Visualize Fractions

Indeed, we can convert every mixed number into an improper fraction. We will discuss this conversion trick in the next section. Read this text, complete the practice problems, and check your answers.




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

TRY IT 4.9

\dfrac{5}{3}=1 \dfrac{2}{3}

TRY IT 4.10

\dfrac{13}{8}=1 \dfrac{5}{8}


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, \dfrac{11}{8}=1 \dfrac{3}{8}.

TRY IT 4.11




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


That leaves us with five more sixths, which is \dfrac{5}{6} \text{(11 sixths minus 6 sixths is 5 sixths)}. So, \dfrac{11}{6}=1 \dfrac{5}{6}.

TRY IT 4.13

1 \dfrac{2}{7}

TRY IT 4.14

1 \dfrac{3}{4}



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

So, 1 \dfrac{4}{5}=\dfrac{9}{5}.


TRY IT 4.15


TRY IT 4.16