How to Divide Fractions Using Invert and Multiply Rule with Examples
A fraction is a part of whole number it consist of two parts numerator and a denominator .A fraction is a representation of ratios or a part of a whole number .It is not an integer but both the numerator and denominators are integers and denominator can never be equal to zero. Fraction can be divided by other Fractions, whole numbers and decimals .In this article we will go through what is dividing fractions, how to divide fraction?Dividing fractions by whole number, how to divide decimal fraction ,how to divide a fraction over a fraction and solve some word problem and examples as we go through the topic.
Dividing Fractions is division of fraction or as same as multiplying the fraction by the reciprocal which is inverse of the other fraction. We can get reciprocal of a fraction by interchanging its numerator with its denominator. This method of dividing the fraction by multiplying with the reciprocal was introduced later as division of fraction by direct method required more effort. Here, we will learn different methods on dividing fractions with some examples.
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How To Divide Fractions?
Fraction can be divided with other fractions, whole numbers and decimals. For dividing the whole number and decimal with fraction it needs to be converted into fractional form. Dividing fractions with fractions just requires a few steps just by reciprocating the other fraction and then multiplying it with the first one.
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Steps For Fraction Divided By Fractions
In these simple steps we can solve division of fraction by converting it into multiplication if fraction.
Reciprocate the second fraction by interchanging its numerator with the denominator.
Multiply the second fraction with the first one by multiplying the numerators and denominators with each other.
Simplify the fraction, if needed.
General Solution:
If a/b is divide by c/d then we can solve it as,
a/b ÷ c/d = a/b × d/c
a/b ÷ c/d = a×d / b×c
a/b ÷ c/d = ad/bc
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Examples -
¾ ÷ ½
Solution: Given ¾ ÷ ½
Reciprocating the second fraction by interchanging its numerator with denominator.
½ after reciprocating will be 2/1
Multiplying both numerator and denominator
3/4 x 2/1 = 6/4
Simplify the fraction
6/4 = 1 2/4
Steps For Dividing Fractions By Whole Numbers
Dividing the whole number is the same as dividing fraction with fraction just by changing the whole number into fractions.
Convert the whole number into fraction by using denominator as 1.
Reciprocate the number by interchanging the denominator with the numerator.
Multiply by the fraction.
Simplify the result, if needed.
General Solution:
If a/b is divide by c then we can solve it as,
a/b ÷ c/1 = a/b × 1/c
a/b ÷ c/1 = a×1 / b×c
a/b ÷ c/1 = a/bc
3/8 ÷ 3
Solution: Given, 3/8 ÷ 3
Convert the whole number into fraction by using denominator as 1.
3 =3/1
Reciprocate the number by interchanging the denominator with the numerator.
Reciprocal of 3/1 will be 1/3.
Multiply by the fraction.
3/8 X 1/3 = 3/24.
Simplify the result, if needed.
Steps For Dividing Fractions By Decimals
Decimal can be expressed as fraction written is a special form whose denominator is the power of ten whose numerator is expressed by figure places for example 5/10 can be also written as ½ which can be further simplified as 0.5, where the zero is in once place and 5 is in the tenth place.
To divide a decimal with a fraction we need to change the decimal into fraction by writing the denominator as 1 and then multiplying both numerator and denominator by 10 for every number after the decimal.
Writing the denominator as 1 for the decimal
Multiplying both numerator and denominator by 10 for every number after the decimal.
Reciprocate the number by interchanging the denominator with the numerator.
Multiply by the fraction.
Simplify the result, if needed
General Solution:
If a/b is divide by c then we can solve it as,
a/b ÷ 0.c= a/b ÷( 0.c/1)
a/b ÷ 0.c= a/b ÷( 0.c/1 x 10/10)
a/b ÷ 0.c= a/b ÷c/10
a/b ÷ 0.c = a/b × 10/c
a/b ÷ 0.c = a×10 / b×c
a/b ÷ 0.c = 10a/bc
Examples
3/8 ÷0.3
Solution: Given, 3/8 ÷ 0.3
Writing the denominator as 1 for the decimal
0.3/1
Multiplying both numerator and denominator by 10 for every number after the decimal.
