$1$ . $1 / 2 \times 5 / 6 \div 5 / 8$ $\newline$ $2$ . $2 \frac{1}{2} \times \frac{1}{3}+1 / 6$ $\newline$ $3$ . $1 \frac{3}{4} \times 1 / 2+2 \frac{1}{3} \div 1 \frac{1}{4}$

Full solution

1

1 / 2 \times 5 / 6 \div 5 / 8

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2

2 \frac{1}{2} \times \frac{1}{3}+1 / 6

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3

1 \frac{3}{4} \times 1 / 2+2 \frac{1}{3} \div 1 \frac{1}{4}

Calculate Expressions: question_prompt: Calculate the results of the given math expressions.
Simplify First Expression: For the first expression $\frac{1}{2} \times \frac{5}{6} \div \frac{5}{8}$ , start by simplifying the multiplication and division as a single operation.
Divide Fractions: Now, divide the fractions by multiplying the first fraction by the reciprocal of the second.
Simplify Fraction: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is $20$ .
Convert Mixed Number: For the second expression $2 \frac{1}{2} \times \frac{1}{3} + \frac{1}{6}$ , convert the mixed number to an improper fraction.
Multiply Improper Fraction: Now, multiply the improper fraction by $\frac{1}{3}$ .
Add Fractions: Add the result to $\frac{1}{6}$ .
Simplify Result: Simplify the fraction to get a whole number.
Convert Mixed Numbers: For the third expression $1\frac{3}{4} \times \frac{1}{2} + 2\frac{1}{3} \div 1\frac{1}{4}$ , convert the mixed numbers to improper fractions.
Multiply First Fraction: Now, multiply the first improper fraction by $\frac{1}{2}$ .
Convert Divisor: Convert the divisor $1\frac{1}{4}$ to an improper fraction.
Divide Mixed Numbers: Divide $2 \frac{1}{3}$ by $1 \frac{1}{4}$ by multiplying $\frac{7}{3}$ by the reciprocal of $\frac{5}{4}$ .
Add Results: Add the result of the multiplication to the result of the division.