Mathematics 2007 JAMB Past Questions - Question 32: Simplify 3/5 : (2/7 x 4/3 /4/9)

Correct Answer

B

Explanation

3/5 /(2/7 *4/3 /4/9) =3/5 /(2/7 x 4/3 x 9/4)=3/5 /6/7=3/5 x 7/6 =7/10To simplify the expression 3/5 : (2/7 x 4/3 / 4/9), we can follow the order of operations (PEMDAS/BODMAS) and simplify the expression inside the parentheses first.Inside the parentheses, we have (2/7 x 4/3 / 4/9). To divide fractions, we multiply by the reciprocal of the divisor. So, we can rewrite the expression as:(2/7) x (4/3) x (9/4)Now, we can multiply the fractions together:(2/7) x (4/3) x (9/4) = (2 x 4 x 9) / (7 x 3 x 4) = 72 / 84To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 12:72 / 84 = (72 ÷ 12) / (84 ÷ 12) = 6/7Now, we can substitute this simplified expression back into the original expression:3/5 : (2/7 x 4/3 / 4/9) = 3/5 : (6/7)To divide fractions, we multiply by the reciprocal of the divisor:3/5 x (7/6) = (3 x 7) / (5 x 6) = 21/30Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:21/30 = (21 ÷ 3) / (30 ÷ 3) = 7/10Therefore, the simplified expression is 7/10.