## Introduction: Adding Fractions

In this instructables we will learn how to add and subtract fractions.

What is a fraction you ask? Well its simple! (trust me)

A fraction is the ratio of two whole numbers. Simply put, its one whole number divided by another whole number. We write a fraction like this:

5 (numerator)

---

7 (denominator)

The top part of the fraction is called the numerator.The bottom part is called the denominator

Normally the numerator is smaller than the denominator, this is called a 'Proper Fraction'. If the numerator is equal to or larger than the denominator then the fraction is called an 'Improper Fraction'.

A proper fraction is always less than the number 1 and we can relate proper fractions to a part of a whole object. We use the denominator to divide the object into that number of parts and then we take the numerator number of parts and we can say we have that fractions part of the whole object.

For example: 3/4's of an orange, that means we have taken the orange, cut it into 4 equal parts, and then taken 3 of these part.

Pretty simple huh?

No lets learn how to add them

What is a fraction you ask? Well its simple! (trust me)

A fraction is the ratio of two whole numbers. Simply put, its one whole number divided by another whole number. We write a fraction like this:

5 (numerator)

---

7 (denominator)

The top part of the fraction is called the numerator.The bottom part is called the denominator

Normally the numerator is smaller than the denominator, this is called a 'Proper Fraction'. If the numerator is equal to or larger than the denominator then the fraction is called an 'Improper Fraction'.

A proper fraction is always less than the number 1 and we can relate proper fractions to a part of a whole object. We use the denominator to divide the object into that number of parts and then we take the numerator number of parts and we can say we have that fractions part of the whole object.

For example: 3/4's of an orange, that means we have taken the orange, cut it into 4 equal parts, and then taken 3 of these part.

Pretty simple huh?

No lets learn how to add them

## Step 1: How to Add Fractions

There are 3 simple steps to adding fractions.

Step 1: Make sure the denominators are the same

Step 2: Add the numerators. Put the answer over the the same denominator as in step 1

Step 3: Simplify the fraction (if needed).

(Note: 1/4 the 1 in the numerator, and the 4 is the denominator.)

Let me explain....

1/4 + 1/4

Since the denominators are the same, you can go straight to step 2, and add the top 2 numbers.

You will get 2/4, and now you simplify.

--HOW TO SIMPLIFY --

To simplify you divide both the top and bottom of the fraction by the Greatest Common Factor.

What is a "Greatest Common Factor" AKA: GCF?

Well lets look at what a factor is first, A factor is any of the numbers that can be multiplied together to make another number. Example: The factors of 12 are 1,2,3,4,6 and 12 ...because 2 * 6 = 12, or 4 * 3 = 12, or 1 * 12 = 12.

Now, what makes a Factor a "Common Factor"?

A factor is a common factor if it is a factor of two or more numbers.

For example:

The factors of 12 are 1, 2, 3, 4, "6" and 12

The factors of 30 are 1, 2, 3, 5, "6", 10, 15 and 30

Notice that 1,2,3 and 6 appear in both lists? So, the common factors of 12 and 30 are: 1, 2, 3 and 6

Ok, now we know what a common factor is but what on earth is the "Greatest Common Factor"?

It is simply the largest of the common factors. In our example above, the largest of the common factors is 6, so the Greatest Common Factor is 6!

To find the GCF, you just play around with the numbers, lets try with 4 and 10!

4: 1, "2", 4

10: 1, "2", 5, 10

The GFC is 2!

Ok? Now lets get back to the adding

2/4

The GCF of the two numbers is 2, so divide both numbers by 2 and you get...

1

---

2

Done, We have now added, and simplified a fraction.

Simple right? Well it gets harder

1/3 + 1/6

The denominator are different, So we cant add them.

In this case we just have to multiply 1/3 by 2, and we get 2/6!

Now we can add! 2/6 + 1/6 and you get 3/6. Now simplify, and you get 1/2.

But what about this problem?

1/3 + 1/5

multiply 1/3 by 5 and 1/5 by 3

So you have 5/15 and 3/15, you are now ready to add.

5/15 + 3/15 = 8/15

No need to simply!

See: https://www.instructables.com/id/Subtracting_Fractions_1/

Step 1: Make sure the denominators are the same

Step 2: Add the numerators. Put the answer over the the same denominator as in step 1

Step 3: Simplify the fraction (if needed).

(Note: 1/4 the 1 in the numerator, and the 4 is the denominator.)

Let me explain....

1/4 + 1/4

Since the denominators are the same, you can go straight to step 2, and add the top 2 numbers.

You will get 2/4, and now you simplify.

--HOW TO SIMPLIFY --

To simplify you divide both the top and bottom of the fraction by the Greatest Common Factor.

What is a "Greatest Common Factor" AKA: GCF?

Well lets look at what a factor is first, A factor is any of the numbers that can be multiplied together to make another number. Example: The factors of 12 are 1,2,3,4,6 and 12 ...because 2 * 6 = 12, or 4 * 3 = 12, or 1 * 12 = 12.

Now, what makes a Factor a "Common Factor"?

A factor is a common factor if it is a factor of two or more numbers.

For example:

The factors of 12 are 1, 2, 3, 4, "6" and 12

The factors of 30 are 1, 2, 3, 5, "6", 10, 15 and 30

Notice that 1,2,3 and 6 appear in both lists? So, the common factors of 12 and 30 are: 1, 2, 3 and 6

Ok, now we know what a common factor is but what on earth is the "Greatest Common Factor"?

It is simply the largest of the common factors. In our example above, the largest of the common factors is 6, so the Greatest Common Factor is 6!

To find the GCF, you just play around with the numbers, lets try with 4 and 10!

4: 1, "2", 4

10: 1, "2", 5, 10

The GFC is 2!

Ok? Now lets get back to the adding

2/4

The GCF of the two numbers is 2, so divide both numbers by 2 and you get...

1

---

2

Done, We have now added, and simplified a fraction.

Simple right? Well it gets harder

1/3 + 1/6

The denominator are different, So we cant add them.

In this case we just have to multiply 1/3 by 2, and we get 2/6!

Now we can add! 2/6 + 1/6 and you get 3/6. Now simplify, and you get 1/2.

But what about this problem?

1/3 + 1/5

multiply 1/3 by 5 and 1/5 by 3

So you have 5/15 and 3/15, you are now ready to add.

5/15 + 3/15 = 8/15

No need to simply!

See: https://www.instructables.com/id/Subtracting_Fractions_1/