Fractions and Decimals
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1 Math Success Reproducible Worksheets Reproducible Worksheets for: Fractions and Decimals These worksheets practice math concepts explained in Fractions and Decimals (ISBN ), written by Lucille Caron and Philip M. St. Jacques. Math Success reproducible worksheets are designed to help teachers, parents, and tutors use the books in the Math Success series in the classroom and home. Teachers, librarians, tutors, and parents are granted permission and encouraged to make photocopies of these worksheets. These worksheets are reproducible for educational use only and are not for resale Enslow Publishers, Inc. Visit and search for the Math Success series and download worksheets for the following titles: Addition and Subtraction Multiplication and Division Fractions and Decimals Percents and Ratios Geometry Pre Algebra and Algebra Titles in this series can be purchased directly from: Enslow Publishers, Inc. 40 Industrial Road, Box 398 Berkeley Heights, NJ Phone: customerservice@enslow.com Web Page:
2 Proper Fractions, Improper Fractions, and Mixed Numbers Pictorial Fractions Write the fraction for the following pictures. Example: 3 5 a. b. c. d. Mixed Numbers Change these mixed numbers to improper fractions. Example: e f g h i j k l ISBN , pages
3 Finding Equivalent Fractions Example: Equivalent Fractions Find an equivalent fraction for 1 2. Step 1: Choose any number you wish. Suppose you chose 9. Step 2: Multiply the numerator and denominator by Step 3: Write the equivalent fraction Write an equivalent fraction for each. a b c d e f g h Reducing Fractions to Lowest Terms Reduce each fraction by dividing by the greatest common factor Example: i. j k. l m. n o. 3 6 p ISBN , pages
4 Comparing Like Fractions Comparing and Ordering Fractions Example: 1 3 and 2 are like fractions; they have the same denominator. 3 To compare them, look at the numerators: 1 is less than 2, so 1 3 is less than 2 3. Compare the following fractions, using symbols,,. a b c Comparing Unlike Fractions Example: 2 5 and 1 are unlike fractions; they have different denominators , so Compare the following fractions, using symbols,,. d e ISBN , pages f g h i j k Ordering Fractions Order the following fractions from least to greatest. m. 2 5, 1 6, 3 n , 7 8, 3 4 l o., , 1 4 p. 3 8, 5, q. 1 2, r. 3 5, 7 8, 3 4
5 Renaming Fractions as Decimals 1 If a fraction has a denominator that can be changed to hundredths ( ), it can easily 100 be turned into a decimal (0.10). Example: Change these fractions to decimals. a b. 1 0 c. 1 4 d e. f You can also rename fractions as decimals by dividing the denominator into the numerator. Example: Change these fractions to decimals. g. 5 8 h i. 5 6 j. 1 3 k. 4 5 l. 1 7 m. 7 8 n. 9 4 o ISBN , pages
6 Adding Like Fractions Adding Like Fractions Add these fractions. Example: a b c d e f Adding Whole Numbers and Fractions Example: Add these numbers and fractions. g h i Adding Two Mixed Numbers Example: Add these mixed numbers. Reduce the answer, if necessary. j k l m Adding Mixed Numbers and Fractions Example: Add and reduce the answer to lowest terms n o p q ISBN , pages
7 Adding Unlike Fractions Example: Add and reduce the answer to lowest terms. a b c d e f g h i j k l ISBN , pages
8 Subtracting Like Fractions Example: Reduce to lowest terms Subtract. a c Subtracting a Fraction from a Whole Number b d Example: Subtract. e f g h. 6 i j Subtracting Two Mixed Numbers Example: Subtract. 3 2 k l m n o p ISBN , pages
9 Subtracting Two Mixed Numbers Example: Subtracting Unlike Fractions Subtract. 9 a b c d e f Subtracting a Fraction from a Mixed Number Example: Subtract. g h i j k l ISBN , pages
