Simplify the expression \frac{3\frac{1}{3} - 1\frac{1}{4}}{\frac{2}{3} \text{ of } 2\frac{… — JAMB UTME

Simplify the expression $\frac{3\frac{1}{3} - 1\frac{1}{4}}{\frac{2}{3} \text{ of } 2\frac{1}{2} + 1\frac{1}{6}}$ and express the answer correct to three significant figures. What is the resulting value?

$0.735$ Answer
B
$0.852$
C
$1.07$
D
$0.736$

Answer

The simplified value correct to three significant figures is

0.735

Simplifying the numerator yields

\frac{25}{12}

. For the denominator, applying BODMAS gives

\frac{2}{3} \times \frac{5}{2} = \frac{5}{3}

, and adding

\frac{7}{6}

results in

\frac{17}{6}

. Dividing the numerator by the denominator gives

\frac{25}{34} = 0.73529...

. Rounding to three significant figures gives

0.735

Step-by-Step Solution

Convert mixed fractions to improper fractions and simplify the numerator.

3\frac{1}{3} - 1\frac{1}{4} = \frac{10}{3} - \frac{5}{4} = \frac{40 - 15}{12} = \frac{25}{12}

Find a common denominator (

12

) to subtract the fractions.

Evaluate the denominator following BODMAS rules (performing 'of' before addition).

\frac{2}{3} \text{ of } 2\frac{1}{2} = \frac{2}{3} \times \frac{5}{2} = \frac{5}{3}

. Then add

1\frac{1}{6}

\frac{5}{3} + \frac{7}{6} = \frac{10 + 7}{6} = \frac{17}{6}

'of' signifies multiplication and takes precedence over addition.

Divide the numerator by the denominator.

\frac{\frac{25}{12}}{\frac{17}{6}} = \frac{25}{12} \times \frac{6}{17} = \frac{25}{2 \times 17} = \frac{25}{34}

Dividing by a fraction is equivalent to multiplying by its reciprocal.

Convert the resulting fraction to a decimal and round to three significant figures.

\frac{25}{34} = 0.735294... \approx 0.735

The first non-zero digit is

7

. The first three significant figures are

7, 3, 5

, followed by

2

, so we round down.

Key Concept

Compound Fraction Operations and Approximation

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