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

`(1)/(2)+(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

`(1)/(2)\cdot5=(5)/(10)`
`(2)/(5)\cdot2=(4)/(10)`

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

`(5)/(10)+(4)/(10)=(5+4)/(10)=(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:

`(1)/(2)-(1)/(5)`

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

`(5)/(10)-(4)/(10)=(5-4)/(10)=(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

`(2)/(5)=(5)/(2)`

2-Multiply the denominator by the reciprocal fraction

`(1)/(2)\cdot(5)/(2)=\text{ }(1\cdot5)/(2\cdot2)=(5)/(4)`

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