Fractions Basics: Understanding Numerators, Denominators, and Operations

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Learn the fundamentals of fractions including numerators, denominators, like fractions, unlike fractions, and operations. Explore how to add, subtract, and simplify fractions, as well as converting unlike fractions to like fractions. Enhance your math skills through exercises and homework practice.

  • Fractions Basics
  • Numerators
  • Denominators
  • Adding Fractions
  • Subtracting Fractions
  • Homework
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  1. ADDING AND SUBTRACTING FRACTIONS

  2. REVIEW What is a numerator? What is a denominator? What does a normal fraction look like? What does a improper fraction look like? What does a mixed number look like?

  3. LIKE FRACTIONS When fractions have the same denominator they are like fractions. You can add or subtract fractions when you have like fractions. These are all like fractions. 4 7 6 3 2 5 5 5 5 5 5 5

  4. ADDING LIKE FRACTIONS Steps: 1. 2. 3. 4. Make sure that you have like fractions. Add the numerators. Write the sum over the denominator. Write the answer in simplest form. 1 6 6 4 5 6 The answer is: 5 6

  5. SUBTRACTING LIKE FRACTIONS Steps: 1. Make sure that you have like fractions. 2. Subtract the numerators. 3. Write the difference over the denominator. 4. Write the answer in simplest form. 7 8 8 3 4 8 The answer is: 1 2

  6. IMPROPER FRACTIONS Improper fractions are easy! Just treat them as if they re normal fractions. That s it!

  7. EXERCISE #1 ADD OR SUBTRACT, SIMPLIFY, USE MIXED NUMBERS 1/5 21/4 3/5 1.1/5 + 2/5 = 8. 4/5 - 3/5 = 15. 12/4 - 3/4 = 1/3 12/8 2 2.2/3 - 1/3 = 9. 7/8 + 3/8 = 16. 3/6 + 9/6 = 5/6 11/4 2/13 3.3/4 + 2/4 = 10. 2/6 + 3/6= 17. 4/13 - 2/13 = 12/7 1/5 8/9 4.5/7 + 3/7 = 11. 5/10 - 3/10= 18. 7/9 - 1/9 = 1 13/7 1/4 5.3/2 - 1/2 = 12. 6/7 + 4/7 = 19. 8/16 - 4/16 = 8/9 1 6.3/9 + 5/9 = 13. 9/12 + 3/12= 20. 2/3 + 5/3 = 21/3 0 1/7 7.2/8 - 2/8 = 14. 2/7 - 1/7 =

  8. HOMEWORK IXLs 6.J.1 6.J.2

  9. UNLIKE FRACTIONS Unlike fractions have different denominators. Adding or subtracting with unlike fractionsisn t that different from adding or subtracting like fractions. You just have to find what their denominators have in common. 2 3 3 4 5 6 5 8

  10. CHANGING UNLIKE TO LIKE Steps: 1. Find a common multiple that will go into both denominators. 2. Multiply the numerator and denominator by the same number so the denominator is the same as the common multiple. WHAT EVER YOU DO TO THE BOTTOM YOU HAVE TO DO TO THE TOP! 4 2 3 Now you re ready to use these fractions for 3, 6, 9, 12, 15, 18 2 2 6 6 addition and subtraction! 5 6 5 6, 12, 18, 24, 30, 36 1 1

  11. ADD OR SUBTRACT FRACTIONS WITH UNLIKE DENOMINATORS 2 METHODS Method 1: Find a common denominator can the smaller denominator go into the larger denominator? Check this first if not Method 2: MAKE a common denominator Use cross products to create a common denominator. Step 1: Multiply each numerator by the other fractions denominator. Step 2: Multiply the two denominators together to create a common denominator. Step 3: Add numerators. Reduce if necessary!

