Multiplying Fractions
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When multiplying fractions with a view to discover the product of two or extra fractions, you simply have to observe these three easy steps principally.
Step 1: Multiply the numerators collectively. The numerators are additionally referred to as prime numbers.
Step 2: Multiply the denominators collectively. The denominators are additionally referred to 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 biggest frequent issue (GCF) of 12 and 24.
3/4 × 4/6 = 1/2
The instance above is easy. Nonetheless, when multiplying fractions, you might marvel concerning the following circumstances.
- Multiplying fractions with completely different denominators
- Multiplying fractions with the identical denominator
- Multiplying fractions with complete numbers
- Multiplying fractions with blended numbers
- Multiplying improper fractions
Relying on which state of affairs(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 all the time convert blended fractions, additionally referred to as blended numbers into improper fractions earlier than multiplying.
Rule 3: Convert complete numbers into fractions earlier than doing multiplication.
Rule 4: Multiplying fractions isn’t the identical as including fractions. Due to this fact, you should not search for the least frequent 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 typical denominator! The rule for including fractions and multiplying fractions will not be the identical.
For instance, discover that we don’t search for a typical 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 biggest frequent 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 complete numbers
Once you multiply fractions with complete numbers, simply bear in mind rule 3 said above. Convert the entire quantity right into a fraction earlier than doing multiplication.
Discover that any complete quantity x may be written as a fraction x/1 since any quantity divided by 1 will return the identical quantity.
For instance if you happen to 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 blended numbers
When multiplying fractions with blended numbers, you will need to keep in mind rule 2. You will need to first convert any blended 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 blended 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 wish to do right here is to transform the improper fractions to blended 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 suggestions and trick to observe when multiplying fractions
1. I like to recommend that you simply turn into conversant in the multiplication desk. It is possible for you to to carry out the multiplication of fractions a lot faster.
Check out the next instance:
|
may be simplified as
1 |
Divide the numerator and the denominator by 10
|
may be simplified as
1 |
Divide the numerator and the denominator by 3
1
10
Check out the next instance:
|
may be simplified as
1 |
After we divide the numerator and the denominator by 10
|
may be simplified as
1 |
After we divide the numerator and the denominator by 3
1
10
3. In case you have three or extra fractions, simply multiply all numerators and all denominators
Going just a little deeper! Why will we multiply fractions straight throughout?
I want to introduce the subject with an fascinating instance about pizza.
Suppose that you simply purchased a medium pizza and the pizza has 8 slices.
4
8
1
2
1
4
of the leftover.
1
2
1
8
Thus, we will see that consuming 1/4 of 1/2 is identical as consuming 1/8.
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 fascinating outcome however all it is advisable to keep 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.
Multiplying fractions quiz. Test to see if now you can multiply fractions.
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