Podcast
Questions and Answers
What is the least common multiple (LCM) of the denominators 6 and 8?
What is the least common multiple (LCM) of the denominators 6 and 8?
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To add fractions with different denominators, it is not necessary to find a common denominator.
To add fractions with different denominators, it is not necessary to find a common denominator.
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If Sarah ate 1/4 of a pizza, and then ate another 1/3 of a pizza, what fraction of the pizza did she eat in total?
If Sarah ate 1/4 of a pizza, and then ate another 1/3 of a pizza, what fraction of the pizza did she eat in total?
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To simplify the fraction 9/12, divide both the numerator and denominator by their greatest common factor, which is __________.
To simplify the fraction 9/12, divide both the numerator and denominator by their greatest common factor, which is __________.
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Match the following fractions to their simplified forms:
Match the following fractions to their simplified forms:
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When adding fractions 3/5 and 1/2, what is the common denominator used?
When adding fractions 3/5 and 1/2, what is the common denominator used?
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The fraction 15/20 can be simplified to 3/4.
The fraction 15/20 can be simplified to 3/4.
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What is the result of adding 1/6 and 1/3?
What is the result of adding 1/6 and 1/3?
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Study Notes
Adding Fractions with Different Denominators
- To add fractions with different denominators, you must first find a common denominator. This is the least common multiple (LCM) of the denominators.
- The common denominator ensures that the fractions have the same size parts, making addition possible.
- Example: Add 1/3 + 2/5. The denominators are 3 and 5. The LCM of 3 and 5 is 15. Rewrite the fractions with a denominator of 15: (1/3) * (5/5) = 5/15 and (2/5) * (3/3) = 6/15. Then add the numerators: 5/15 + 6/15 = 11/15.
Word Problems With Fractions
- Word problems often describe situations where fractions need to be combined.
- Read the problem carefully to identify the fractions involved and the operation (addition, subtraction, multiplication, or division).
- Determine what the problem is asking for.
- Convert words to mathematical expressions.
- Solve the expression and check your answer.
- Interpret the solution in the context of the problem.
- Example: Sarah ate 1/4 of a pizza, and then ate another 1/2 of a pizza. How much pizza did she eat in total? The problem involves adding 1/4 + 1/2, which becomes 1/4 + 2/4 = 3/4. Therefore Sarah ate 3/4 of the pizza
Finding Common Denominators
- Find the multiples of each denominator.
- Identify the smallest multiple common to both denominators. This is the least common multiple (LCM).
- Convert each fraction to an equivalent fraction with the common denominator.
- Example: To find a common denominator for 1/2 and 3/4, find the multiples of 2 and 4. Multiples of 2 are 2, 4, 6, 8, 10... Multiples of 4 are 4, 8, 12, 16... The least common multiple is 4. 1/2 can be converted to 2/4
Simplifying Fractions
- Simplify fractions to express them in their simplest form.
- Divide both the numerator and denominator by their greatest common factor (GCF).
- Doing this doesn't change the value of the fraction.
- Example: The fraction 2/4 can be simplified by dividing the numerator and denominator by 2. This results in 1/2.
- Simplifying fractions often makes calculations quicker and more straightforward.
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Description
This quiz covers the process of adding fractions with different denominators, focusing on finding a common denominator through the least common multiple (LCM). You'll also tackle real-world word problems that involve combining fractions. Test your understanding and enhance your fraction addition skills with practical examples.
