Mathematics 2008 JAMB Past Questions - Question 3: Evaluate 3/8 / 1/2 -1/3 / 1/8 x 2/3+1/3

Correct Answer

D

Explanation

To evaluate the expression, let's simplify each fraction first:3/8 / 1/2 = (3/8) * (2/1) = 6/8 = 3/4-1/3 / 1/8 = (-1/3) * (8/1) = -8/32/3 + 1/3 = 3/3 = 1Now, let's substitute the simplified fractions back into the expression:3/4 - 8/3 * 1 + 1/3To simplify further, we need to find a common denominator for the fractions involved:The common denominator for 4, 3, and 3 is 12.Rewriting the expression with the common denominator:(9/12) - (32/12) + (4/12)Now, we can combine the fractions:(9 - 32 + 4) / 12 = -19/12Therefore, the value of the expression is -19/12.To evaluate the expression \(\frac{3}{8} \div \frac{1}{2} - \frac{1}{3} \div \frac{1}{8} \times \frac{2}{3} + \frac{1}{3}\), we can follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).First, let's simplify the division and multiplication:\(\frac{3}{8} \div \frac{1}{2} - \frac{1}{3} \div \frac{1}{8} \times \frac{2}{3} + \frac{1}{3}\)\(= \frac{3}{8} \div \frac{1}{2} - \frac{1}{3} \div \frac{1}{8} \times \frac{2}{3} + \frac{1}{3}\)\(= \frac{3}{8} \times 2 - \frac{1}{3} \times 8 \times \frac{2}{3} + \frac{1}{3}\)\(= \frac{3}{4} - \frac{16}{3} \times \frac{2}{3} + \frac{1}{3}\)Now, let's simplify the multiplication and subtraction:\(= \frac{3}{4} - \frac{32}{9} + \frac{1}{3}\)To add and subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 9 is 36.Converting all the fractions to have a denominator of 36:\(= \frac{27}{36} - \frac{128}{36} + \frac{12}{36}\)Now we can add and subtract:\(= -\frac{89}{36}\)So, the value of the expression is \(-\frac{89}{36}\).