Question
adding and subtracting mixed numbers with unlike denominators
What is the first step?
7 11/12
-
2 3/4
Subtract to get new fractions
Find a common denominator- LCM
What is the first step?
7 11/12
-
2 3/4
Subtract to get new fractions
Find a common denominator- LCM
Answers
GPT-4o mini
To subtract the mixed numbers \(7 \frac{11}{12}\) and \(2 \frac{3}{4}\), we first need to find a common denominator for the fractions \( \frac{11}{12} \) and \( \frac{3}{4} \).
### Step 1: Find the Least Common Denominator (LCD)
1. The denominators are 12 and 4.
2. The multiples of 12 are: 12, 24, 36, ...
3. The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
4. The least common multiple (LCM) of 12 and 4 is **12**.
### Step 2: Rewrite the Fractions with the Common Denominator
- The fraction \( \frac{3}{4} \) needs to be converted to have a denominator of 12.
To convert \( \frac{3}{4} \) to a fraction with a denominator of 12:
- Multiply both the numerator and denominator by 3:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]
### Step 3: Rewrite the Mixed Numbers
Now we can rewrite both mixed numbers:
- \(7 \frac{11}{12}\) remains as \(7 \frac{11}{12}\).
- \(2 \frac{3}{4}\) becomes \(2 \frac{9}{12}\).
### Step 4: Convert the Mixed Numbers to Improper Fractions
Convert the mixed numbers to improper fractions for easier subtraction:
- \(7 \frac{11}{12} = 7 \times 12 + 11 = 84 + 11 = 95\), so \(7 \frac{11}{12} = \frac{95}{12}\).
- \(2 \frac{9}{12} = 2 \times 12 + 9 = 24 + 9 = 33\), so \(2 \frac{3}{4} = \frac{33}{12}\).
### Step 5: Subtract the Improper Fractions
Now we subtract:
\[
\frac{95}{12} - \frac{33}{12} = \frac{95 - 33}{12} = \frac{62}{12}
\]
### Step 6: Simplify the Result (if needed)
Now, simplify \( \frac{62}{12} \):
1. The numerator and denominator can both be divided by 2:
\[
\frac{62 \div 2}{12 \div 2} = \frac{31}{6}
\]
### Step 7: Convert Back to a Mixed Number (if needed)
Convert \( \frac{31}{6} \) back to a mixed number:
- \(31\) divided by \(6\) is \(5\) with a remainder of \(1\).
- Thus, \( \frac{31}{6} = 5 \frac{1}{6} \).
### Final Answer
So, \(7 \frac{11}{12} - 2 \frac{3}{4} = 5 \frac{1}{6}\).
### Step 1: Find the Least Common Denominator (LCD)
1. The denominators are 12 and 4.
2. The multiples of 12 are: 12, 24, 36, ...
3. The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
4. The least common multiple (LCM) of 12 and 4 is **12**.
### Step 2: Rewrite the Fractions with the Common Denominator
- The fraction \( \frac{3}{4} \) needs to be converted to have a denominator of 12.
To convert \( \frac{3}{4} \) to a fraction with a denominator of 12:
- Multiply both the numerator and denominator by 3:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]
### Step 3: Rewrite the Mixed Numbers
Now we can rewrite both mixed numbers:
- \(7 \frac{11}{12}\) remains as \(7 \frac{11}{12}\).
- \(2 \frac{3}{4}\) becomes \(2 \frac{9}{12}\).
### Step 4: Convert the Mixed Numbers to Improper Fractions
Convert the mixed numbers to improper fractions for easier subtraction:
- \(7 \frac{11}{12} = 7 \times 12 + 11 = 84 + 11 = 95\), so \(7 \frac{11}{12} = \frac{95}{12}\).
- \(2 \frac{9}{12} = 2 \times 12 + 9 = 24 + 9 = 33\), so \(2 \frac{3}{4} = \frac{33}{12}\).
### Step 5: Subtract the Improper Fractions
Now we subtract:
\[
\frac{95}{12} - \frac{33}{12} = \frac{95 - 33}{12} = \frac{62}{12}
\]
### Step 6: Simplify the Result (if needed)
Now, simplify \( \frac{62}{12} \):
1. The numerator and denominator can both be divided by 2:
\[
\frac{62 \div 2}{12 \div 2} = \frac{31}{6}
\]
### Step 7: Convert Back to a Mixed Number (if needed)
Convert \( \frac{31}{6} \) back to a mixed number:
- \(31\) divided by \(6\) is \(5\) with a remainder of \(1\).
- Thus, \( \frac{31}{6} = 5 \frac{1}{6} \).
### Final Answer
So, \(7 \frac{11}{12} - 2 \frac{3}{4} = 5 \frac{1}{6}\).