10 Multiplying Fractions and Mixed Numbers Multiplying Fractions Example: Multiply. Reduce the fractions, when you can, before multiplying. 2 1 a b c d e f Multiplying a Fraction and a Mixed Number Example: Multiply. g h i j k l Multiplying a Whole Number and a Mixed Number Example: Multiply. m n o p q r s t u ISBN , pages
11 Dividing Fractions and Mixed Numbers Dividing a Fraction by a Fraction Example: Divide. Reduce fractions, when you can, before multiplying. 1 2 a b c e d f g h Dividing a Whole Number by a Mixed Number Example: Divide. Remember to invert the divisor before multiplying. 6 1 i j k l m n o p ISBN , pages
12 Estimating Fractions Round each height to the nearest whole number. Height, ft. Compare the fractional part to 1 Round to nearest whole number 2 Example: a b c d e Estimate the weights of these five children. Weight, lbs. Compare the fractional part to 1 Round to nearest whole number 2 f g h i j k. What is the average weight of these five children? ISBN , pages
13 Fractions and Percents Changing a Fraction to a Percent There are a few ways to change a fraction to a percent. Example: Change 1 to a percent % 100% 50% ? % Change these fractions to percents. a. 1 4 b c. 1 0 d. 1 5 e. 3 8 f. 1 8 g. 4 5 h. 5 6 i. 7 8 j k. 1 0 l. 2 3 m. 3 4 n. 5 8 o. 2 5 p q. 1 0 r. 4 2 ISBN , pages
14 Fractions and Ratios Ratios compare two quantities, such as 10 chocolate cookies and 15 vanilla cookies. Fraction Words Colon to 15 10:15 Write a ratio three ways for the following comparisons. Fraction Words Colon a. 12 blondes and 15 brunettes b. 16 wins and 20 losses c. 5 triangles and 15 circles Write equal ratios for the following fractions. Example: d. 2 3 e. 3 4 f. 3 8 Finding the Ratio of Units of Measure Example: Find the ratio of 5 feet to 20 inches inches inches to 20 inches Reduce. 60 inches to 20 inches 3 to 1 Express the following units of measure as ratios. g. 4 feet to 8 inches h. 2 feet to 3 inches ISBN , pages
15 Reading and Writing Decimals PLACE VALUE Digit In Words Standard Form 9 ten thousands 90,000 1 thousands 1,000 3 hundreds tens 40 6 ones 6. decimal point. 5 tenths hundredths thousandths ten thousandths hundred thousandths Writing Decimals in Words Example: eighty-nine thousandths a b c d Writing Decimals Example: twenty-five hundredths 0.25 e. sixty-two hundredths f. four and fifteen thousandths g. twelve and two hundredths h. seventeen and four tenths ISBN , pages
16 Comparing and Ordering Decimals Comparing Decimals Example: Compare and 15.6 Line up the decimal points Add zeros to give each number the same number of digits Compare. a b c d e f Ordering Decimals Order the numbers from least to greatest. Example: 3.102, 6.92, 3.12, and g. 1.65, 1.076, 2.101, 3.22 h. 2.9, 2.019, 1.999, 1.85 i. 6.66, 6.162, 6.006, 6.4 ISBN , pages
17 Rounding Decimals Example: Round to the nearest tenth The number to the right of the tenth s place is 5 or greater, so rounds to Round to the nearest tenth. a b c d e f g h i j k l Rounding Money to the Nearest Dollar Example: Round $19.34 to the nearest dollar (ones place). $ is less than 5 so $19.34 rounds to $19.00 Round to the nearest dollar (ones place). m. $16.42 n. $36.75 o. $45.10 p. $18.38 q. $72.63 r. $28.56 s. $94.49 t. $ u. $31.63 ISBN , pages
18 Example: 125 1,000 Renaming Decimals as Fractions Write as a fraction. The digit farthest to the right of the decimal point (5) will tell you what the denominator should be. 5 is in the thousandths place, so the denominator is 1, , Change these decimals to fractions. a. 0.6 b c d e f Renaming a Mixed Decimal as a Mixed Number Example: Write 17.6 as a mixed number or g. 2.5 h i j k l m n o ISBN , pages
