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Operations with Fractions Practice Questions

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Updated on Oct 3, 2011

To review Operations with Fractions, go to Operations with Fractions Study Guide.

Operations with Fractions Practice Questions

Practice

  1. Which fraction is greater, or ?
  2. Convert. to a mixed number.
  3. Convert. to an improper fraction.

Solutions

1. The two fractions already have a common denominator, so combine the numerators, and keep the denominator. Then simplify: .
2. First, find a common denominator, the LCM of 15 and 30. The LCM is 30. Convert the first fraction to have a denominator of 30: Now combine to get .
3. Change each mixed number to an improper fraction: . The fractions have the same denominator, so combine the numerators and keep the denominator: .
4. When you multiply fractions, multiply straight across and then simplify: .
5. Change and 6 to improper fractions. Then change the operation to multiply by the reciprocal of 6: . Multiply the numerators and the denominators straight across and simplify: .
6. These fractions are like fractions, because they have the same denominator. To add two like fractions, add the numerators of the fractions: 6 + 3 = 9. The denominator of our answer is the same as the denominator of the two fractions that you are adding. Both fractions have a denominator of 11, so the denominator of our answer will be 11: .
7. Because these fractions are unlike, you must find common denominators for them before adding. First, you find the least common multiple of 4 and 7:
  4: 4, 8, 12, 16, 20, 24, 28, 32, . . .
  7: 7, 14, 21, 28, 35, 42, 49, . . .
  The least common multiple of 4 and 7 is 28. Convert both fractions to a number over 28. Because , the new denominator of the fraction is seven times larger. The new numerator must also be seven times larger, so that the value of the fraction does not change: . Because, the new denominator of the fraction is four times larger. Multiply the numerator of the fraction by four: . Now that you have like fractions, you can add the numerators: 7 + 8 = 15. Because the denominator of the fractions you are adding is 28, the denominator of our answer is 28: .
8. These fractions are like fractions, so you can subtract the numerator of the second fraction from the numerator of the first fraction: 10 – 6 = 4. The denominator of both fractions is 17, so the denominator of our answer is 17: .
9. Because these fractions are unlike, you must find common denominators for them before subtracting. First, you find the least common multiple of 4 and 5:
  4: 4, 8, 12, 16, 20, 24, . . .
  5: 5, 10, 15, 20, 25, . . .
  The least common multiple of 4 and 5 is 20. Convert both fractions to a number over 20. Because = 5, the new denominator of the fraction is five times larger. Therefore, the new numerator must also be five times larger, so that the value of the fraction does not change: 3 × 5 = 15; . Because = 4, the new denominator of the fraction is four times larger. Multiply the numerator of the fraction by four: 2 × 4 = 8; . Now that you have like fractions, you can subtract the second numerator from the first numerator: 15 – 8 = 7. The denominator of the fractions is 20, so the denominator of our answer is 20: .
10. The product of two fractions is equal to the product of the numerators over the product of the denominators. Multiply the numerators: 2 × 9 = 18. Multiply the denominators: 3 × 13 = 39; . You can reduce your answer by dividing the numerator and denominator by their greatest common factor. The greatest common factor of 18 and 39 is 3: = 6 and = 13, so .
11. First, list the factors of the numerator and the denominator. The factors of 16 are 1, 2, 4, 8, and 16, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor (the largest number that is a factor of both 16 and 24) is 8. Divide the numerator and denominator of by 8: = 2 and = 3. reduces to .
12. To convert an improper fraction to a mixed number, divide the numerator by the denominator: 19 ÷ 5 = 3 with 4 left over. You express the remainder as a fraction. The improper fraction has a denominator of 5, so our remainder has a denominator of 5: 19 ÷ 5 = .
13. To convert a mixed number to an improper fraction, you begin by multiplying the whole number, 6, by the denominator of the fraction, 8: 6 × 8 = 48. Next, add to that product the numerator of the fraction: 48 + 5 = 53. Finally, put that sum over the denominator of the fraction: .
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