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Test Review

This comprehensive guide covers procedures for adding, subtracting, multiplying, dividing fractions, changing between improper and mixed numbers, and simplifying fractions. Improve your math expertise with step-by-step instructions.

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Test Review

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  1. Test Review • The test will be on the following: • Improper to Mixed • Mixed to Improper • Simplification • Adding and subtracting fractions with like and unlike denominators • Adding and subtracting mixed numbers with like and unlike denominators • Multiplying and dividing fractions • Multiplying with Mixed numbers • Reciprocal

  2. Rules for Mixed to Improper Step 1: Multiply the whole number with the denominator. Step 2: Take the answer from step 1 and add it to the numerator. Step 3: Take the answer from step 2 and put it over the original denominator. Ex) 2 3 = 2 x 5 = 10 + 3 = 15 5 5

  3. Mixed to Improper • 6 1/3 • 2 1/5 • 3 2/7 • 8 1/2

  4. Answers to Mixed to Improper: • 9/3 • 11/5 • 23/7 • 17/2

  5. Changing Improper to Mixed Numbers Step 1: Divide the denominator into the numerator. Step 2. The quotient is now your Whole number; the remainder is now your numerator and the divisor is now your denominator. Ex) 18 ÷ 5 = 5 18 15 3 Answer: 3 3 5 3 Whole number Denominator numerator

  6. Improper to Mixed • 8/5 • 20/9 • 22/7 • 13/3

  7. Answers to changing improper to mixed numbers • 1 2/5 • 2 2/9 • 3 1/7 • 4 1/3

  8. Simplifying Fractions In order to simply fractions you need to see what number will go into the numerator and the denominators. You need to get it in the simplest form. Ex) 9 ÷ 3 = 3 ÷ 3 = 1 36 ÷ 3 = 12 ÷ 3 = 4

  9. Simplification of Fractions • 20/24 • 2/8 • 3/9 • 36/63

  10. Simplification answers • 5/6 • ¼ • 1/3 • 4/7

  11. Adding and Subtracting with like denominators Step 1: The denominators are the same then just bring the denominator straight down Step2: Then add or subtract the numerators Step 3: Simplify your answer Ex) 9 + 7 = 16 ÷ 2 = 8 = 1 3 10 10 10 ÷ 2 5 5

  12. Adding and Subtracting with Like denominators • 3/8 + 5/8 = • 10/12 – 4/12 = • 9/11 + 8/11 = • 10/15 - 1/15 =

  13. Adding and Subtracting with like denominators answer • 8/8 = 1 • 6/12 = ½ • 17/11 = 1 6/11 • 9/15 = 3/5

  14. Adding and Subtracting Mixed Numbers • 1 - 9/10 = • 37 13/18 - 24 7/18 = • 2 3/10 + 4 1/10 = • 7 3/5 + 9 2/5 =

  15. Adding and Subtracting Mixed Numbers answer: • 1/10 • 13 6/18 = 13 1/3 • 6 4/10 = 6 2/5 • 16 5/5 = 16 + 1 = 17

  16. Renaming to Subtract • 2 ½ - 1 ¾ = • 8 2/9 - 2 7/9 = • 3 2/6 - 1 2/3 = • 7 ¼ - 4 11/12 =

  17. Adding and Subtracting with Unlike denominators • ¾ - ½ = • 1/6 + 5/12 = • 5/6 - ¾ = • ½ + 3/7 =

  18. Adding and Subtracting Mixed Numbers with Unlike Denominators • 7 1/12 + 3 1/3 = • 2 1/6 + 2 3/8 = • 8 5/6 - 2 ¾ = • 6 6/7 - 1 ½ =

  19. Comparing Fractions When comparing fractions we use the butterfly method. You go diagonally across from the denominator to the numerator and multiply and put the number at the top of the numerator and compare those numbers. • 5 7 9 27 < 35

  20. Comparing Fractions • 3/5 ____ 4/9 • 4/7 ___ ¾ • 2/3 ____ 5/8 • 3/25 ___ 6/50

  21. Comparing fractions answers: • > • < • > • =

  22. Multiplying Fractions Step 1: Multiply the numerators Step 2: Multiply the denominators Step 3: Simplify if necessary Ex) 3 x 4 = 12 ÷ 3 = 4 5 3 15 ÷ 3 5

  23. Multiplying Fractions • 3/8 x 2/9 = • 6/4 x 3/2 = • 8/11 x 5/4 = • 5/7 x 14/5 =

  24. Answers to multiplying fractions: • 1/12 • 9/4 = 2 ¼ • 10/11 • 14/7 = 2

  25. Multiplying Mixed Numbers Step 1: Change all mixed numbers into improper fractions Step 2: Multiply the numerators Step 3: Multiply the denominators Step 4: Simplify if necessary Ex) 1 3 x 2 4 = 8 x 10 = 80 ÷ 5 = 16 = 5 1 5 3 5 3 15 ÷ 5 3 3

  26. Multiplying with Mixed Numbers • 1 1/3 x 6/7= • 2 2/9 x 1 3/5 = • 2 7/8 x 3 1/3 = • 2 ½ x 3 ½ =

  27. Multiplying with mixed numbers answer: • 24/21 = 8/7 = 1 1/7 • 160/ 45 = 32/9 = 3 5/9 • 230/ 24 = 115/12 = 9 7/12 • 35/4 = 8 3/4

  28. Reciprocal To find the reciprocal of a number you are just flipping the fraction. The denominator becomes the numerator and the numerator becomes the denominator. Ex) 3 = 5 5 3

  29. Reciprocal of Fractions • 8/9 = • 2/5 = • 3/10 = • 7 =

  30. Answer to Reciprocal • 9/8 • 5/2 • 10/3 • 1/7

  31. Dividing Fractions Step 1: Keep the first fraction the same (Keep It) Step 2: Change division to multiplication (Change It) Step 3: Take the reciprocal of the second fraction (flip it) Step 4: Multiply numerators Step 5: Multiply denominators Step 6: Simplify if necessary Ex) 4 ÷ 3 = 4 x 5 = 10 = 1 1 3 5 3 3 9 9

  32. Dividing Fractions 1. 5 ÷ 2/3 = • 6/5 ÷ 3/9 = • 7/8 ÷ 5 = • 11/5 ÷ 6/5 =

  33. Answers to dividing Fractions • 15/2 = 7 ½ • 18/5 = 3 3/5 • 7/40 • 11/6 = 1 5/6

  34. Dividing Fractions Step 1: All mixed numbers must be made improper Step 2: Keep the first fraction the same (Keep It) Step 3: Change division to multiplication (Change It) Step 4: Take the reciprocal of the second fraction (flip it) Step 5: Multiply numerators Step 6: Multiply denominators Step 7: Simplify if necessary Ex) 2 4 ÷ 3 3 = 10 ÷ 18 = 10 x 5 = 50 ÷ 2 = 25 3 5 3 5 3 18 54÷ 2 27

  35. Dividing with Mixed Numbers 1. 1 1/5 ÷ 2 2/3 = • 3 2/9 ÷ 4 1/5 = • 7 1/6 ÷ 2 3/5 = • 3 ¼ ÷ 2 ½ =

  36. Answers to dividing mixed numbers • 9/20 • 145/189 • 215/78 = 2 59/78 • 2 3/5

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