Evaluate 1 - ($\frac{1}{5}$ x $\frac{2}{3}$) + ( 5 + $\frac{2}{3}$)

To solve this expression, we must follow the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, and Subtraction).

Expression: $1 - (\frac{1}{5} \times \frac{2}{3}) + (5 + \frac{2}{3})$

Step 1: Solve the operations inside the brackets

• First bracket: $(\frac{1}{5} \times \frac{2}{3}) = \frac{1 \times 2}{5 \times 3} = \frac{2}{15}$
• Second bracket: $(5 + \frac{2}{3})$ • To add these, find a common denominator: $5 = \frac{15}{3}$ • $\frac{15}{3} + \frac{2}{3} = \frac{17}{3}$

Step 2: Substitute the results back into the expression

Now the expression looks like this: $1 - \frac{2}{15} + \frac{17}{3}$

Step 3: Simplify the expression

To perform the addition and subtraction, find the Least Common Multiple (LCM) of the denominators (1, 15, and 3), which is 15.

• $1 = \frac{15}{15}$
• $\frac{2}{15} = \frac{2}{15}$
• $\frac{17}{3} = \frac{17 \times 5}{3 \times 5} = \frac{85}{15}$

Now combine them: $\frac{15}{15} - \frac{2}{15} + \frac{85}{15}$

$= \frac{15 - 2 + 85}{15}$ $= \frac{13 + 85}{15}$ $= \frac{98}{15}$

Conclusion

Comparing our result with the provided options, we see that it matches option D.

Exam Tip: When dealing with fractions in JAMB, always convert whole numbers to fractions with the same denominator as the other terms. It makes addition and subtraction much faster and reduces the risk of calculation errors.