Exercise 1 Page 661

To add the fractions, they should have a common denominator. In this exercise, we have two fractions with different denominators.

\frac{6}{5} + \frac{5}{6}

30 .

Let's rewrite our expression so that both fractions have a denominator of

30 .

To do this, we will multiply the numerator and denominator in the first fraction by

6

and by multiplying the numerator and denominator in the second fraction by

5 .

\frac{6}{5} + \frac{5}{6}

$\frac{a}{b} = \frac{a \cdot 6}{b \cdot 6}$

\frac{6 \cdot 6}{5 \cdot 6} + \frac{5}{6}

$\frac{a}{b} = \frac{a \cdot 5}{b \cdot 5}$

\frac{6 \cdot 6}{5 \cdot 6} + \frac{5 \cdot 5}{6 \cdot 5}

\frac{3 6}{3 0} + \frac{2 5}{3 0}

Now that we have a common denominator, we can proceed to simplify the expression.

\frac{3 6}{3 0} + \frac{2 5}{3 0}

Add fractions

\frac{3 6 + 2 5}{3 0}

Add terms

\frac{6 1}{3 0}

Therefore,

\frac{6 1}{3 0}

is the answer to the sum of the fractions. However, we can also write our answer as a mixed number.

\frac{6 1}{3 0}

▼

Write as mixed number

Rewrite $61$ as $60 + 1$

\frac{6 0 + 1}{3 0}

Write as a sum of fractions

\frac{6 0}{3 0} + \frac{1}{3 0}

Calculate quotient

2 + \frac{1}{3 0}

Finally, the expression

2 + \frac{1}{3 0}

can be read as

2

and

\frac{1}{3 0}

. Therefore, it can be written as

2 \frac{1}{3 0} .

\frac{6}{5} + \frac{5}{6} = \frac{6 1}{3 0} \Leftrightarrow \frac{6}{5} + \frac{5}{6} = 2 \frac{1}{3 0}