Question

ging the fractions to equivalent fractions. simplify your answer
ii) (3\frac{2}{3}+\frac{5}{6})
= (3+\frac{2}{3}+\frac{5}{6})
= (3+\frac{8}{12}+\frac{10}{12})
= (3\frac{18}{12}=4\frac{6}{12})
ked number by regrouping 1 whole as a fraction.
(3 + 1\frac{1}{3}=3\frac{4}{3})
) (5\frac{1}{2}) iii) (1\frac{1}{6}) iv) (2\frac{3}{4}) v)
ing the first mixed number as in part a):
(\frac{4}{20}-1\frac{15}{20}) ii) (4\frac{1}{3}-2\frac{3}{5})
= (1\frac{9}{20})

Explanation:

Step1: Convert mixed - number to improper fraction and find common denominator

The mixed - number \(3\frac{2}{3}\) can be written as \(3+\frac{2}{3}=\frac{9 + 2}{3}=\frac{11}{3}\). The common denominator of \(\frac{11}{3}\) and \(\frac{5}{6}\) is 6. So \(\frac{11}{3}=\frac{11\times2}{3\times2}=\frac{22}{6}\).

Step2: Add the fractions

\(\frac{22}{6}+\frac{5}{6}=\frac{22 + 5}{6}=\frac{27}{6}\).

Step3: Simplify the fraction and convert to mixed - number

\(\frac{27}{6}=\frac{24+3}{6}=4\frac{3}{6}=4\frac{1}{2}\).

Answer:

\(4\frac{1}{2}\)