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Add $1\frac{5}{8}$ and $4\frac{4}{5}$

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Convert between improper fractions and mixed numbers

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Q. Add

1\frac{5}{8}

and

4\frac{4}{5}

Convert to Improper Fractions: Convert the mixed numbers to improper fractions to make addition easier. $\newline$ $1 \frac{5}{8}$ can be converted by multiplying the whole number by the denominator and adding the numerator: $(1 \times 8) + 5 = \frac{13}{8}$ . $\newline$ $4 \frac{4}{5}$ can be converted by multiplying the whole number by the denominator and adding the numerator: $(4 \times 5) + 4 = \frac{24}{5}$ .
Find Common Denominator: Find a common denominator for the two fractions to add them. $\newline$ The least common denominator for $8$ and $5$ is $40$ . $\newline$ Convert $\frac{13}{8}$ to a fraction with a denominator of $40$ : $(13 \times 5) = \frac{65}{40}$ . $\newline$ Convert $\frac{24}{5}$ to a fraction with a denominator of $40$ : $(24 \times 8) = \frac{192}{40}$ .
Add Fractions: Add the two fractions with the common denominator. $\newline$ $\frac{65}{40} + \frac{192}{40} = \frac{65 + 192}{40} = \frac{257}{40}$ .
Convert to Mixed Number: Convert the improper fraction back to a mixed number. $257$ divided by $40$ is $6$ with a remainder of $17$ , so the mixed number is $6 \frac{17}{40}.$

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