0.3/1 x10/10 = 3/10
Reciprocate the number by interchanging the denominator with the numerator.
Reciprocal of 3/10 will be 10/3.
Multiply by the fraction.
3/8 X 10/3 = 30/24.
Simplify the result, if needed.
30/24 = 1 7/24
Questions To Be Solved:
7/8÷3/9
3/4÷5/8
4/8÷ 9
6/7 ÷18
3/4÷0.5
4/8÷ 0.8
Solved Example:-
Question 1: ¾ ÷ ½
Solution: Given ¾ ÷ ½
Reciprocating the second fraction by interchanging its numerator with denominator.
½ after reciprocating will be 2/1
Multiplying both numerator and denominator
3/4 x 2/1 = 6/4
Simplifying the fraction,
6/4 = 3/2
Interesting Facts-
Every fraction has two parts numerator and denominator the numerator of the fraction sums up the equal number of parts we have and the denominator part of the fraction sums up the total number of parts as a whole.
The denominator of a fraction can never be less than or equal to zero.
Multiplication and division of fraction do not require a common denominator.
FAQs on Dividing Fractions Made Simple
1. What is dividing fractions?
Dividing fractions means multiplying the first fraction by the reciprocal of the second fraction. In simple terms, you keep the first fraction the same, flip the second fraction, and then multiply.
- Reciprocal means swapping the numerator and denominator.
- This method is often called "keep, change, flip".
- Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
2. How do you divide fractions step by step?
To divide fractions, use the rule keep, change, flip and then multiply. Follow these steps:
- Keep the first fraction the same.
- Change the division sign (÷) to multiplication (×).
- Flip the second fraction to get its reciprocal.
- Multiply numerators and denominators.
- Simplify the final answer.
3. Why do you flip the second fraction when dividing?
You flip the second fraction because dividing by a fraction is the same as multiplying by its reciprocal. Mathematically, a ÷ b = a × (1/b), which explains why the divisor is inverted.
- Example: 4 ÷ 1/2 = 4 × 2 = 8.
- This works because multiplying by the reciprocal cancels the original fraction.
4. What is the formula for dividing fractions?
The formula for dividing fractions is a/b ÷ c/d = a/b × d/c. This means you multiply the first fraction by the reciprocal of the second.
- Multiply numerators: a × d
- Multiply denominators: b × c
- Simplify the result if possible.
5. How do you divide fractions with whole numbers?
To divide fractions with whole numbers, first write the whole number as a fraction with denominator 1. Then apply the usual division rule.
- Example: 3 ÷ 2/5
- Write 3 as 3/1.
- 3/1 ÷ 2/5 = 3/1 × 5/2 = 15/2.
6. How do you divide mixed numbers?
To divide mixed numbers, first convert them into improper fractions and then apply the division rule. Follow these steps:
- Convert each mixed number to an improper fraction.
- Use keep, change, flip.
- Multiply and simplify.
7. Can you give an example of dividing fractions?
An example of dividing fractions is 5/6 ÷ 2/3, which equals 5/4. Here is the working:
- Keep 5/6.
- Change ÷ to ×.
- Flip 2/3 to get 3/2.
- Multiply: 5/6 × 3/2 = 15/12.
- Simplify: 15/12 = 5/4.
8. What are common mistakes when dividing fractions?
Common mistakes when dividing fractions include not flipping the second fraction and forgetting to simplify the final answer. Watch out for these errors:
- Flipping the wrong fraction.
- Multiplying without changing ÷ to ×.
- Not converting mixed numbers properly.
- Leaving the answer unsimplified.
9. Do you need a common denominator to divide fractions?
You do not need a common denominator to divide fractions because division uses multiplication by the reciprocal. Unlike adding or subtracting fractions, no denominator matching is required.
- Example: 2/5 ÷ 3/7 = 2/5 × 7/3 = 14/15.
- The method works directly without finding a least common denominator (LCD).
10. What happens when you divide a fraction by 1?
When you divide a fraction by 1, the fraction stays the same value. This is because any number divided by 1 equals itself.
- Example: 7/8 ÷ 1 = 7/8.
- Since the reciprocal of 1 is 1, multiplication does not change the fraction.
