Question
Sharon states that 7 5/8-5 1/3= 2 4/5 Because 7 - 5 = 2 5 - 1 = 4 and 8- 3 equals 5 first state whether you agree or disagree then explain briefly how to subtract mixed numbers with unlike the nominators be sure to show your solution as A subtraction equation
Answers
GPT-4o mini
I disagree with Sharon's calculation. The method she used is incorrect because it does not account for the mixed numbers correctly.
To subtract mixed numbers with unlike denominators, you first need to find a common denominator. Let's solve the subtraction \( 7 \frac{5}{8} - 5 \frac{1}{3} \) step by step.
### Step 1: Convert to Improper Fractions
1. Convert each mixed number to an improper fraction.
- For \( 7 \frac{5}{8} \):
\[
7 \times 8 + 5 = 56 + 5 = 61 \quad \text{so, } 7 \frac{5}{8} = \frac{61}{8}
\]
- For \( 5 \frac{1}{3} \):
\[
5 \times 3 + 1 = 15 + 1 = 16 \quad \text{so, } 5 \frac{1}{3} = \frac{16}{3}
\]
### Step 2: Find a Common Denominator
The denominators are \( 8 \) and \( 3 \). The least common multiple (LCM) of \( 8 \) and \( 3 \) is \( 24 \).
### Step 3: Convert to the Common Denominator
- Convert \( \frac{61}{8} \) to a denominator of \( 24 \):
\[
\frac{61}{8} = \frac{61 \times 3}{8 \times 3} = \frac{183}{24}
\]
- Convert \( \frac{16}{3} \) to a denominator of \( 24 \):
\[
\frac{16}{3} = \frac{16 \times 8}{3 \times 8} = \frac{128}{24}
\]
### Step 4: Subtract the Improper Fractions
Now that we have the same denominator, we subtract:
\[
\frac{183}{24} - \frac{128}{24} = \frac{183 - 128}{24} = \frac{55}{24}
\]
### Step 5: Convert Back to a Mixed Number
To convert \( \frac{55}{24} \) back to a mixed number:
- Divide \( 55 \) by \( 24 \): \( 2 \) (since \( 24 \times 2 = 48 \)), remainder \( 7 \).
- So \( \frac{55}{24} = 2 \frac{7}{24} \).
### Final Answer
Thus, the correct answer is:
\[
7 \frac{5}{8} - 5 \frac{1}{3} = 2 \frac{7}{24}
\]
### Conclusion
In summary, Sharon's approach of directly subtracting whole numbers and fractions separately is incorrect for mixed numbers with unlike denominators. Instead, we must convert them to improper fractions, find a common denominator, and then perform the subtraction.
To subtract mixed numbers with unlike denominators, you first need to find a common denominator. Let's solve the subtraction \( 7 \frac{5}{8} - 5 \frac{1}{3} \) step by step.
### Step 1: Convert to Improper Fractions
1. Convert each mixed number to an improper fraction.
- For \( 7 \frac{5}{8} \):
\[
7 \times 8 + 5 = 56 + 5 = 61 \quad \text{so, } 7 \frac{5}{8} = \frac{61}{8}
\]
- For \( 5 \frac{1}{3} \):
\[
5 \times 3 + 1 = 15 + 1 = 16 \quad \text{so, } 5 \frac{1}{3} = \frac{16}{3}
\]
### Step 2: Find a Common Denominator
The denominators are \( 8 \) and \( 3 \). The least common multiple (LCM) of \( 8 \) and \( 3 \) is \( 24 \).
### Step 3: Convert to the Common Denominator
- Convert \( \frac{61}{8} \) to a denominator of \( 24 \):
\[
\frac{61}{8} = \frac{61 \times 3}{8 \times 3} = \frac{183}{24}
\]
- Convert \( \frac{16}{3} \) to a denominator of \( 24 \):
\[
\frac{16}{3} = \frac{16 \times 8}{3 \times 8} = \frac{128}{24}
\]
### Step 4: Subtract the Improper Fractions
Now that we have the same denominator, we subtract:
\[
\frac{183}{24} - \frac{128}{24} = \frac{183 - 128}{24} = \frac{55}{24}
\]
### Step 5: Convert Back to a Mixed Number
To convert \( \frac{55}{24} \) back to a mixed number:
- Divide \( 55 \) by \( 24 \): \( 2 \) (since \( 24 \times 2 = 48 \)), remainder \( 7 \).
- So \( \frac{55}{24} = 2 \frac{7}{24} \).
### Final Answer
Thus, the correct answer is:
\[
7 \frac{5}{8} - 5 \frac{1}{3} = 2 \frac{7}{24}
\]
### Conclusion
In summary, Sharon's approach of directly subtracting whole numbers and fractions separately is incorrect for mixed numbers with unlike denominators. Instead, we must convert them to improper fractions, find a common denominator, and then perform the subtraction.