  12. 16 10 16 20+10 =26 20 = 16 20= 13 20 10 20 8 4 8 32+ 4 32 =12 32 6 16=3 = 8 32 5 16 =21 40 5 40+16 40 40

  13. EXERCISE #2 ADD FRACTIONS, PUT THEM IN SIMPLEST FORM 1.1/2 + 1/3 = 6.3/4 + 3/20 = 5/6 9/10 2.1/3 + 1/5 = 7.6/7 + 3/4 = 8/15 117/28 3.5/6 + 1/3 = 8.1/9 + 2/3 = 11/6 7/9 4.1/8 + 3/4 = 9.3/6 + 2/9 = 7/8 13/18 5.3/3 + 5/6 = 10.1/6 + 5/12 = 15/6 7/12

  14. EXERCISE #3 SUBTRACT FRACTIONS, PUT THEM IN SIMPLEST FORM 1.1/5 - 2/5 = 6.3/5 - 1/3 = 1/10 4/15 2.1/4 - 1/6 = 7.1/3 - 1/6 = 1/12 1/6 3.7/8 - 2/3 = 8.9/10 - 2/5 = 5/24 1/2 4.4/5 - 3/10 = 9.2/3 - 1/2 = 1/2 1/6 5.8/9 - 1/3 = 10.4/5 - 1/3 = 7/15 5/9

  15. IMPROPER FRACTIONS Improper fractions are easy! Just treat them as if they re normal fractions. That s it!

  16. UNLIKE IMPROPER FRACTIONS 5/2 15/6 8/6 7/6 4/3 1 1/6 or

  17. MIXED NUMBERS There are two ways to change mixed numbers so you can add or subtract. Change the mixed number into an improper fraction. Change just the fraction and leave the whole number alone.

  18. MIXED NUMBERS When subtracting unlike Mixed Numbers, you should first only change fractions to have common denominators. Then convert the Mixed number to improper to subtract. You could also do a borrow method, but this can be confusing to some. Pick which works for YOU the BEST!

  19. ADDING MIXED NUMBERS 1 1/5 2 3 Steps: 1. Add the fractions together. 2. Add the whole numbers. 3. You may have to convert improper fractions to mixed and add whole numbers 3/5 The answer is : 34/5 4/5

  20. ADDING MIXED NUMBERS 1 4/5 2 3 Steps: 1. Add the fractions together. 2. Add the whole numbers. 3. You may have to convert improper fractions to mixed and add whole numbers 3/5 The answer is : 42/5 7/5 7/5 = 12/5

  21. ADDING UNLIKE MIXED NUMBERS Steps: 1. Change the unlike fractions to like fractions. 2. Add the fractions. 3. Add the whole numbers. 4. If the fraction is improper, change it to mixed and add the whole numbers. 1/2 312/6 4 1 25/6 5/6 1/2 The answer is: 4 1/3 8/6 3/6

  22. SUBTRACT UNLIKE MIXED NUMBERS Steps: 1. Change the unlike fractions to like fractions. 2. Subtract the numerators if possible. 3. Subtract the whole numbers. 4. Reduce if needed. 2 11/6 1/6 1/2 1/2 The answer is: 1 2/6 3/6 1 1/3 1/6

  23. SUBTRACT UNLIKE MIXED NUMBERS Steps: 1. Change the unlike fractions to like fractions. 2. Subtract the numerators if possible. (Its not!) 3. Convert to Improper fractions. 4. Reduce if needed. The answer is: 1 2/3 4 25/6 Cannot do this So convert to Improper Fractions (6 2)+5/6 10/6 5/6 1/2 3/6 1/2 - 5/6 (6 4) +3/6 27/6 17/6 5/3

  24. EXERCISE #4 ADD OR SUBTRACT, WRITE IN SIMPLEST FORM 1. 1 3/8 - 11/8 = 6. 2 2/5 + 1 1/10 = 1/4 31/2 2. 2 2/5 + 1 1/5 = 7. 3 1/4 2 1/2 = 3/4 33/5 3. 1 7/8 1 6/8 = 8. 5 2/3 + 3 1/2 = 1/8 91/6 4. 3 4/7 + 2 3/7 = 9. 3 5/6 1 3/5 = 27/30 6 5. 4 8/9 - 2 1/9 = 10.6 1/4 - 3 2/3 = 10 27/9

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