Question

adding and subtracting mixed numbers with unlike denominators
7 11/12
-
2 3/4
What is the least common denominator?


12


48

Answer 1

To find the least common denominator (LCD) of the fractions \( \frac{11}{12} \) and \( \frac{3}{4} \), we first look at the denominators 12 and 4.

The multiples of 12 are:
- 12, 24, 36, 48, ...

The multiples of 4 are:
- 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...

The smallest common multiple in both lists is 12. Therefore, the least common denominator (LCD) is 12.

To confirm:

- \( \frac{11}{12} \) already has 12 as its denominator.
- To convert \( \frac{3}{4} \) to have a denominator of 12, we can multiply the numerator and denominator by 3:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

Now we can proceed to subtract the mixed numbers:

1. Convert the mixed numbers to improper fractions:
- \( 7 \frac{11}{12} = \frac{7 \times 12 + 11}{12} = \frac{84 + 11}{12} = \frac{95}{12} \)
- \( 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \)

2. Subtract the improper fractions:
\[
\frac{95}{12} - \frac{33}{12} = \frac{95 - 33}{12} = \frac{62}{12}
\]

3. Simplify \( \frac{62}{12} \):
- Divide both the numerator and denominator by 2:
\[
\frac{62 \div 2}{12 \div 2} = \frac{31}{6}
\]

4. Convert \( \frac{31}{6} \) back to a mixed number:
- Divide 31 by 6. The quotient is 5 and the remainder is 1.
\[
5 \frac{1}{6}
\]

So, the final result of \( 7 \frac{11}{12} - 2 \frac{3}{4} \) is:
\[
5 \frac{1}{6}
\]