your denominator stays the same. 127 = 1 57Convert each improper fraction into a mixed number.1. 154 = 2. 204 = 3. 127 = 4. 358 = 5. -73 = 6. 9-4 = 7. -43 = 8. -64 = Rules for Converting Mixed Numbers into Improper Fractions 1. Multiply your denominator by your whole number.2. Add the product to the numerator.3. Place your final answer over the original denominator.345 = 195Problem Set: – Turn the following mixed numbers into an improper fraction.1. 1232. 2243. -3134. -2145. -3126. -435Lesson 4 – Adding and Subtracting FractionsHOMEWORKPerform the given operation.1) 14+ 15162) 23+ 123) 59+ 13+ 564) 7+ 11165) 218+ 9786) 412+ 3167) 15 678) 10 9109) 41112- 134 - 837 - 311010) 34+ 2311) 910+ 78+ 3512) 7516+ 3143) 1145+ 5614) 12 3415) 91720- 45 - 512Lesson 5 – Multiplying FractionsAim: I can multiply fractions.Warm up: Add and Subtract fractions (remember Integer rules): 1) 310 -(-25 )2) -57 -15 3) 24 -1520A. Multiplying Fractions What is 138?3 ?929792124257Think of pizzas. 100266516510-2857545720138 is one pizza and 3 eighths of another pizza1002665304165-28575333375First, convert the mixed fraction, 138 , to an improper fraction, 118 .Cut the whole pizza into eighths and how many eighths do you have in total?________________________________________________Now multiply that by 3.-2857542545100266513335138?3= 118?3=You have _______!100266512700-2857541910And lastly, convert to a mixed number!-2857543815100266514605Rules for Multiplying Fractions1. Convert each mixed number into an improper fraction2. Simplify/ Reduce vertically3. Simplify/ Reduce diagonally4. Multiply across5. If possible, convert back to a mixed numberB. Guided practice.1) 12 × 142) 15 ? 3103) -45 × 584) 38 ? 495) -25 × -15166) 3?14*7) 2?12*8) 56? 65*What do you notice about both of the products in #’s 5 & 6 ? _______________________________________________*What property does this illustrate? _____________________________________________________C. Apply: 1) What is 12 of 40? 2) What is 23 of 60? 3) David allows 13 hour per pound to cook the roast. How long will it take to cook a 412 – pound roast?Lesson 5 – Multiplying FractionsHOMEWORKSolve. Write all answers in simplest form.1a. 12 ? 21b. 13 ? 31c. 8 ? 181d. Explain how questions 1a - 1c are similar.1e. What property does this illustrate?Solve. Write all answers in simplest from.2) 16 ? -23) -34 ? -164) 45 25) -512 ? 26) -235 ? -1167) 23 ? -1458) 12 39) 315 ? -21410) 413 ? 12311) 6 ? 1312) 123 ×- 1213) 10 × 41514) 217 × 21315) 25 × 334Lesson 6 – Dividing Fractions and Complex FractionsAim: I can divide and simplify complex fractions.Warm up: What property is illustrated below? 34?43=1 ______________________________ The ______________________________________________ Property states that __________________________ _____________________________________________________________________________________________________________A. VocabularyComplex Fraction: _______________________________________________________________________Reciprocal: ______________________________________________________________________________Find the reciprocal of each number.1.352. 673. 5234. -2175. 10 12 35B. Complex FractionsWhen working with complex fractions, what we want to do first is get rid of the denominator, so we can work the problem easier.?=56 12 35 53 53 We can use the multiplicative inverse property to make ?the value of the denominator equal to 1.You might also recall that whatever we do to the fraction’s denominator, we must also do to its numerator, so as not to change the overall fraction “value”.Here’s what happened…Multiplying the numerator and denominator of our complex fraction by 35 , allowed us to use the Rule: When dividing fractions we can just _______________________ the numerator by the _________________________ of the denominator!multiplicative inverse property to eliminate the denominator. Without our helpful rule, we would have to use all of the steps above every time we wanted to divide fractions. The rule for dividing fractions saves us a lot of steps!Rules for Dividing Fractions1. Convert each mixed number into an improper fraction2. Change the operation from division to multiplication 3. Flip the second fraction4. Continue the problem using the multiplication rulesDivide.1) 12 ÷ 142) 310 ÷ 153) 38 ÷ 7164) -23 ÷ 565) 316 ÷ 5126) -79 ÷-77) 37 ÷ 378) -5 ÷ 359) 9 ÷ 21410) 2 112 ÷ 334Rules for Dividing and Simplifying Complex Fractions "Keep. Change. Flip."1. Convert any Mixed Number into an Improper Fraction2. Keep the top fraction as is3. Change the operation from division to multiplication 4. Flip the bottom fraction next to the first fraction5. Continue the problem using the multiplication rulesSimplify. 