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1(5)/(20)+1(1)/(5)

$1 \frac{5}{20}+1 \frac{1}{5}$

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Convert between percents, fractions, and decimals: word problems

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Q.

1 \frac{5}{20}+1 \frac{1}{5}

Convert to Improper Fractions: Convert the mixed numbers to improper fractions. $\newline$ $1\left(\frac{5}{20}\right)$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $(1 \times 20) + 5 = 25$ , so we have $\frac{25}{20}$ . $\newline$ Similarly, $1\left(\frac{1}{5}\right)$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $(1 \times 5) + 1 = 6$ , so we have $\frac{6}{5}$ .
Simplify Fractions: Simplify the fractions if possible. $\newline$ $\frac{25}{20}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $5$ : $25 \div 5 = 5$ and $20 \div 5 = 4$ , so we have $\frac{5}{4}$ . $\newline$ $\frac{6}{5}$ is already in simplest form.
Find Common Denominator: Find a common denominator for the fractions $\frac{5}{4}$ and $\frac{6}{5}$ . The least common denominator (LCD) for $4$ and $5$ is $20$ .
Convert to Common Denominator: Convert each fraction to an equivalent fraction with the common denominator of $20$ . $\newline$ $\frac{5}{4}$ is converted to $(\frac{5 \times 5}{4 \times 5}) = \frac{25}{20}$ . $\newline$ $\frac{6}{5}$ is converted to $(\frac{6 \times 4}{5 \times 4}) = \frac{24}{20}$ .
Add Fractions: Add the fractions with the common denominator. $\newline$ $\frac{25}{20} + \frac{24}{20} = \frac{25 + 24}{20} = \frac{49}{20}$ .
Convert to Mixed Number: Convert the improper fraction back to a mixed number if possible. $\newline$ $\frac{49}{20}$ is an improper fraction. To convert it to a mixed number, divide the numerator by the denominator: $49 \div 20 = 2$ with a remainder of $9$ . $\newline$ So, $\frac{49}{20}$ as a mixed number is $2\left(\frac{9}{20}\right)$ .

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