Home Math Multiplying Fractions

### Multiplying Fractions

When multiplying fractions in an effort to discover the product of two or extra fractions, you simply have to observe these three easy steps mainly.

Step 1: Multiply the numerators collectively. The numerators are additionally known as high numbers.

Step 2: Multiply the denominators collectively. The denominators are additionally known as backside numbers.

Step 3: Lastly, attempt to simplify the product if wanted to get the ultimate reply.

For instance, discover what we do once we multiply the next fractions: 3/4 × 4/6.

Step 1: Multiply 3 and 4 to get 12 and 12 is the numerator of the product

Step 2: Multiply 4 and 6 to get 24 and 24 is the denominator of the product

3/4 × 4/6 = (3 × 4)/(4 × 6) = 12/24

Step 3: Divide each the numerator and the denominator by 12 to simplify the fraction. 12 is the best widespread issue (GCF) of 12 and 24.

3/4 × 4/6 = 1/2

The instance above is simple. Nevertheless, when multiplying fractions, chances are you’ll surprise in regards to the following instances.

• Multiplying fractions with completely different denominators
• Multiplying fractions with the identical denominator
• Multiplying fractions with entire numbers
• Multiplying fractions with combined numbers
• Multiplying improper fractions

Relying on which state of affairs(s) you encounter, there are guidelines to observe once you multiply fractions with various kinds of fractions .

## Guidelines of multiplying fractions

Rule 1: A very powerful rule is to multiply straight throughout. In different phrases, multiply the numerators to get the brand new numerator or the numerator of the product. Multiply the denominators to get the brand new denominator or the denominator of the product.

Rule 2: One other necessary rule is to at all times convert combined fractions, additionally known as combined numbers into improper fractions earlier than multiplying.

Rule 3: Convert entire numbers into fractions earlier than doing multiplication.

Rule 4: Multiplying fractions shouldn’t be the identical as including fractions. Due to this fact, it’s essential to not search for the least widespread denominator!

Rule 5: Simplify the product or write the fraction you finish with after performing multiplication in lowest phrases if wanted.

## Multiplying fractions with completely different denominators

Whenever you multiply fractions with completely different denominators, simply have in mind rule 4 said above. Don’t search for a standard denominator! The rule for including fractions and multiplying fractions will not be the identical.

For instance, discover that we don’t search for a standard denominator once we multiply the next fractions: 1/5 × 2/3.

Step 1: Multiply 1 and a couple of to get 2

Step 2: Multiply 5 and three to get 15

1/5 × 2/3 = (1 × 2)/(5 × 3) = 2/15

Step 3: 2/15 is already written in lowest phrases for the reason that best widespread issue of two and 15 is 1.

1/5 × 2/3 = 1/2

## Multiplying fractions with the identical denominator

Whenever you multiply fractions with the identical denominator, simply do the identical factor you do when the fractions have not like denominators.

Instance: Multiply 3/4 and 1/4

3/4 × 1/4 = (3 × 1)/(4 × 4) = 3/16

## Multiplying fractions with entire numbers

Whenever you multiply fractions with entire numbers, simply have in mind rule 3 said above.  Convert the entire quantity right into a fraction earlier than doing multiplication.

Discover that any entire quantity x might be written as a fraction x/1 since any quantity divided by 1 will return the identical quantity.

For instance for those who multiply the entire quantity 5 by one other fraction, write 5 as 5/1 earlier than you multiply.

Instance: Multiply 5 and a couple of/3

5 × 2/3 = 5/1 × 2/3

5 × 2/3 = (5 × 2)/(1 × 3) = 10/3

## Multiplying fractions with combined numbers

When multiplying fractions with combined numbers, you will need to bear in mind rule 2. It’s essential to first convert any combined quantity right into a fraction earlier than you multiply.

Suppose you’re multiplying a fraction by 2 1/3. Since 2 1/3 is a combined quantity, it’s essential to convert it right into a fraction.

2 1/3 = (2 × 3 + 1)/3 = (6 + 1) / 3 = 7/3

Instance: Multiply 1/6 and a couple of 1/3

1/6 × 2 1/3 = 1/6 × 7/3

1/6 × 7/3 = (1 × 7)/(6 × 3) = 7/18

## Multiplying improper fractions

The multiplication of improper fractions is carried out by following rule 1. Simply multiply straight throughout. One factor you positively do not need to do right here is to transform the improper fractions to combined numbers.

This will likely be very counterproductive as you’ll have to convert them proper again into improper fractions.

Instance: Multiply 9/2 and three/5

9/2 × 3/5 = (9 × 3)/(2 × 5) = 27/10

## A few ideas and trick to observe when multiplying fractions

1. I like to recommend that you simply turn out to be conversant in the multiplication desk. It is possible for you to to carry out the multiplication of fractions a lot faster.

2. Typically, it’s a good suggestion to simplify the fractions earlier than multiplying to make calculations simpler.

Check out the next instance:

 might be simplified as   1 / 2

Divide the numerator and the denominator by 10

 might be simplified as   1 / 5

Divide the numerator and the denominator by 3

This fashion, it’s simpler to do the multiplication to get

1
/
10

2. Typically, it’s a good suggestion to simplify the fractions earlier than multiplying.

Check out the next instance:

 might be simplified as   1 / 2

After we divide the numerator and the denominator by 10

 might be simplified as   1 / 5

After we divide the numerator and the denominator by 3

This fashion, it’s simpler to do the multiplication to get

1
/
10

3. When you’ve got three or extra fractions, simply multiply all numerators and all denominators

## Going a bit deeper! Why can we multiply fractions straight throughout?

I wish to introduce the subject with an attention-grabbing instance about pizza.

Suppose that you simply purchased a medium pizza and the pizza has 8 slices.

If somebody eats half of your pizza, or 4 slices, you’re left with

4
/
8

From the illustration beneath, you can too see that the leftover is identical as

1
/
2

Should you resolve that you’re solely going to eat 1 slice out of the 4 slices remaining, you’re consuming

1
/
4

of the leftover.

Do not forget that the leftover is

1
/
2

It’s also possible to argue that you simply solely ate 1 slice out of 8 slices or

1
/
8

Thus, we are able to see that consuming 1/4 of 1/2 is identical as consuming 1/8.

One other method to get

1
/
8

is to carry out the next multiplication:

We get this reply by multiplying the numbers on high (numerators): 1 × 1 = 1

and by multiplying the numbers on the backside (denominators): 4 × 2 = 8

That is an attention-grabbing end result however all you’ll want to bear in mind is the next:

Whenever you multiply fractions, it’s essential to multiply straight throughout.

When the phrase ‘of‘ is positioned between two fractions, it means multiplication.