Simplify $\frac{m}{n} + \frac{(m - 1)}{5n} = \frac{(m - 2)}{10n}$ where n $\neq$ 0

The question as written has an "=" sign, which looks like a typo. The original WASSCE question is most likely: simplify m/n + (m−1)/(5n) + (m−2)/(10n). Let's work with that.

Step 1: Find the common denominator

The denominators are n, 5n and 10n, so the LCD is 10n.

Step 2: Convert each fraction

• m/n = 10m/(10n)
• (m−1)/(5n) = 2(m−1)/(10n) = (2m − 2)/(10n)
• (m−2)/(10n) stays the same

Step 3: Add the numerators

10m + (2m − 2) + (m − 2) = 13m − 4

So the sum is (13m − 4)/(10n).

Checking against the options

None of the options match this:

• A: (m−3)/(10n)
• B: 11m/(10n)
• C: (m+1)/(10n)
• D: (11m+4)/(10n)

Let me test other readings of the question.

If the sign between the second and third terms is a minus: m/n + (m−1)/(5n) − (m−2)/(10n) = [10m + 2m − 2 − m + 2]/(10n) = 11m/(10n). This matches option B.

So the intended question is almost certainly m/n + (m−1)/(5n) − (m−2)/(10n), and the "=" in the text was a garbled minus sign.

Answer: B, 11m/(10n)

Note: As literally typed (an equation with "="), the question can't be simplified into any of the options. Only the minus-sign reading gives an option, and it matches B.

Exam tip: With fractions that have different denominators, find the LCD first, multiply each numerator by the right factor, and be careful to distribute a minus sign over every term in the bracket (−(m−2) = −m + 2).