# Self-Directed Course: Transitional Math Module 2: Fractions

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1 Lesson #1: Comparing Fractions Comparing fractions means finding out which fraction is larger or smaller than the other. To compare fractions, use the following inequality and equal signs: - greater than is > *If the fractions are not equal, the - less than is < inequality sign always points to the - equal to is = smallest fractions. A fraction can be made up of three parts: - a denominator (bottom number) - a numerator (top number) - a whole number (number in front of the denominator and numerator) whole number 5 numerator denominator Before you can compare fractions, the denominators have to be the same. If the denominators are different, you will need to come up with a common denominator. Let s compare the following fraction: Since the denominators are different, we have to find a common denominator to make them the same. Both 4 and 5 go into 20, so our new denominator will be 20. Now we need to figure out the numerator. To do that, we multiply the numerator by whatever we multiplied the denominator by to get 20. x = x = Our new fractions are. Now we can compare them because the denominators are the same. Since 15 is smaller than 16, we use the less than sign: <. Therefore, <

2 Compare the following fraction: Step #1: Find a common denominator Step #2: Find the new numerators x = x = Step #3: Compare new fractions > Step #4: Write final answer > *Remember, the inequality sign always points to the smallest fractions.

3 Assignment #1: Comparing Fractions Compare the following fractions by using an inequality or equal sign. 1) 6) 2) 7) 3) 8) 4) 9) 5) 10)

4 Lesson #2: Converting Mixed Numbers to Improper Fractions There are three types of fractions: 1) Proper Fractions the numerator is smaller than the denominator: 2) Improper Fractions the numerator is larger than the denominator: 3) Mixed Numbers a proper fraction next to a whole number: 3 Example #1 To change 3 (a mixed number) into an improper fraction, use the following steps: 1) Multiply the denominator by the whole number 6 x 3 = 18 2) Add the numerator to your answer = 22 3) Place this value over the original denominator Example #2 Change 2 into an improper fraction: 1) Multiply the denominator by the whole number 7 x 2 = 14 2) Add the numerator to your answer = 17 3) Place this value over the original denominator Example #3 To change (an improper fraction) into a mixed number, use the following steps: 1) Divide the numerator by the denominator 7 3 = ) The number in front of the decimal is your whole number 2 3) Multiply you whole number by your denominator 2 x 3 = 6 4) Subtract this number from your numerator 7 6 = 1 5) Place this value over the denominator and place it after the 2 Number you found in step2.

5 Assignment #2: Converting Mixed Numbers to Improper Fractions Write each mixed number as an improper fraction. 1) 8 15) 2 2) 7 16) 6 3) 1 17) 1 4) 10 18) 3 5) 7 19) 5 6) 4 20) 9 7) 9 21) 5 8) 1 22) 7 9) 5 23) 7 10) 4 24) 9 11) 7 25) 8 12) 3 26) 4 13) 4 27) 8 14) 4 28) 10

6 Lesson #3: Multiply and Reduce Fractions Self-Directed Course: Transitional Math When multiplying fractions you need to multiply the numerators together and the denominators together. If your answer is an improper fraction, be sure to convert it to a mixed numbers. Make sure you reduce your answers to lowest terms by dividing the numerator and denominator by the same number. If the numerator and denominator can t be divided by the same number, then you have lowest terms. For example: x = = x = = = x = = = 1

7 Assignment #3: Multiply and Reduce Fractions Multiply the following fractions and reduce them to lowest terms when possible. 1) x 8) x 2) x 9) x 3) x 10) x 4) x 11) x 5) x 12) x 6) x 13) 2 x 7) x 14) x 3

8 15) x 8 23) 5 x 16) x 7 24) x 3 17) x 6 25) 9 x 18) x 4 26) 7 x 19) 7 x 27) 1 x 20) x 9 28) 2 x 21) 8 x 29) 6 x 22) 2 x 30) 7 x

9 31) 2 x 38) 8 x 5 32) 5 x 39) 2 x 3 33) 3 x 40) 7 x 5 34) 2 x 41) 7 x 4 35) 1 x 4 42) 1 x 3 36) 3 x 1 43) 9 x 1 37) 6 x 4 44) 9 x 5

