7/8 – 6/7
The Correct Answer and Explanation is :
To solve the expression ( \frac{7}{8} – \frac{6}{7} ), follow these steps:
Step 1: Find a common denominator
To subtract fractions, they must have the same denominator. The denominators are 8 and 7. The least common denominator (LCD) is the least common multiple (LCM) of 8 and 7, which is 56.
Step 2: Adjust the fractions to have the same denominator
Now, rewrite each fraction with a denominator of 56:
- For ( \frac{7}{8} ), multiply both the numerator and denominator by 7:
[
\frac{7}{8} = \frac{7 \times 7}{8 \times 7} = \frac{49}{56}
] - For ( \frac{6}{7} ), multiply both the numerator and denominator by 8:
[
\frac{6}{7} = \frac{6 \times 8}{7 \times 8} = \frac{48}{56}
]
Step 3: Subtract the fractions
Now that both fractions have the same denominator, subtract the numerators:
[
\frac{49}{56} – \frac{48}{56} = \frac{49 – 48}{56} = \frac{1}{56}
]
Final Answer:
[
\frac{7}{8} – \frac{6}{7} = \frac{1}{56}
]
Explanation:
To subtract fractions, having the same denominator is crucial. When fractions have different denominators, the only way to perform operations is to find a common denominator. The LCD for 8 and 7 is 56. After converting both fractions to have 56 as their denominator, the subtraction can be done directly with the numerators. This results in ( \frac{1}{56} ).
The subtraction process involves:
- Identifying the LCD,
- Rewriting each fraction with the LCD,
- Subtracting the numerators while keeping the denominator the same.
This approach works for any subtraction of fractions, whether the denominators are prime, composite, or relatively prime (as in this case).