Math Problem Statement
Solution
Let's solve the first few problems in the image step-by-step. I'll begin with the initial ones and provide detailed explanations. Please let me know if you'd like solutions for all of them or any specific problems.
Problem 3
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Convert the mixed numbers to improper fractions:
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Find a common denominator for the fractions: The denominators are 5, 10, and 6. The least common multiple is 30.
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Convert each fraction to have a denominator of 30:
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Add the fractions:
So, the answer for problem 3 is approximately:
Problem 4
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Convert the mixed numbers to improper fractions:
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Find a common denominator for the fractions: The denominators are 8, 10, and 4. The least common multiple is 40.
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Convert each fraction to have a denominator of 40:
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Add the fractions:
So, the answer for problem 4 is:
Problem 5
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Convert the mixed numbers to improper fractions:
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Find a common denominator for the fractions: The denominators are 2, 12, and 3. The least common multiple is 12.
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Convert each fraction to have a denominator of 12:
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Subtract the fractions:
So, the answer for problem 5 is:
Would you like me to continue with the other problems or clarify any steps?
Follow-up Questions:
- How do you handle subtraction with mixed numbers?
- What are the advantages of converting mixed numbers to improper fractions?
- Can these problems be simplified further without converting to improper fractions?
- How can finding the least common multiple aid in adding fractions?
- What methods can be used to check for calculation accuracy?
Tip:
When working with fractions, always check if you can simplify each fraction early to make calculations easier.
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Math Problem Analysis
Mathematical Concepts
Addition and subtraction of fractions
Mixed numbers
Improper fractions
Common denominators
Formulas
Convert mixed numbers to improper fractions
Find least common multiple (LCM) for denominators
Addition and subtraction of fractions with a common denominator
Theorems
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Suitable Grade Level
Grade 5-7
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