1) 32810 2) 253 3) -14564) -34 43 5) -32-810 6) 6212Lesson 6 – Dividing Fractions and Complex FractionsHOMEWORK1) 38 ÷ 672) -67 ÷ 383) 12 ÷ 7164) -45 ÷ -295) 25 ÷ 256) 3423 7) 2543 8) -165129) -25 -85 10) 31825 11) 1313812) -614 21213) 18 + 110 35 14) 23 + 19 45 + 815Lesson 7 – Converting Between Fractions and DecimalsAim: I can convert a fraction into a decimal and a decimal into a fraction.Warm up: Multiply or Divide.1) 513×6 342) -413 ? -2233) 414 ÷778Types of FractionsExample1. _______________________________________________2. _______________________________________________3. _______________________________________________Types of DecimalsExample1. _______________________________________________2. _______________________________________________3. _______________________________________________Fractions to Remember14= .25 12= .5 34= .75 15= .2 25= .4 35= .6 45= .813= .3 23= .6 18= .125 38= .375 58= .625 78= .87519= .129= .249= .459= .579= .789= .8110= .1210= .2310= .3410= .4510= .5610= .6710= .7810= .8910= .91010= 1A. Converting Fractions to Decimals: Divide the denominator into the numerator.1) 142) 493) 3254) 4895) 2786) 195B. Converting Decimals to Fractions or Mixed Numbers.Determine what place the decimal goes to (tenth, hundredth, thousandth, etc.)Write the number in the numerator of a fraction with the place value in the denominatorSimplify if possible1) 0.752) 0.93) 2.1254) 0.2345) 3.26) 0.8757) 0.48) 3.99) 0.4510) The Mets won 77 out of 162 games in the 2011 regular season. a) Express this as a fraction.b) Convert the fraction to a decimal (round to the nearest hundredth).Lesson 7 – Converting Between Fractions and DecimalsHOMEWORKConvert each fraction or mixed number to a decimal (round to the nearest hundredth if necessary):1. 192. 783. 354. 2495. 3186. 757. 5118. 2379. 47Convert each decimal to a fraction or mixed number:13. 0.514. 0.9115. 0.1516. 0.2317. 0.25118. 0.62519. 0.220. 3.0521. 0.36Classify each of the following rational numbers as terminating or repeating decimals.22.78 _____________________23.23 _____________________Lesson 8 – Compare and Order Rational NumbersAim: I can compare and order rational numbers.Warm up: The Yankees won 97 out of 162 games in the 2011 regular season. [a] Express this as a fraction.[b] Convert the fraction to a decimal (round to the nearest hundredth).A. Ordering Rational Numbers from Least to GreatestMethod 1Convert all numbers to decimals (all to the same place value).Compare and Order. ex: 310 , 14 , 38 , 0.5 , 0.7Method 2Convert all numbers to fractions with a common pare and Order.ex: 310 , 14 , 38 , 0.5 , 0.7Compare1. 0.6 0.525 2. 34 383. 0.8 1720 4. 358 3.6255. -0.25 - 0.2 6. -45 -797. 0.5 1120 8. 478 3.9Order the given set of numbers from least to greatest.1. 710 , -18 , 0.25 , 0.9 2. 58 , -34 , 138 , 1.25 , -1.13. 13 , 52 , 0.6 , 0.64. 35 , -14 , -34 , πPlot the given set of numbers on the number line.1. 710 , -18 , 0.25 , 0.9 2. 258 , -14 , -114 , 0.25 , -1.75Lesson 8 – Compare and Order Rational NumbersHOMEWORKCompare.1. 0.7 0.60 2. 320 7403. 0.4 920 4. 314 3.35. -0.5 -0.7 6. -49 -597. 0.7 1520 8. 618 6.129. 0.4 0.4 10. -312 -1411. -0.75 -0.7 12. 419 4.5Order the given set of numbers from least to greatest:13. 34 , -18 , -0.5 , 0.1 14. 78 , -54 , 538 , -1115. 25 , 45 , -25, 35 16. 75 , 115 , -56 , πPlot the given set of numbers which are from #13 and #14 above on the number line:17. 34 , -18 , -0.5 , 0.1 18. 