Fractions and mixed numbers

45/8 can be changed to an mixed number.

Divide the numerator 45 by the denominator 8.

Dividing will give a whole number of 5.

The remainder will now be made into a fraction of 5/8.  This means 5 out of the 8 are left.

The final answer is 5 5/8.

3 2/5 can be made into an improper fraction.

Multiply the denominator 5 by 3 the whole number.  This will give you 15

Add 15 to the numerator of 2.  This will give you 17.

The improper fraction will be 17/5.

When you multiply fractions, multiply the numerators and the denominators. Simplify if you need to in the end.

 $\frac{3}{4}\times\frac{24}{15}\ =\ \frac{3\ x\ 24}{4\ \times\ 15}\ =\ \frac{72}{60}=\ \frac{6}{5}\ =\ 1\frac{1}{5}$  

Notice: the improper fraction was simplified before being made back into an mixed number.

Dividing fractions is similar to multiplying fractions, the difference is the second fraction is flipped or reciprocals are used.

 $\frac{3}{5}\div\frac{12}{15}=\frac{3}{5}\ x\ \frac{15}{12}\ =\ \frac{45}{60}=\frac{3}{4}$  

In the example, the second fraction  $\frac{12}{15}$  was the reciprocal.  When the flip takes place the problem then becomes multiplication.  The final answer was simplified by dividing by 15.

When you have a whole number in the problem and you are multiplying or dividing, you can make the whole number into a fraction by putting the whole number over 1.

Ex: 5 x  $\frac{1}{2}$  =  $\frac{5}{1\ }\ \times\ \frac{1}{2}=\frac{5}{2}=\ 2\ \frac{1}{2}$  

Division will use the same method but you need to pay attention where the whole number is in the problem.  If it is the second term then this will be the reciprocal term.

When working with mixed numbers, it is easier to convert the mixed number into an improper fraction before solving the problem.

 $1\ \frac{2}{3\ }\times\ \frac{3}{5}\ \ =\ \frac{5}{3}\ x\ \frac{3}{5}\ =\ \frac{15}{15}=\ 1$  

The next slides will review what you learned in this lesson.