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Calculate $3 \frac{1}{4}$ divided by $1 \frac{1}{2}$ .

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Convert between improper fractions and mixed numbers

Full solution

Q. Calculate

3 \frac{1}{4}

divided by

1 \frac{1}{2}

.

Convert to Improper Fractions: First, we need to convert the mixed numbers into improper fractions to make the division easier. $\newline$ For $3\frac{1}{4}$ , multiply the whole number $3$ by the denominator $4$ and add the numerator $1$ to get the new numerator. The denominator remains the same. $\newline$ $3 \times 4 + 1 = 12 + 1 = 13$ $\newline$ So, $3\frac{1}{4}$ becomes $\frac{13}{4}$ .
Divide Improper Fractions: For $1\frac{1}{2}$ , multiply the whole number $1$ by the denominator $2$ and add the numerator $1$ to get the new numerator. The denominator remains the same. $\newline$ $1 \times 2 + 1 = 2 + 1 = 3$ $\newline$ So, $1\frac{1}{2}$ becomes $\frac{3}{2}$ .
Perform Multiplication: Now, divide the improper fraction $\frac{13}{4}$ by $\frac{3}{2}$ . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. $\newline$ The reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$ . $\newline$ So, we multiply $\frac{13}{4}$ by $\frac{2}{3}$ .
Simplify Fraction: Perform the multiplication: $\newline$ egin{equation} $\newline$ \left(\frac{ $13$ }{ $4$ }\right) * \left(\frac{ $2$ }{ $3$ }\right) = \left(\frac{ $13$ * $2$ }{ $4$ * $3$ }\right) = \frac{ $26$ }{ $12$ } $\newline$ d{equation}
Convert to Mixed Number: Simplify the fraction $\frac{26}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $26 \div 2 = 13$ $\newline$ $12 \div 2 = 6$ $\newline$ So, $\frac{26}{12}$ simplifies to $\frac{13}{6}$ .
Convert to Mixed Number: Simplify the fraction $\frac{26}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $26 \div 2 = 13$ $\newline$ $12 \div 2 = 6$ $\newline$ So, $\frac{26}{12}$ simplifies to $\frac{13}{6}$ .Convert the improper fraction $\frac{13}{6}$ back to a mixed number. $\newline$ $13$ divided by $6$ is $2$ with a remainder of $2$ $0$ . $\newline$ So, $\frac{13}{6}$ is equal to $2$ $2$ .

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