Convert to Improper Fractions: Convert the mixed numbers to improper fractions to make addition easier. 1 5/8 can be converted by multiplying the whole number by the denominator and adding the numerator: (1 × 8) + 5 = 13/8. 4 4/5 can be converted by multiplying the whole number by the denominator and adding the numerator: (4 × 5) + 4 = 24/5.Find Common Denominator: Find a common denominator for the two fractions to add them. The least common denominator for 8 and 5 is 40. Convert 13/8 to a fraction with a denominator of 40: (13 × 5) = 65/40. Convert 24/5 to a fraction with a denominator of 40: (24 × 8) = 192/40.Add Fractions: Add the two fractions with the common denominator. 65/40 + 192/40 = (65 + 192)/40 = 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 17/40.

Grade 6

Convert between improper fractions and mixed numbers

Full solution

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 $6 \frac{17}{40}.$