Study Guide and Review - Rational Numbers
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1 Choose the correct term or number to complete the sentence is an example of a (terminating, repeating) decimal. Because the digits end, is a terminating decimal. terminating 2. A common denominator for the fractions and is (7, 12). Because it is a multiple of both 3 and 4, 12 is a common denominator for the fractions and To add like fractions, add the (numerators, denominators). When adding like fractions, add the numerators and write the result over the denominator. numerators 4. When dividing by a fraction, multiply by its (value, reciprocal). When dividing by a fraction, multiply by its multiplicative inverse, or reciprocal. reciprocal 5. Fractions with different denominators are called (like, unlike) fractions. Fractions with different denominators are called unlike fractions. unlike esolutions Manual - Powered by Cognero Page 1
2 6. The mixed number can be renamed as. can be renamed as because represents the same value as. 7. When multiplying fractions, multiply the numerators and (multiply, keep) the denominators. To multiply fractions, multiply the numerators and multiply the denominators. multiply 8. Fractions, terminating decimals, and repeating decimals are (integers, rational numbers). Rational numbers can be fractions, terminating decimals, and repeating decimals. rational numbers is expressed in (scientific notation, standard form). The number 3.16 is between 1 and 10. So, is expressed in scientific notation. scientific notation 10. The least common denominator for and is (4, 24) The least common denominator for 8 and 12 is 24 because 24 is the least number that is a multiple of both 8 and esolutions Manual - Powered by Cognero Page 2
3 Write the decimal as a fraction in simplest form The final digit, 7, is in the tenths place. So, 0.7 = The final digit, 4, is in the hundredths place. So, 0.44 = The final digit, 5, is in the hundredths place. So, 0.05 =. esolutions Manual - Powered by Cognero Page 3
4 14. RUNNING Jeremy ran a mile in 5 minutes and 8 seconds. Write this time in minutes as a decimal. Because there are 60 seconds in one minute, 5 minutes and 8 seconds can be represented by the mixed number. Think of the mixed number as a sum. Write as a decimal. So,. So, the time is. esolutions Manual - Powered by Cognero Page 4
5 Replace the with <, >, or = to make a true sentence % Write 37.5% as a fraction by first writing it as a decimal. The last digit is in the thousandths place. So, 37.5% is equal to. Find equivalent fractions. The LCD is 24. Since, then. < Write as a decimal. So, = Since 0.45 = 0.45, then 0.45 =. = esolutions Manual - Powered by Cognero Page 5
6 17. SCHOOL Michael received a on his English quiz and an 81% on his biology test. In which class did he receive the higher score? Compare and 81%. Write as a decimal. 18. = Write 81% as a decimal. 81% = 0.81 Since > 0.81, then > 81%. So, Michael received a higher score in English than in biology. English Add or subtract. Write in simplest form. esolutions Manual - Powered by Cognero Page 6
7 esolutions Manual - Powered by Cognero Page 7
8 22. Add or subtract. Write in simplest form. Rename using the LCD, Rename using the LCD, esolutions Manual - Powered by Cognero Page 8
9 24. RUNNING Teresa ran mile while Yolanda ran mile. By what fraction did Teresa run more than Yolanda? Subtract Yolanda s distance from Teresa s distance. Rename using the LCD, 12. So, Teresa ran mile more than Yolanda. 25. Add or subtract. Write in simplest form. 26. Since is less than, rename before subtracting. esolutions Manual - Powered by Cognero Page 9
10 27. Rename using the LCD, Rename using the LCD, 12. esolutions Manual - Powered by Cognero Page 10
11 29. BABYSITTING Lucas watched his little sister for hours on Friday, hours on Saturday, and hours on Sunday. For how many hours did Lucas watch his little sister? Find the sum of the hours Lucas spent watching his sister on Friday, Saturday, and Sunday. Rename using the LCD, 12. So, Lucas watched his sister for hours. 30. Multiply. Write in simplest form. esolutions Manual - Powered by Cognero Page 11
12 esolutions Manual - Powered by Cognero Page 12
13 FOOD An average slice of American cheese is about -inch thick. What is the height in simplest form of a package containing 20 slices? Multiply the thickness of one slice by the number of slices to find the height of the package. So, the height of a package containing 20 slices of cheese is inches. esolutions Manual - Powered by Cognero Page 13
14 35. COOKIES A cookie jar contains three types of cookies: oatmeal, chocolate chip, and sugar. Sixty percent are chocolate chip. Half of the remaining cookies are oatmeal. If there are 9 oatmeal cookies, how many cookies are in the jar? Use the draw a diagram strategy. 36. If sixty percent of the cookies are chocolate chip, then forty percent of the cookies are either oatmeal or sugar. If half of the remaining cookies are oatmeal, then twenty percent of all the cookies must be oatmeal and twenty percent must be sugar. If 9 oatmeal cookies make up twenty percent of the jar, then there are 45 cookies in the jar. 5 20% = 100% 5 9 cookies = 45 cookies 45 cookies Divide. Write in simplest form. Multiply by the reciprocal of. esolutions Manual - Powered by Cognero Page 14
15 37. Multiply by the reciprocal of Rename as. Multiply by the reciprocal of. esolutions Manual - Powered by Cognero Page 15
16 39. Multiply by the reciprocal of. 40. MEASUREMENT How many -inch lengths are in inches? Divide by. Rename as. Multiply by the reciprocal of. So, there are 54 -inch lengths in inches. 54 esolutions Manual - Powered by Cognero Page 16
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Name: Date: College Prep Math. Find two fractions equivalent to the following fraction. Enter the numerator. = = 5 5. Find the equivalent fraction with the indicated denominator. 8 9 = 6? 8 9 = 6. Find