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Name: ________________________ Class: ___________________ Date: __________ ID: A Fractions Short Answer 1. Write the decimal 2.47 as a fraction or mixed number. 2. Write the number 7 as a decimal. 8 3. Order the fractions and decimals from least to greatest. 0.88, 0.6, 4 5 6 4. Find two equivalent fractions for 14 . 5. Find the missing number that makes the fractions equivalent. 7 8 70 = ? 6. Write the fraction 2 8 in simplest form. 7. Compare the fractions. Write <, >, or =. 2 2 6 9 8. Mary Ann needs 3 1 9. Order 7 , 4 , and 10. Kunio used 19 3 1 3 5 8 cup of sugar to bake a cake. She has 1 4 cup. Will that be enough? Prove it. from least to greatest. gallons of paint to paint the outside of his house. Write 1 19 3 as a mixed number. 1 11. Annie used 8 2 yards of fabric to make new curtains. Write 8 2 as an improper fraction. 2 12. Write 5 3 as an improper fraction. 13. Peter surveyed his friends and family to see what they like to drink with breakfast. He found that people like to drink grapefruit juice and 3 8 1 8 of the of them like to drink orange juice. The rest prefer either milk or coffee. What part of the people surveyed prefer grapefruit or orange juice with breakfast? Write your answer in simplest form. 14. Subtract, and write the answer in simplest form. 3 3 13 – 2 13 19 15. Evaluate the expression for n = 1 20 . Write the answer in simplest form. n– 1 20 1 Name: ________________________ ID: A 7 16. Multiply 2 • 9 . Write the answer as a mixed number in simplest form, if necessary. 1 17. Evaluate 5n for n = 3 . Write the answer as a mixed number in simplest form, if necessary. 18. A farmer collected 24 eggs from his henhouse one morning, and 2 3 of the eggs were brown. How many brown eggs were there? 19. The Reynolds family saw 48 butterflies at an exhibit, and 2 3 of them were Monarch butterflies. How many of the butterflies were Monarchs? 20. Multiply the following fractions, and simplify if possible. 2 • 3 5 8 21. Evaluate the expression x • 2 5 4 for x = 9 . 22. Multiply the following fractions, and simplify if possible. 1 17 × 7 9 23. Multiply the following mixed numbers, and simplify if possible. 3 1 14 × 32 3 24. What is the reciprocal of 1 4 ? 25. Divide, and simplify if possible. 4 1 15 ÷ 13 2 ID: A Fractions Answer Section SHORT ANSWER 1. ANS: 47 2 100 If there is a number to the left of the decimal, write that as the whole number. Write the decimal part as a fraction over 100, and simplify. REF: Page 167 OBJ: 4-4.1 Writing Decimals as Fractions or Mixed Numbers STO: 1.03 TOP: 4-4 Decimals and Fractions KEY: decimal, fraction, mixed number NOT: /A/ Should the digits after the decimal point be the denominator?/B/ Correct! /C/ Is this an exact answer, or did you round to just one decimal place? /D/ Are you sure about the whole number part of the answer? 2. ANS: 0.875 To write a mixed number as a decimal, keep the whole number, and divide the numerator by the denominator for the part to the right of the decimal point. REF: Page 168 OBJ: 4-4.2 Writing Fractions as Decimals STO: 1.03 TOP: 4-4 Decimals and Fractions KEY: fraction, decimal NOT: /A/ Should you add all of the digits? /B/ How do you write a fraction as a decimal? /C/ Should you multiply all of the digits?/D/ Correct! 3. ANS: 4 0.6, 5 , 0.88 Write all of the numbers as decimals with the same number of places. Order the numbers from least to greatest by comparing the digits from left to right. REF: Page 168 OBJ: 4-4.3 Comparing and Ordering Fractions and Decimals STO: 1.03 TOP: 4-4 Decimals and Fractions KEY: fraction, decimal, compare, order NOT: a/ Correct! /b/ Did you write each of the numbers as a decimal with the same number of places so you could compare them? /c/ Does the problem ask for the numbers to be ordered from greatest to least? /d/ Did you write each of the numbers as a decimal before trying to compare them? 4. ANS: 3 7 and 12 28 Multiply or divide the numerator and denominator by the same nonzero number. REF: Page 172 OBJ: 4-5.1 Finding Equivalent Fractions STO: 1.03 TOP: 4-5 Equivalent Fractions KEY: equivalent fraction NOT: /A/ Correct! /B/ Did you multiply or divide both the numerator and denominator by the same number? /C/ Did you confuse the numerator and denominator by inverting the fractions?