Question

top heavy fractions may contain common factors as well. they will need to be divided out either before or after the top heavy fraction is changed to a mixed number.
\\(\frac{26}{8}=\

$$\begin{array}{r}3\\\\8\\enclose{longdiv}{26}\\\\24\\\\\\hline2\\end{array}$$

=3\frac{2}{8}\\) but \\(\frac{2}{8}\\) can be divided by \\(\frac{2}{2}\\). then \\(3\frac{2}{8}\div\frac{2}{2}=3\frac{1}{4}\\)
if you had noticed that both 26 and 8 are even, you could divide out \\(\frac{2}{2}\\) right away and then go for the mixed number. either way, the mixed number is the same.
\\(\frac{26}{8}=\frac{26\div2}{8\div2}=\frac{13}{4}=\

$$\begin{array}{r}3\\\\4\\enclose{longdiv}{13}\\\\12\\\\\\hline1\\end{array}$$

=3\frac{1}{4}\\)
exercise 8 (answers on page 39)

1. \\(\frac{65}{10}=\\) 2. \\(\frac{40}{6}=\\) 3. \\(\frac{22}{4}=\\) 4. \\(\frac{22}{8}=\\) 5. \\(\frac{30}{9}=\\)

Explanation:

1. Solve \(\boldsymbol{\frac{65}{10}}\)

Step1: Find GCD of 65 and 10

GCD of 65 and 10 is 5. Divide numerator and denominator by 5.
\(\frac{65\div5}{10\div5}=\frac{13}{2}\)

Step2: Convert to mixed number

Divide 13 by 2: \(13\div2 = 6\) with remainder 1.
So \(\frac{13}{2}=6\frac{1}{2}\)

Step1: Find GCD of 40 and 6

GCD of 40 and 6 is 2. Divide numerator and denominator by 2.
\(\frac{40\div2}{6\div2}=\frac{20}{3}\)

Step2: Convert to mixed number

Divide 20 by 3: \(20\div3 = 6\) with remainder 2.
So \(\frac{20}{3}=6\frac{2}{3}\)

Step1: Find GCD of 22 and 4

GCD of 22 and 4 is 2. Divide numerator and denominator by 2.
\(\frac{22\div2}{4\div2}=\frac{11}{2}\)

Step2: Convert to mixed number

Divide 11 by 2: \(11\div2 = 5\) with remainder 1.
So \(\frac{11}{2}=5\frac{1}{2}\)

Answer:

\(6\frac{1}{2}\)

2. Solve \(\boldsymbol{\frac{40}{6}}\)