1. Using LCM to Add and Subtract Fractions
Presented by Mr. Laws
6th Grade Math
JCMS

2. Goal/Standard
6.NS.4 – Find the least common multiple LCM of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators.
Tip: Add your own speaker notes here.

3. Essential Question:
How do I use LCM to add and subtract fractions with unlike denominators?
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4. Least Common Denominator (LCD)
Key Vocabulary
Numerator
Common Denominator
Denominator
Least Common Denominator (LCD)
Least Common Multiple
Multiples

5. Adding and Subtraction Fractions.
1. Fractions have a numerator and denominator.
2. The numerator is the number above the line in a common fraction.
3. A denominator is the number below the line in a common fraction; also known as the divisor.
4. Fractions with the same denominator are called, “Liked Fractions”
5. You can add or subtract like fractions by adding or subtracting the numerator, and writing the sum or difference over the common denominator.

6. Adding and Subtraction Fractions.
Example #1: Adding and Subtracting fractions with the same denominator.
Add the Numerators
Subtract the Numerators
𝟏 𝟓
𝟑 𝟓 +
𝟓 𝟒
𝟐 𝟒 _
𝟒 𝟓
𝟑 𝟒

7. Using the LCM to Add or Subtract Fractions w/unlike Denominators.
6. Before you add or subtract fractions with different denominators, you must find the equivalent fraction with the same denominator.
7. You can use the least common multiple (LCM) to help you add or subtract fractions with unlike denominators.
8. When solving fractions with unlike denominators, the LCM is called the least common denominator (LCD)

8. Multiplying the Denominator to find a Common Denominator.
Example # 2 Jason walked 5/8 mile from his house to the store. He then walked 1/6 mile to his friend’s house. What is the total distance Jason walked?
Step 1: Multiply the denominators to find a common denominator. (ex. 8 x 6 = 48)
Method # 1
5 𝟖 = 𝟒𝟖
1 𝟔 = 𝟒𝟖 +

9. Multiplying the Denominator to find a Common Denominator.
Example # 2 Jason walked 5/8 mile from his house to the store. He then walked 1/6 mile to his friend’s house. What is the total distance Jason walked?
Step 1: Multiply the denominators to find a common denominator. (ex. 8 x 6 = 48)
Method # 1
𝟓 𝟖 = 𝟒𝟖
𝟏 𝟔 = 𝟒𝟖 +
X 6
Step 2: Write equivalent fractions using the common denominator.
X 6
X 8
X 8

10. Multiplying the Denominator to find a Common Denominator.
Example # 2 Jason walked 5/8 mile from his house to the store. He then walked 1/6 mile to his friend’s house. What is the total distance Jason walked?
Step 1: Multiply the denominators to find a common denominator. (ex. 8 x 6 = 48)
Method # 1
𝟓 𝟖 = 𝟑𝟎 𝟒𝟖
𝟏 𝟔 = 𝟖 𝟒𝟖 +
X 6
Step 2: Write equivalent fractions using the common denominator.
X 6
X 8
Step 3: Add the fractions. (Note: always reduce fractions to its simplest form – both the numerator and denominator was divided by 2.)
X 8
𝟑𝟖 𝟒𝟖 = 𝟏𝟗 𝟐𝟒

11. How can I use the LCM as the common denominator?
Example # 2 Jason walked 5/8 mile from his house to the store. He then walked 1/6 mile to his friend’s house. What is the total distance Jason walked?
Method # 2
Step 1: Make a factor tree of each number to find the prime factorization.
Step 2: Use prime factorization to find the LCM of the denominator. OR
8: 8, 16, 24, 32, 40, 48
6: 6, 12, 18, 24, 30, 36, 42, 48
Step 1: Find LCM for 8 and 6.

12. How can I use the LCM as the common denominator?
Method # 2 cont.
Step 3: Write equivalent fractions using the LCM as the common denominator. LCM = 24
𝟓 𝟖 = 𝟏𝟓 𝟐𝟒
𝟏 𝟔 = 𝟒 𝟐𝟒 +
X 3
X 4
Step 4: Add the fractions.
What method do you find easier to do, Method 1 (Multiplying denominators) or Method 2 (Finding the LCM)?
𝟏𝟗 𝟐𝟒

13. How can I use the LCM as the common denominator?
Ex # 3 : Using the LCM, what is the difference between and ?
Step 1: Write equivalent fractions using the LCM as the common denominator. LCM = 20
𝟗 𝟐𝟎 =
𝟐 𝟓 = _
X 1
𝟗 𝟐𝟎 𝟐𝟎
X 1
X 4 𝟐𝟎
𝟖 𝟐𝟎
Step 2: Subtract the fractions.
X 4
𝟏 𝟐𝟎

14. Your Turn:

15. Part II
Essential Questions: How do I use the LCM to add or subtract mixed numbers?

16. What is a Mixed Number?
A mixed number consist of a number and a fraction.
You can add and subtract mixed numbers by adding or subtracting like or unlike fraction and then add or subtract the numbers.