/D/ Are these two fractions equal to each other? 1 ID: A 5. ANS: 80 Multiply both the numerator and the denominator of the first fraction by the same number to obtain the second fraction. REF: Page 172 OBJ: 4-5.2 Multiplying and Dividing to Find Equivalent Fractions STO: 1.03 TOP: 4-5 Equivalent Fractions KEY: fraction, equivalent fraction, multiplication, division NOT: /A/ Can this number be the same as it was in the first fraction if the other number has changed? /B/ Did you find the factor used to obtain the other number in the new fraction? Use it to find this number as well. /C/ Did you multiply both the numerator and denominator by the same number to obtain the second fraction?/D/ Correct! 6. ANS: 1 4 If the GCF of both the numerator and the denominator is 1, then the fraction is already in simplest form. Otherwise, divide the numerator and denominator by the GCF to simplify it. REF: Page 173 OBJ: 4-5.3 Writing Fractions in Simplest Form STO: 1.03 TOP: 4-5 Equivalent Fractions KEY: fraction, simplest form NOT: /A/ Did you divide the numerator by the same number you used to simplify the denominator? /B/ Did you divide the denominator by the same number you used to simplify the numerator? /C/ Correct! /D/ This fraction is equivalent, but is it the simplest form? 7. ANS: > Compare the two fractions. Be sure to first write them with common denominators if they are unlike fractions. REF: Page 178 OBJ: 4-6.1 Comparing Like Fractions STO: 1.03 TOP: 4-6 Comparing and Ordering Fractions KEY: fraction, like fraction, compare NOT: /A/ Correct! /B/ Did you write the fractions with common denominators and compare the numerators? /C/ Did you write the fractions with common denominators and compare the numerators? 8. ANS: no Write the fractions with a common denominator and then compare the fractions. REF: STO: KEY: NOT: Page 179 OBJ: 4-6.2 Application: Compare and Order Fractions 1.03 TOP: 4-6 Comparing and Ordering Fractions fraction, compare, order /A/ Did you write the fractions with a common denominator to compare them?/B/ Correct! 2 ID: A 9. ANS: 1 1 , 3, 4 First write the fractions so that they have a common denominator. Then order them from least to greatest by comparing the numerators. REF: Page 179 OBJ: 4-6.3 Ordering Fractions STO: 1.03 TOP: 4-6 Comparing and Ordering Fractions KEY: fraction, order NOT: /A/ Correct! /B/ Did you compare the numerators of the fractions after writing them with common denominators? /C/ Did you write the fractions with common denominators to compare them? /D/ Did you put the fractions in order from least to greatest? 10. ANS: 1 63 Divide the numerator by the denominator. To form the fractional part of the quotient, use the remainder as the numerator and the divisor as the denominator. Or use a model to find the answer. REF: Page 182 OBJ: 4-7.1 Application: Write Improper Fractions as Mixed Numbers and Mixed Numbers as Improper Fractions STO: 1.03 TOP: 4-7 Mixed Numbers and Improper Fractions KEY: improper fraction, mixed number NOT: /A/ Did you double-check your calculations? Is the whole number correct?/B/ Correct! /C/ Do you remember that the fraction bar means "divided by"? /D/ Did you use the correct numerator to perform your calculations? 