19 Adding Decimals Example: Add a b c d Adding Whole Numbers and Mixed Decimals Example: Add e f g h ISBN , pages
20 Subtracting Decimal Fractions Example: Subtracting Decimals Subtract. a. 0.9 b. 0.2 c. 0.7 d. 0.8 e Subtracting a Mixed Decimal and a Decimal Fraction Example: Subtract. f. 6.8 g. 7.2 h. 8.9 i. 4.7 j Subtracting a Mixed Decimal and a Whole Number Example: k l m n o p ISBN , pages
21 Subtracting Decimals with Regrouping Subtracting Mixed Decimal Numbers Example: Check by Adding Subtract. Check your answer with addition. Check a b Check c d e f g h i j ISBN , pages
22 Multiplying Decimals Multiplying a Whole Number by a Decimal When you multiply decimal numbers you do not have to line up the decimal points. Example: one decimal place in example 3.5 one decimal place in answer Multiply. a. 6 b. 8 c. 4 d. 7 e Multiplying a Mixed Decimal by a Decimal Fraction Example: decimal place decimal places decimal places in answer (Always count from right to left.) Multiply. f. 7.4 g. 4.3 h. 8.1 i j k l m n. 9.7 o p q ISBN , pages
23 Dividing Decimals Dividing a Decimal by a Whole Number Example: Divide. a b c d e f Dividing Two Whole Numbers.5 Example: Divide. g h i ISBN , pages
24 Dividing Two Decimal Fractions Examples: Divide. Always move the decimal point first and place the decimal point in the answer. a b c d e f g h i ISBN , page
25 Multiplying and Dividing Decimals by Powers of Ten Multiply by a power of ten. Move the decimal to the right. Example 10 1 place places ,000 3 places ,000 2,780 Divide by a power of ten. Move the decimal to the left. Example 10 1 place places ,000 3 places , Multiply each by 10, 100, and 1,000. Example: ,000 4,400 a b c Divide each by 10, 100, and 1,000. Example: , a b c ISBN , pages
26 Estimating with Decimals Methods Used to Estimate Sums A. By rounding to the greatest place of the larger number: ² estimated sum B. By rounding to the greatest place of the smaller number: ² estimated sum C. By rounding to a specified decimal place, such as hundredths: ² estimated sum Round to the greatest place value and add to find the estimated sum. a b c Round to the nearest hundredths place and subtract to find the estimated difference. d e f Round to the nearest tenth and multiply to find the estimated product. g h i Round to the greatest place value of the smaller number and divide to find the estimated quotient. j k l m ISBN , pages
27 Repeating and Terminating Decimals Terminating Decimals Example: Change 1 to a decimal If the remainder is 0, the answer is 8 called a terminating decimal Changing a mixed number to a decimal: Change the following fractions to decimals. a. 1 5 b c. 3 4 d Example: Change to a decimal Write this answer The bar above shows that 18 repeats Change the following fractions to decimals. e. 1 3 f g. 2 9 h ISBN , pages
28 Renaming Repeating Decimals as Fractions Repeating decimal Multiply Place answer over 9 Reduce , Rename these repeating decimals as fractions. Reduce your answer to lowest terms. a b. 0.3 c d e f g h ISBN , pages
29 Changing a Decimal to a Percent Example: Decimals and Percents Change 0.07 to a percent. Multiply by 100% % 7% Change these decimal numbers to percents. a b c d e f g h i j k l m n o p q r s t ISBN , pages