78 , -54 , 538 , -11Lesson 9 – Using the CalculatorAim: I can use a calculator to some fraction problems.Warm up:Ricardo, Emily, and Cara participated in a Quiz Bowl. Ricardo answered 11 questions and got 8 correct. Emily answered 25 questions and got 18 correct. Cara answered 18 questions and got 13 correct. For each contestant, write the fraction of the questions that he or she answered correctly. Then write each fraction as a decimal.RicardoFraction: _______Decimal: ________EmilyFraction: _______Decimal: ________CaraFraction: _______Decimal: ________**Which contestant answered the greatest fraction of their questions correctly? ____________Solve the following using your calculator:1) 16+23=2) 0.98 - 6.3=3) 514-223=4) 9.65 ×78.54=5) -310 ÷ 413= 6) 918?225=Convert the following into a mixed number using your calculator:7) 166=8) -2235= 9) -65425=Convert the following into an improper fraction using your calculator:10) 217=11) -8514=12) -2245=Use your calculator to solve:13) Mrs. Kurka’s family went for a trip. To make the journey interesting, they traveled the first 5314 miles by car and the remaining 1023 miles by horse. What was the total distance of the trip?14) 47 of birthday cake was eaten on your birthday. The next day your dad ate half of what was left. You get to finish the cake. How much was left?15) The recipe for mint chocolate chip ice cream requires 2.25 cups of cream for 5 people. You need ice cream for 10 people. How much cream will you need?16) One parking lot at MetLife Stadium will hold 1000 vehicles. At 10:00 there were 400 cars and some trucks in the parking lot. The parking lot was 34 full. How many trucks were in the parking lot?Lesson 9 – Using the CalculatorHOMEWORKSolve the following using your calculator:1) 15+27=2) 94110+(-1538)=3) 64.6 ×-93.1=4) -1215×14=5) -849 ÷ -237= 6) 1057×-269=Convert the following into a mixed number using your calculator:7) 258= 8) -38716=9) -6763Use your calculator to solve.10) Vincent ordered pizza for him and his wife for dinner. When they had finished, they realized that 58 of the pizza was gone. For lunch the next day, Vincent decided to eat 14 of what was left. How much was left after lunch?11) Ms. Renalds decided to participate in a triathlon. She first had to run 4.5 miles. Next, she swam 3.25 miles and then finished the remaining 15.75 miles by bike. What was the total distance of the triathlon?12) Mr. Manning was baking brownies. His recipe called for 3 12 cups of melted chocolate to make enough brownies for 24 people. He is having 72 people over for his birthday. How much chocolate will he need?Name: _______________________________________Period: __________7R Unit 2 Review SheetRound the following decimals to the:nearest tenth:nearest hundredth:nearest whole number: 18.1286 2) 2.42343) 3.2978Write each fraction or mixed number as a decimal.4) QUOTE 23 5) QUOTE 15 6) Write each decimal as a fraction.7) .68) .459) 4.3Replace with <, >, or =.10) QUOTE 45 11) .35 QUOTE 13 12) 5.1 Order the set of rational numbers from least to greatest. Graph on the number line.13) QUOTE 1 6 , 3.8, , 0.7514) 63, 1.5, 213, 438 Graph on the number line. Graph on the number line. 0 1 2 3 4 1 2 3 4 5Convert the following into a mixed number or an improper fraction:15) 213 16) 16517) 656Find the sum or difference:18) 4.1 + 2.9 19) -12.8 + 320) 12.362 – (-3.41)Find the product: 21) (4.3)(1.45) 22) (6.3)(-7.4)23) (-13.1)(-2.6)Find the quotient:24) 15.8 2 25) -220.426) 12.152.7Find each sum or difference:27) 14+3628) 712-1329) 35-1330) 3310-(-135)31) 4-231032) -312+-413Find each product or quotient:33) 58? 2534) 38 ÷ 2335) 234536) 356? 21437) 3 35 ÷ 11538) 6335 39) What is 34 of 24?Word Problems:40) Monica had 18 cookies. If Monica ate 16 of the cookies after dinner, how many cookies were left?41) Joe made two types of desserts. He used 23 cups of sugar for one recipe and 14 cups of sugar for the other recipe. How much sugar did he use in all?42) Six cases of paper cost $43.50. How much does one case cost? Unit 2 Vocabulary:Sum: ____________________________________________Simplify: __________________________Difference: _______________________________________Convert: ___________________________Product: _________________________________________LCD: _____________________________Quotient: ________________________________________Complex Fraction: ___________________Numerator: ____________________________________________________________________Denominator: _____________________________________Reciprocal: _______________________________________Improper Fraction: _________________________________Mixed Number: ___________________________________ ................
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