11. ANS: 17 2 Multiply the whole number by the denominator. Then add the numerator and write this sum over the denominator. Or use a model to find the answer. REF: Page 182 OBJ: 4-7.1 Application: Write Improper Fractions as Mixed Numbers and Mixed Numbers as Improper Fractions STO: 1.03 TOP: 4-7 Mixed Numbers and Improper Fractions KEY: improper fraction, mixed number NOT: /A/ Should you write the whole number in the numerator? /B/ Should the answer be the reciprocal of the given fraction?/C/ Did you double-check your calculations? /D/ Correct! 12. ANS: 17 3 Multiply the denominator by the whole number, and then add the numerator. Write the result over the denominator. Or use a model to find the answer. REF: Page 183 OBJ: 4-7.2 Writing Mixed Numbers as Improper Fractions STO: 1.03 TOP: 4-7 Mixed Numbers and Improper Fractions KEY: improper fraction, mixed number NOT: /A/ Correct! /B/ Did you add when you should have multiplied? /C/ How do you find the numerator of the improper fraction?/D/ Should you add the whole number and the numerator to find the numerator of the improper fraction? 3 ID: A 13. ANS: 1 2 Since the fractions have a common denominator, just add the numerators and simplify if necessary. REF: Page 188 OBJ: 4-8.1 Application: Add or Subtract Fractions with Like Denominators STO: 1.04 TOP: 4-8 Adding and Subtracting with Like Denominators KEY: fraction, addition, subtraction, like denominators NOT: /A/ Correct! /B/ Did you subtract instead of adding? /C/ Did you remember to add the numerators and keep the denominator? /D/ Did you remember to add the numerators? Should you add the denominators together? 14. ANS: 1 3 13 Subtract the numerators of the fractions and write the result over the common denominator. Then subtract the whole numbers, and simplify if necessary. REF: Page 188 OBJ: 4-8.2 Subtracting Like Fractions and Mixed Numbers STO: 1.04, 5.02 TOP: 4-8 Adding and Subtracting with Like Denominators KEY: fraction, like fraction, mixed number, subtraction NOT: /A/ Did you remember the rules for subtracting fractions? Subtract the numerators and keep the denominator. /B/ Correct! /C/ Did you subtract the fractions or add them? /D/ Did you remember that you keep the common denominator when subtracting fractions? 15. ANS: 9 1 10 Substitute for the variable, add or subtract the numerators, and write the result over the common denominator. When applicable add the whole numbers. Reduce if necessary. REF: Page 189 OBJ: 4-8.3 Evaluating Expressions with Fractions STO: 1.04 TOP: 4-8 Adding and Subtracting with Like Denominators KEY: fraction, expression NOT: /A/ Correct! /B/ Did you perform the correct operation? Also, what do you do with the denominator when adding and subtracting fractions?/C/ Did you subtract the fractions or add them? /D/ Do you remember the rules for adding and subtracting fractions? 16. ANS: 5 19 Write the whole number as a fraction. Multiply numerators and denominators. Write the answer in simplest form. REF: Page 192 OBJ: 4-9.1 Multiplying Fractions and Whole Numbers STO: 1.04 TOP: 4-9 Multiplying Fractions by Whole Numbers KEY: fraction, multiplication NOT: /A/ Correct! /B/ Did you multiply the whole number by the numerator, or did you add them together? /C/ Did you write the whole number as a fraction over 1 and then multiply the numerators and the denominators? /D/ Did you multiply the whole number by the fraction, or did you add them together? 4 ID: A 17. ANS: 2 13 Substitute for the variable. Write the whole number as a fraction. Multiply numerators and denominators. Write the answer in simplest form. REF: Page 192 OBJ: 4-9.2 Evaluating Fraction Expressions STO: 5.02 TOP: 4-9 Multiplying Fractions by Whole Numbers KEY: fraction, expression NOT: /A/ Did you multiply the whole number by the numerator, or did you add them together? /B/ Correct! /C/ Did you multiply the whole number by the fraction, or did you add them together?