Wondering how to multiply problems on whole numbers and fractions, don’t worry this page will help you in understanding the complete concept and provides it all in one place. Get acquainted with details on the definitions of both fractional numbers as well as whole numbers. In addition find the Rules for Multiplying Fractional Numbers with Whole Numbers, Steps on How to Multiply a Fractional Number with a Whole Number along with Solved Examples.
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What are Fractional Numbers and Whole Numbers?
Fractional Numbers: A number is said to be a fractional number if it is of the form \(\frac {b }{d} \)
Whole Numbers: Whole numbers are the natural numbers that including zero. The whole numbers are 0, 1, 2, 3, 4, 5, and so on… We use natural numbers to represent these fractional numbers.
Multiplication of Fractional Number by a Whole Number
Multiplication of Whole numbers and Fractional numbers may look a little difficult. If we observe the whole numbers are just simple numbers. This is not the same for Fractional Numbers. Fractional Numbers look a little complex because they are in the form of \(\frac {b }{d} \). So, multiplying these two numbers looks a little difficult. So here, we are to provide you with a simple explanation that helps you easily understand the multiplication of whole numbers and Fractional numbers.
If we observe the Fractional numbers, they will have a numerator and a denominator, but the whole numbers will only have a numerator, not a denominator. So what do you think we should do to multiple these two numbers? don’t worry we are here to help you. Simply follow the below-mentioned steps.
Rules to Multiply Fraction Numbers
Whenever we are multiplying fractions, always remember to multiple the numerators together, then multiply the denominators.
Which means, \(\frac {a }{b} \)Â * \(\frac {c }{d} \)
\(\frac {a*c }{b*d} \)
Now that we know the rule to multiple fraction numbers, we can use that to multiply fractions with whole numbers.
How to Multiply a Whole Number with a Fraction?
We need to follow few simple steps to multiply a whole number with a fraction number as mentioned below.
Step 1: As we already know that the whole number does not have a denominator. So, we just need to put 1 as the denominator for the given whole number, because whenever a number is divided with 1 the result will remain the same.
Step 2:Â Now after adding 1 as the denominator for the given whole number, the given whole number looks like a fraction number.
Step 3: We know the rule to multiply the fraction numbers, we should multiply the numerator with a numerator first and then multiply the denominator with a denominator.
Step 4: After doing the multiplication the solution will be a fraction number if the obtained result can be simplified further you should simplify it.
Which means,
If a*\(\frac {b }{c} \) is the given equation,
Then we need to change the equation as \(\frac {a }{1} \)* \(\frac {b }{c} \)
So according to step 3 our equation now becomes \(\frac {a*b }{1*c} \)
Solve the equation to obtain the result.
Multiplication of a Whole Number by a Fraction Number Examples
Let’s solve few examples for better understanding the concept.
Example 1:Â
Solve 3 * \(\frac {2 }{7} \)?
Solution:
Initially, we need to covert the given whole number into a fraction number. To do so we need to add 1 as the denominator for 3
So, the given equation becomes \(\frac {3 }{1} \)Â * \(\frac {2 }{7} \)
We need to apply the rule.
Now the given equation becomes \(\frac {3*2 }{1*7} \)
Which gives us \(\frac {6 }{7} \)
The obtained result can’t be simplified further so the answer remains the same.
Example 2:
Solve 5 * \(\frac {9 }{10} \)?
Solution:
Initially, we need to covert the given whole number into a fraction number. To do so we need to add 1 as the denominator for 5.
So, the given equation becomes \(\frac {5}{1 } \)Â * \(\frac {9 }{10} \)
We need to apply the rule.
Now the given equation becomes \(\frac {5*9 }{1*10 } \)
Which gives, \(\frac { 45 }{10 } \)
45 and 10 these 2 numbers can be divided by 5 so the obtained result can be simplified as \(\frac {9 }{2 } \)
Multiplying a Whole Number with a Mixed Fraction Number
Now we got to know how to multiply a whole number with a fraction number. But if the given fraction number is a mixed fraction then what are we supposed to do.
In order to multiply a whole number with the mixed fraction number, first, we need to change the mixed fraction number to a normal fraction number which will help us to solve the problem with the same process that we used before.
How to Multiply a Whole Number with a Mixed Fraction Number?
We need to follow few simple steps to multiply a whole number with a mixed fraction number as mentioned below.
Step 1:Â First we need to change the mixed fraction number to a normal fraction number.
Step 2: After converting a mixed fraction number to a normal fraction number. Now we already know that the whole number does not have a denominator. So, we just need to put 1 as the denominator for the given whole number, because whenever a number is divided with 1 the result will remain the same.
Step 3: Now after adding 1 as the denominator for the given whole number, the given whole number looks like a fraction number.
Step 4: We know the rule to multiply the fraction numbers, we should multiply the numerator with a numerator first and then multiply the denominator with a denominator.
Step 5: After doing the multiplication the solution will be a fraction number now we need to covert the obtained fraction number to a mixed fraction number.
Examples of Multiplying Whole Numbers by a Mixed Fraction Number
Let’s solve few examples for better understanding the concept.
Example 1:Â
Solve 7 * 2\(\frac { 1 }{3 } \)?
Solution:
First, we need to write the mixed fraction number 2 \(\frac { 1 }{3 } \) as a fraction number.
2 \(\frac { 7 }{3 } \) = \(\frac { 2*3 +1 }{3 } \) = \(\frac { 7 }{3 } \)
Now we need to rewrite the whole number 7 as a fraction number.
which gives \(\frac { 7 }{1 } \)
Now we have \(\frac { 7 }{1 } \) * \(\frac { 7 }{3 } \)
According to the rule we need to multiply numerators and denominators.
\(\frac { 7*7 }{ 1*3 } \)
Now we need to covert the obtained fraction number to a mixed fraction number.
\(\frac { 49 }{ 3 } \) can be written as 16 \(\frac { 1 }{ 3 } \)
Let’s solve few examples for better understanding the concept.
Example 2:
Solve 5* 1 \(\frac { 3 }{ 4 } \)?
Solution:
First, we need to write the mixed fraction number 1 \(\frac { 3 }{ 4 } \) as a fraction number.
1 \(\frac { 3 }{ 4 } \) = \(\frac { 1*4 +3 }{ 4 } \)
= \(\frac { 7 }{ 4 } \)
Now we need to rewrite the whole number 5 as a fraction number.
which gives \(\frac { 5 }{1 } \)
Now we have \(\frac { 5 }{1 } \) * \(\frac { 7 }{4 } \)
According to the rule we need to multiply numerators and denominators.
\(\frac { 5 }{1 } \)> * \(\frac { 7 }{4 } \) = \(\frac { 5*7 }{1*4 } \) = \(\frac { 35 }{4 } \)
Now we need to covert the obtained fraction number to a mixed fraction number.
\(\frac { 35 }{4 } \) can be written as 8 \(\frac { 3 }{4 } \)
FAQs on Multiplication of a Whole Number by a Fraction
1. Can we multiply Fraction numbers with whole numbers?
Yes, We can multiply fraction numbers with whole numbers
2. What does the word product mean?
Whenever we are multiplying two numbers the obtained result is called the product.
3. How to Multiply a Whole Number with a Fraction?
Add 1 as the denominator to the whole number and it looks the same as a fraction. Now, multiply the numerators of the fractions and denominators of the fractions individually. Simplify the resultant fraction obtained to the possible extent and that itself is the result.