4.1 Visualize fractions  (Page 3/11)

Solution

Each circle is divided into three pieces, so each piece is $\frac{1}{3}$ of the circle. There are four pieces shaded, so there are four thirds or $\frac{4}{3}.$ The figure shows that we also have one whole circle and one third, which is $1\frac{1}{3}.$ So, $\frac{4}{3}=1\frac{1}{3}.$

Solution

The denominator of the improper fraction is $8.$ Draw a circle divided into eight pieces and shade all of them. This takes care of eight eighths, but we have $11$ eighths. We must shade three of the eight parts of another circle.

So, $\frac{11}{8}=1\frac{3}{8}.$

Solution

We start with $11$ sixths $\left(\frac{11}{6}\right).$ We know that six sixths makes one whole.

That leaves us with five more sixths, which is $\frac{5}{6}\left(11\text{sixths minus}6\text{sixths is}5\text{sixths}\right).$

So, $\frac{11}{6}=1\frac{5}{6}.$

Solution

The mixed number $1\frac{4}{5}$ means one whole plus four fifths. The denominator is $5,$ so the whole is $\frac{5}{5}.$ Together five fifths and four fifths equals nine fifths.

So, $1\frac{4}{5}=\frac{9}{5}.$

Solution

	$\frac{11}{6}$
Divide the denominator into the numerator.	Remember $\frac{11}{6}$ means $11÷6$ .
Identify the quotient, remainder and divisor.
Write the mixed number as $\frac{\text{remainder}}{\text{divisor}}$ .	$1\frac{1}{6}$
So, $\frac{11}{6}=1\frac{1}{6}$

Solution

	$\frac{33}{8}$
Divide the denominator into the numerator.	Remember, $\frac{33}{8}$ means $8\overline{)33}$ .
Identify the quotient, remainder, and divisor.
Write the mixed number as quotient $\frac{\text{remainder}}{\text{divisor}}$ .	$4\frac{1}{8}$
	So, $\frac{33}{8}=4\frac{1}{8}$