Question

Can someone elaborate the rule of common denominators?

Answer 1

Only things that are the same can be added or subtracted. Hence fractions can only be added or subtracted with a common denominator.

Explanation:

Apples and Oranges can not be added. Change both to fruit ( a common denominator) Now Apples and Oranges can be added find to a total number of pieces of fruit.

Fractions with a different denominator are like Apples and Oranges they can not be added. Change both fractions to fractions with the same denominator. Now the fractions can be aded or subtracted.

Answer 2

Refer to the explanation.

Explanation:

When adding or subtracting fractions, they must have the same denominator; a common denominator. So what do we do if they don't have a common denominator? We can convert them into equivalent fractions by multiplying by a fractional form of `1;` a fraction with the same numerator and denominator. For example, `3/3=1`. This will change the numbers, but not the value of the fraction.

Example: What is `3/8 + 1/4`?

We can see that the denominators are not common. We can also see that the denominator `4` can become `8` by multiplying `1/4` by `2/2`.

`3/8+1/4xxcolor(teal)(2/2`

Simplify.

`3/8+2/8`

Now add the fractions.

`3/8+2/8=5/8`

Example: What is `3/12-2/15`?

In this example, the denominators are not multiples of each other, so we must first determine the least common denominator (LCD) of `12` and `15`. List the multiples of `12` and `15`. The lowest number they have in common is the LCD.

`12:` `12,24,36,48,color(red)60,72,84...`

`15:` `15,30,45,color(red)60...`

The LCD is `60`.

Now go back to the question.

`3/12-2/15`

Now we must multiply each fraction by a fractional form of `1` that gives them a denominator of `60`.

`12xx5=60`

`15xx4=60`

Multiply each fraction by the appropriate fractional form of `1`.

`3/12xxcolor(teal)(5/5)-2/15xxcolor(magenta)(4/4`

Simplify.

`15/60-8/60`

Simplify.

`7/60`

Since `7` is a prime number, `7/60` cannot be reduced.