If A = $\frac{1}{2}$h (a + b), make ‘a’ the subject of the formula

Analyze the question: We need to rearrange A = ½h(a + b) so that "a" stands alone on one side.

Concept: To make a variable the subject, undo the operations around it in reverse order, doing the same thing to both sides each time.

Step-by-step solution:

1. Start with the formula: A = ½h(a + b)

2. Multiply both sides by 2 to remove the fraction: 2A = h(a + b)

3. Divide both sides by h: 2A ÷ h = a + b

4. Subtract b from both sides: a = (2A ÷ h) − b

5. Put everything over the common denominator h: a = (2A − bh) ÷ h

Checking the options:

• A. (2A − 2bh) ÷ b: wrong denominator and wrong term
• B. (2A − bh) ÷ h: matches our result
• C. (2A − bh) ÷ b: wrong denominator (it should be h)
• D. (A − 2bh) ÷ h: the 2 is in the wrong place
• E. (2A − h) ÷ bh: does not match

Quick check with numbers: Let h = 2, a = 3, b = 1. Then A = ½(2)(4) = 4. Using B: (2·4 − 1·2) ÷ 2 = 6 ÷ 2 = 3, which is correct.

Exam tip: When the subject is inside brackets, first clear the fraction, then divide by the factor outside the brackets, then move the other term across. Always do a quick substitution with small numbers to confirm your answer.