/D/ Did you write the whole number as a fraction over 1 and then multiply the numerators and the denominators? 18. ANS: 16 Multiply the fraction by the whole number by writing the whole number over 1 and then multiplying the numerators and the denominators. Simplify if possible. REF: Page 193 OBJ: 4-9.3 Application: Multiply Fractions by Whole Numbers STO: 1.04 TOP: 4-9 Multiplying Fractions by Whole Numbers KEY: fraction, multiplication NOT: /A/ Did you subtract the numerator from the whole number instead of multiplying them? /B/ Did you write the whole number as a fraction over 1 and then multiply the numerators and the denominators? /C/ Did you double-check your calculations?/D/ Correct! 19. ANS: 32 Multiply the fraction by the whole number by writing the whole number over 1 and then multiplying the numerators and the denominators. Simplify if possible. REF: Page 193 OBJ: 4-9.3 Application: Multiply Fractions by Whole Numbers STO: 1.04 TOP: 4-9 Multiplying Fractions by Whole Numbers KEY: fraction, multiplication NOT: /A/ Did you double-check your calculations?/B/ Did you write the whole number as a fraction over 1 and then multiply the numerators and the denominators? /C/ Why did you subtract the numerator from the whole number instead of multiplying them? /D/ Correct! 20. ANS: 5 12 Multiply the fractions by multiplying the numerators and multiplying the denominators, and then simplify if possible. REF: Page 212 OBJ: 5-1.1 Multiplying Fractions STO: 1.04 TOP: 5-1 Multiplying Fractions KEY: fraction, multiplication NOT: /A/ Are you supposed to be dividing the fractions?/B/ Are you supposed to be adding the fractions? /C/ Is this how you multiply fractions? /D/ Correct! 5 ID: A 21. ANS: 8 45 Multiply the fractions by multiplying the numerators and multiplying the denominators, and then simplify if possible. REF: Page 213 OBJ: 5-1.2 Evaluating Fraction Expressions STO: 5.02 TOP: 5-1 Multiplying Fractions KEY: fraction, expression, evaluate NOT: /A/ Correct! /B/ Is this how you multiply fractions? /C/ Are you supposed to be dividing the fractions?/D/ Are you supposed to be adding the fractions? 22. ANS: 8 9 First write any mixed numbers as improper fractions, and then multiply the numerators and multiply the denominators. Simplify if possible. REF: Page 216 OBJ: 5-2.1 Multiplying Fractions and Mixed Numbers STO: 1.04 TOP: 5-2 Multiplying Mixed Numbers KEY: fraction, mixed number, multiplication NOT: /A/ Are you supposed to be adding the fractions? /B/ Are you performing the correct operation?/C/ Is this how you multiply fractions? /D/ Correct! 23. ANS: 1 68 First write the mixed numbers as improper fractions, and then multiply the numerators and multiply the denominators. Simplify if possible. REF: Page 217 OBJ: 5-2.2 Multiplying Mixed Numbers STO: 1.04 TOP: 5-2 Multiplying Mixed Numbers KEY: mixed number, multiplication NOT: /A/ Is this how you multiply fractions? /B/ Correct! /C/ Are you supposed to be adding the fractions? /D/ Are you performing the correct operation? 24. ANS: 4 7 A number multiplied by its reciprocal equals 1. REF: Page 222 OBJ: 5-3.1 Finding Reciprocals STO: 1.04 TOP: 5-3 Dividing Fractions and Mixed Numbers KEY: reciprocal, fraction NOT: /A/ Did you calculate the reciprocal properly?/B/ Does this multiplied by the original number equal 1? /C/ Correct! /D/ Is your math correct? 6 ID: A 25. ANS: 7 1 20 To divide fractions, first write any mixed numbers as improper fractions, and then multiply the first fraction by the reciprocal of the second fraction. Simplify if possible. REF: Page 223 OBJ: 5-3.2 Using Reciprocals to Divide Fractions and Mixed Numbers STO: 1.04 TOP: 5-3 Dividing Fractions and Mixed Numbers KEY: reciprocal, fraction, division NOT: /A/ Correct! /B/ Are you using the reciprocal at the right time?/C/ Are you performing the correct operation? /D/ Did you use the reciprocal of the right fraction? 7