30 Fractions and Decimals Answers Proper Fractions, Improper Fractions, and Mixed Numbers, page 2 a. 3 6 ; b. 3 ; c ; d. 5 ; e ; f. 7 7 ; g. 2 2 ; h. 3 2 ; i. 8 5 ; j. 4 9 ; k. 7 1 ; l Equivalent Fractions, page 3 Finding equivalent fractions: a. 2; b. 36; c. 36; d. 6; e. 20; f. 6; g. 15; h. 24 Reducing to lowest terms: i. 2 3 ; j. 1 3 ; k. 1 6 ; l. 3 7 ; m. 2 5 ; n. 3 5 ; o. 1 8 ; p Comparing and Ordering Fractions, page 4 a. <; b. >; c. <; d. <; e. <; f. >; g. >; h. >; i. ; j. >; k. ; l. <; m. 1 6, 3, ; n. 2 3, 3 4, 7 8 ; o. 1 4, 5, ; p. 5, , 2 3 ; q. 1, , 1 2 ; r. 3 5, 3 4, 7 8 Renaming Fractions as Decimals, page 5 a. 0.50; b. 0.30; c. 0.25; d. 0.60; e. 0.08; f. 0.02; g ; h. 0.20; i ; j ; k. 0.80; l ; m ; n. 0.90; o Adding Like Fractions, page 6 a. 5 8 ; b. 3 5 ; c. 4 9 ; d. 6 7 ; e. 5 6 ; f. 1 0 ; g ; h ; i ; j ; k ; l ; m ; n ; o ; p ; q Adding Unlike Fractions, page 7 a ; b. 10 ; c ; d ; e ; f. 6 ; g. 8 ; h ; i ; j ; 30 k ; l Subtracting Like Fractions, page 8 a. 1 2 ; b. 2 3 ; c. 1 2 ; d. 1 6 ; e ; f ; g ; h. 5 1 ; i ; j ; k ; l ; m ; n. 2 5 ; o ; p Subtracting Unlike Fractions, page a. 18 ; b. 11 ; c. 18 ; d. 7 ; e. 9 ; f. 5 ; g. 5 ; h. 3 ; i. 9 ; j. 2 ; k. 20 ; l
31 Multiplying Fractions and Mixed Numbers, page 10 1 a. ; b ; c. 2 7 ; d. 1 4 ; e. 4 7 ; f. 2 3 ; g. 2 3 ; h ; i ; j. 1 9 ; k. 3; l ; m ; n ; o ; p. 11; q ; r ; s ; t. 20; u Dividing Fractions and Mixed Numbers, page 11 a. 7 9 ; b. 1 3 ; c. 3 5 ; d. 4 7 ; e. 1 2 ; f ; g. 1 0 ; h ; i ; j ; k ; l. 2 2 ; m. 5; 3 n. 3 ; o. 16; p Estimating Fractions, page 12 a. 5; b. 5; c. 4; d. 6; e. 5; f. 96; g. 86; h. 108; i. 110; j. 90; k. 98 pounds Fractions and Percents, page 13 a. 25%; b. 150%; c. 30%; d. 20%; e %; f %; g. 80%; h %; i %; j. 125%; k. 90%; l %; m. 75%; n %; o. 40%; p. 120%; q. 70%; r. 200% 2 Fractions and Ratios, page 14 a. 1 2, 12 to 15, 12:15; b , 16 to 20, 16:20; c., 5 to 15, 5:15; d , 6 9, 8 ; e , 9, ; f.,, 1 2 ; g. 6 to 1; h. 8 to Reading and Writing Decimals, page 15 a. two and two hundredths; b. sixteen thousandths; c. four and one hundredth; d. fifty-three hundredths; e. 0.62; f ; g ; h Comparing and Ordering Decimals, page 16 a. ; b. ; c. ; d. ; e. ; f. ; g , 1.65, 2.101, 3.22; h , 1.999, 2.019, 2.9; i , 6.162, 6.4, 6.66 Rounding Decimals, page 17 a. 64.2; b. 17.4; c ; d ; e ; f ; g ; h ; i. 12.2; j ; k ; l ; m. $16.00; n. $37.00; o. $45.00; p. $18.00; q. $73.00; r. $29.00; s. $94.00; t. $126.00; u. $32.00 Renaming Decimals as Fractions, page 18 a. 3 5 ; b. 1 4 ; c. 3 ; d ; e. 2 5 ; f. 3 8 ; g ; h ; i ; j ; k. 23 ; l. 8 ; m ; n ; o Adding Decimals, page 19 a. 4.05; b. 7.86; c. 9.72; d ; e ; f ; g ; h
32 Subtracting Decimals, page 20 a. 0.7; b. 0.1; c. 0.3; d. 0.5; e. 0.3; f. 6.6; g. 7.1; h. 8.5; i. 4.4; j. 0.1; k. 2.15; l ; m. 6.46; n ; o ; p Subtracting Decimals with Regrouping, page 21 a ; b ; c ; d. 66.9; e ; f ; g. 28.7; h ; i. 86.5; j Multiplying Decimals, page 22 a. 2.4; b. 4.8; c. 3.6; d. 5.6; e. 1.8; f ; g ; h ; i ; j ; k ; l ; m ; n ; o ; p ; q Dividing Decimals, page 23 a. 2.2; b. 2.4; c. 27.8; d. 61.4; e. 30.4; f. 12.9; g. 0.6; h. 0.2; i. 0.8 Dividing Two Decimal Fractions, page 24 a ; b. 20; c. 290; d. 45.5; e. 4.6; f. 36; g. 1.3; h. 22.4; i. 3.5 Multiplying and Dividing Decimals by Powers of Ten, page 25 a. 35.6, 356, 3560; b. 826, 8260, 82,600; c , 67,235, 672,350; d , , ; e. 8.26, 0.826, ; f , , Estimating with Decimals, page 26 a. 5; b. 70; c. 40; d. 3.48; e. 5.96; f. 9.24; g ; h. 0.74; i ; j. 2; k. 6; l. 7; m. 2 Repeating and Terminating Decimals, page 27 a. 0.20; b. 3.25; c. 0.75; d. 1.75; e. 0.33; f. 6.66; g. 0.22; h Renaming Repeating Decimals as Fractions, page 28 2 a. 1 1 ; b. 1 3 ; c. 82 ; d ; e ; f. 4 9 ; g. 1 9 ; h Decimals and Percents, page 29 a. 16%; b. 16.2%; c. 75%; d. 81.5%; e. 23.8%; f. 7.2%; g. 10%; h. 12.5%; i. 8%; j. 0.7%; k. 42%; l. 1.6%; m. 10.6%; n. 90%; o. 73%; p. 5%; q. 11.1%; r. 9%; s. 6.3%; t. 87% 32
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