Question

add.
4\frac{1}{3}
5\frac{1}{6}
+ 1\frac{5}{9}

the answer is . (type an integer, proper fraction, or mixed number.)
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Explanation:

Step1: Separate whole - numbers and fractions

Separate the whole - number parts and fraction parts of the mixed numbers. The whole - number parts are \(4 + 5+1=10\). The fraction parts are \(\frac{1}{3}+\frac{1}{6}+\frac{5}{9}\).

Step2: Find a common denominator

The least common multiple of 3, 6, and 9 is 18. Rewrite the fractions with the common denominator. \(\frac{1}{3}=\frac{1\times6}{3\times6}=\frac{6}{18}\), \(\frac{1}{6}=\frac{1\times3}{6\times3}=\frac{3}{18}\), \(\frac{5}{9}=\frac{5\times2}{9\times2}=\frac{10}{18}\).

Step3: Add the fractions

\(\frac{6}{18}+\frac{3}{18}+\frac{10}{18}=\frac{6 + 3+10}{18}=\frac{19}{18}\).

Step4: Convert the improper fraction and add to the whole - number

\(\frac{19}{18}=1\frac{1}{18}\). Then \(10+1\frac{1}{18}=11\frac{1}{18}\).

Answer:

\(11\frac{1}{18}\)