Simplify. $\newline$ $12 \frac{1}{2}-4 \frac{7}{10}= \_\_\_\_\_$

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Algebra 1

Powers with decimal and fractional bases

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Q. Simplify.

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12 \frac{1}{2}-4 \frac{7}{10}= \_\_\_\_\_

Convert to Improper Fractions: Convert mixed numbers to improper fractions. $\newline$ $12\left(\frac{1}{2}\right)$ can be converted to an improper fraction by multiplying the whole number $12$ by the denominator $2$ and adding the numerator $1$ , then placing the result over the original denominator. $\newline$ $12\left(\frac{1}{2}\right) = \left(12 \times 2 + 1\right)/2 = \left(24 + 1\right)/2 = 25/2.$ $\newline$ Similarly, $4\left(\frac{7}{10}\right)$ can be converted to an improper fraction by multiplying the whole number $4$ by the denominator $10$ and adding the numerator $7$ , then placing the result over the original denominator. $\newline$ $4\left(\frac{7}{10}\right) = \left(4 \times 10 + 7\right)/10 = \left(40 + 7\right)/10 = 47/10.$
Subtract Fractions: Subtract the two improper fractions. $\newline$ To subtract fractions, they must have a common denominator. The least common denominator (LCD) for $2$ and $10$ is $10$ . We need to convert $\frac{25}{2}$ to a fraction with a denominator of $10$ . $\newline$ $\frac{25}{2} = \left(\frac{25 \times 5}{2 \times 5}\right) = \frac{125}{10}$ . $\newline$ Now we can subtract $\frac{47}{10}$ from $\frac{125}{10}$ . $\newline$ $\frac{125}{10} - \frac{47}{10} = \left(\frac{125 - 47}{10}\right) = \frac{78}{10}$ .
Simplify Resulting Fraction: Simplify the resulting fraction. $\frac{78}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\frac{78}{10} = \frac{(78/2)}{(10/2)} = \frac{39}{5}$ .
Convert Back to Mixed Number: Convert the improper fraction back to a mixed number if necessary. $\newline$ Since $\frac{39}{5}$ is an improper fraction, we can convert it back to a mixed number. $39$ divided by $5$ is $7$ with a remainder of $4$ . $\newline$ $\frac{39}{5} = 7\left(\frac{4}{5}\right)$ .