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Wednesday, March 29, 2023

Multiplying Fractions

When multiplying fractions with a purpose to discover the product of two or extra fractions, you simply must observe these three easy steps mainly.

Step 1: Multiply the numerators collectively. The numerators are additionally known as prime 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 after 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 easy. Nevertheless, when multiplying fractions, you might marvel 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 scenario(s) you encounter, there are guidelines to observe if you multiply fractions with various kinds of fractions .

Guidelines of multiplying fractions

Rule 1: An important 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 is just not the identical as including fractions. Subsequently, you should 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

Once you multiply fractions with completely different denominators, simply bear 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 after 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 because the best widespread issue of two and 15 is 1.

1/5 × 2/3 = 1/2

Multiplying fractions with the identical denominator

Once 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

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

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

For instance should you 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, it is very important bear in mind rule 2. You need to first convert any combined quantity right into a fraction earlier than you multiply.

Suppose you might be multiplying a fraction by 2 1/3. Since 2 1/3 is a combined quantity, you should 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 just grow to be accustomed to the multiplication desk. It is possible for you to to carry out the multiplication of fractions a lot faster.

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

Check out the next instance:

 could be simplified as   1 / 2

Divide the numerator and the denominator by 10

 could 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. Generally, it’s a good suggestion to simplify the fractions earlier than multiplying.

Check out the next instance:

 could be simplified as   1 / 2

After we divide the numerator and the denominator by 10

 could 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 will we multiply fractions straight throughout?

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

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

If somebody eats half of your pizza, or 4 slices, you might be left with

4
/
8

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

1
/
2

In the event you resolve that you’re solely going to eat 1 slice out of the 4 slices remaining, you might be consuming

1
/
4

of the leftover.

Do not forget that the leftover is

1
/
2

You can too argue that you just 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 similar as consuming 1/8.

One other approach to get

1
/
8

is to carry out the next multiplication:

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

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

That is an attention-grabbing consequence however all you want to bear in mind is the next:

Once you multiply fractions, you should multiply straight throughout.

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