Question

t ( 7\frac{2}{3} + 2\frac{7}{12} ) e ( \frac{3}{8} \times \frac{5}{6} ) r ( 4\frac{1}{2} \times 1\frac{2}{3} ) x ( 20 div 3\frac{1}{2} )

Explanation:

Step1: Solve T: Convert to improper fractions

$7\frac{2}{3} = \frac{7\times3+2}{3} = \frac{23}{3}$, $2\frac{7}{12} = \frac{2\times12+7}{12} = \frac{31}{12}$

Step2: Solve T: Find common denominator, add

$\frac{23}{3} = \frac{23\times4}{12} = \frac{92}{12}$
$\frac{92}{12} + \frac{31}{12} = \frac{123}{12} = \frac{41}{4} = 10\frac{1}{4}$

Step3: Solve E: Multiply numerators and denominators

$\frac{3}{8} \times \frac{5}{6} = \frac{3\times5}{8\times6}$

Step4: Solve E: Simplify the fraction

$\frac{15}{48} = \frac{5}{16}$

Step5: Solve R: Convert to improper fractions

$4\frac{1}{2} = \frac{9}{2}$, $1\frac{2}{3} = \frac{5}{3}$

Step6: Solve R: Multiply and simplify

$\frac{9}{2} \times \frac{5}{3} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}$

Step7: Solve X: Convert to improper fraction, invert divisor

$3\frac{1}{2} = \frac{7}{2}$, so $20 \div \frac{7}{2} = 20 \times \frac{2}{7}$

Step8: Solve X: Calculate the product

$20 \times \frac{2}{7} = \frac{40}{7} = 5\frac{5}{7}$

Answer:

T: $10\frac{1}{4}$
E: $\frac{5}{16}$
R: $7\frac{1}{2}$
X: $5\frac{5}{7}$