Question

i need help with subtracting,multiplying,dividing,and adding fractions.

Answer 1

Adding fractions

To add two fractions, you have to make sure that the numbers in the denominator are the same.

For the fractions

$\frac{1}{2}+\frac{2}{5}$

The denominators are different, you have to look for a common factor between 2 and 5, the quickest way is to multiply them, you know that 10 is both a multiple of 2 and of 5.

Multiply 1/2 by 5 to obtain the equivalent expressed in tenths and multiply 2/5 by 2 to obtain the equivalent fraction in tenths

$\frac{1}{2}\cdot5=\frac{5}{10}$$\frac{2}{5}\cdot2=\frac{4}{10}$

Now that both fractions have the same denominator you can add them

$\frac{5}{10}+\frac{4}{10}=\frac{5+4}{10}=\frac{9}{10}$

Subtracting Fractions

You must apply the same procedure when subtracting two different fractions. First find a common factor so that the denominator is the same for both fractions:

$\frac{1}{2}-\frac{1}{5}$

As before, the common factor is 10, so the equivalent fractions will be:

$\frac{5}{10}-\frac{4}{10}=\frac{5-4}{10}=\frac{1}{10}$

Dividing fractions

To divide two fractions you have to do the following steps.

1- Invert the fraction that corresponds to the denominator of the division, i.e. the one you want to divide for (the second one).

This is called a reciprocal fraction.

2-Multiply the first fraction, the one you want to divide by the reciprocal fraction.

3-If possible, simplify the result.

1-Invert the denominator of the division

$\frac{2}{5}=\frac{5}{2}$

2-Multiply the denominator by the reciprocal fraction

$\frac{1}{2}\cdot\frac{5}{2}=\text{ }\frac{1\cdot5}{2\cdot2}=\frac{5}{4}$

1/2 divided by 2/5 equals 5/4