10 Lesson #4: Dividing Fractions Self-Directed Course: Transitional Math Dividing fractions is very similar to multiplying fractions. Instead of dividing, you multiply the fractions together by flipping the second fraction upside-down. This is called multiplying by the reciprocal. After you have flipped the second fraction, follow the same steps for multiplying fraction together. Be sure to reduce your answers to lowest terms and to convert all improper fractions to mixed numbers. For example: = x = = x = = = 1 = x = = Sometimes you might see a question like this: 6. To do this simply change the 6 (a whole number) to a fraction by placing a 1 under it and carry out the normal steps to solve it. 6 = x = =

11 Assignment #4: Dividing Fractions Self-Directed Course: Transitional Math Divide the following fractions. 1) 8) 2) 9) 3) 10) 4) 11) 2 5) 12) 3 6) 13) 1 7) 14) 7

12 15) 8 23) 5 16) 7 24) 6 17) 5 25) 4 18) 2 26) 6 19) 9 27) 3 20) 1 28) 6 21) 6 29) 4 22) 7 30) 7

13 31) ) ) ) ) ) ) ) 1 4

14 Lesson #4: Adding Fractions When adding fractions, make sure that the denominators are the same. If they are different, you have to find a common denominator. Be sure to reduce your answers to lowest terms and to convert all improper fractions to mixed numbers. For example: Example #1 + Step #1: Find a common denominator + Step #2: Find the new numerators x = + x = Step #3: Re-write new addition statement + Step #4: Add fractions together + = = = 1 Example #2 + Step #1: Find a common denominator + Step #2: Find the new numerators x = + x = Step #3: Re-write new addition statement + Step #4: Add fractions together + = = 1

15 Assignment #4: Adding Fractions Add the following fractions. 1) + 6) + 2) + 7) + 3) + 8) + 4) + 9) + 5) + 10) +

16 11) + 15) + 12) + 16) + 13) + 17) + 14) + 18) +

17 Lesson #5: Adding Mixed Numbers Self-Directed Course: Transitional Math When adding mixed numbers, you follow the same steps as you would when adding proper fractions. The only difference is there is an additional step because you have to add the whole numbers. Make sure the denominators are the same when adding and reduce your answers to lowest terms. Example # Step #1: Find a common denominator + Step #2: Find the new numerators 3 x = x = 5 Step #3: Re-write new addition statement Step #4: Add the whole numbers = 8 Step #4: Add numerators Step #5: Place whole number in front of fraction + = 8 Example # Step #1: Find a common denominator + Step #2: Find the new numerators Step #3: Re-write new addition statement 6 x = x = 2 Step #4: Add the whole numbers = 8 Step #4: Add numerators Step #5: Add whole numbers + = = = 9

18 Assignment #5: Adding Mixed Numbers Self-Directed Course: Transitional Math Add the following mixed numbers. 1) ) + 4 2) ) ) ) 3 2 4) ) ) ) 1 + 3

19 11) ) ) ) ) ) ) )

20 Lesson #6: Subtracting Improper Fractions When subtracting fractions, you follow some of the same steps as you would when adding fractions. You have to make sure the denominators are the same and reduce your answers to lowest terms. Example #1 Step #1: Find a common denominator + Step #2: Find the new numerators x = x = Step #3: Re-write new subtraction statement Step #4: Subtract numerators = Example #2 6 2 Step #1: Find a common denominator Step #2: Find the new numerators 6 x = 6 2 x = 2 Step #3: Re-write new subtraction statement 6 2 Step #4: Subtract the whole numbers 6 2 = 4 Step #4: subtract numerators = Step #5: Place whole numbers in front 4

21 Assignment #6: Subtracting Improper Fractions Subtract the following Improper Fractions. 1) 6) 2) 1 7) 1 3) 8) 4) 9) 5) 10)

22 11) 2 17) 12) 19 18) 20 13) 19) 14) 2 20) 15) 1 21) 4 16) 22) 1 1

23 23) ) ) ) ) 4 31) ) ) ) ) ) ) 9

24 35) ) ) 4 38) 12 6

25 Assignment #7: Adding and Subtracting Fractions and Mixed Numbers Add or Subtract the following Fractions and Mixed Numbers. 1) 2 + 6) + 2) + 7) + 3) 8) + 4) + 9) 6 5) + 10) +

26 11) ) ) 18) ) 2 19) ) ) ) ) ) )

27 23) ) ) ) ) ) ) + 30)

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