17. Using the LCM to add or subtract mixed numbers.
𝟏 𝟑 =
Example# 4: Solve:
= 𝟏𝟓
= 𝟏𝟓 +
Step 1: Find the least common multiple of 5 and 3.
Multiples 5 : 5, 10, 15
Multiples 3: 3, 6, 9, 12, 15,
LCM is 15

18. Using the LCM to add or subtract mixed numbers.
𝟏 𝟑 =
Example# 4: Solve:
Step 1: Find the least common multiple of 5 and 3.
Multiples 5 : 5, 10, 15
Multiples 3: 3, 6, 9, 12, 15,
LCM is 15
= 𝟏𝟓
= 𝟏𝟓 +
X 3
X 3
X 5
X 5
Step 2: Write equivalent fractions using the common denominator.

19. Using the LCM to add or subtract mixed numbers.
𝟏 𝟑 =
Example# 4: Solve:
Step 1: Find the least common multiple of 5 and 3.
Multiples 5 : 5, 10, 15
Multiples 3: 3, 6, 9, 12, 15,
LCM is 15
= 𝟔 𝟏𝟓
= 𝟓 𝟏𝟓 +
X 3
X 3
X 5
X 5
Step 2: Write equivalent fractions using the common denominator.
8 𝟏𝟏 𝟏𝟓
Step 3: Add the fractions and the whole numbers.

20. Using the LCM to add or subtract mixed numbers.
3 4 5 −2 𝟓 𝟏𝟐 =
Example# 5: Solve:
Step 1: Find the
Multiples 5 : 5, 10, 15…60
Multiples 12: 12, 24, 36, 48,…60,
LCM is 60
= 𝟔𝟎
= 𝟔𝟎 _

21. Using the LCM to add or subtract mixed numbers.
3 4 5 −2 𝟓 𝟏𝟐 =
Example# 5: Solve:
Step 1: Find the
Multiples 5 : 5, 10, 15…60
Multiples 12: 12, 24, 36, 48,…60,
LCM is 60
= 𝟔𝟎
= 𝟔𝟎 _
x12
x12
X 5
Step 2: Write equivalent fractions using the common denominator.
X 5

22. Using the LCM to add or subtract mixed numbers.
3 4 5 −2 𝟓 𝟏𝟐 =
Example# 5: Solve:
Step 1: Find the
Multiples 5 : 5, 10, 15…60
Multiples 12: 12, 24, 36, 48,…60,
LCM is 60
= 𝟒𝟖 𝟔𝟎
= 𝟐𝟓 𝟔𝟎 _
x12
x12
X 5
Step 2: Write equivalent fractions using the common denominator.
X 5
𝟏 𝟐𝟑 𝟔𝟎
Step 3: Subtract the fractions and the whole numbers.

23. Using the LCM to subtract mixed numbers.
Example # 6 Lazarus is training to run a half marathon. So far, his longest run has been 6 ½ miles. A half marathon is 𝟏𝟑 𝟏 𝟏𝟎 miles long. What is the difference between Lazarus’s longest run and a half marathon?
Step 1: Find the least common multiple of 10 and 2.
Multiples 10 : 10, 20
Multiples 2: 2, 4, 6, 8, 10,
LCM is 10
= 𝟏𝟎
= 1 𝟏𝟎 _

24. Using the LCM to subtract mixed numbers.
Example # 6 Lazarus is training to run a half marathon. So far, his longest run has been 6 ½ miles. A half marathon is 𝟏𝟑 𝟏 𝟏𝟎 miles long. What is the difference between Lazarus’s longest run and a half marathon?
Step 1: Find the least common multiple of 10 and 2.
Multiples 10 : 10, 20
Multiples 2: 2, 4, 6, 8, 10,
LCM is 10
X 1
= 𝟏 𝟏𝟎
= 6 𝟓 𝟏𝟎 _
X 1
Step 2: Write equivalent fractions using the common denominator.
X 5
X 5

25. Using the LCM to subtract mixed numbers.
Example # 6 Lazarus is training to run a half marathon. So far, his longest run has been 6 ½ miles. A half marathon is 𝟏𝟑 𝟏 𝟏𝟎 miles long. What is the difference between Lazarus’s longest run and a half marathon?
Step 3: Convert one whole number from the number 13 and turn it into a fraction 10/10. Note do this if the top fraction is smaller than the bottom.
X 1
= 𝟏 𝟏𝟎
= 6 𝟓 𝟏𝟎 _
=𝟏𝟐 𝟏𝟏 𝟏𝟎
X 1
Step 4 : Add 12 𝟏𝟎 𝟏𝟎 to 𝟏 𝟏𝟎 =𝟏𝟐 𝟏𝟏 𝟏𝟎
X 5
=𝟔 𝟓 𝟏𝟎
X 5
Step 5 : Subtract the mixed number. Make sure the answer is in its simplest form.
6 𝟔 𝟏𝟎 =6 𝟑 𝟓

26. Summary What have you learned about this lesson?
What are some important steps to remember when using the LCM to add or subtract fractions with unlike denominators?
Do you have any more questions about this lesson?
Make sure you review your notes, add additional questions or notes, and write a summary or reflection.