Division of a Fractional Number
This topic would discuss about division of a fractional number with another fractional number. In this case if any one or both of the fractional number are in mixed fraction then we will have to change that mixed fraction into improper fraction.
The rule of division of fractional number is that:
Fraction ÷ Another Fraction = Fraction × Multiplicative Inverse or, Reciprocal of the Another Fraction
Here are few examples to show division of a fraction by another fraction:
1. (i) 14 2/5 ÷ 1 11/25
⟹ 72/5 ÷ 36/25; [Changing into improper fraction]
⟹ 72/5 × 25/36; [Multiplicative inverse of the second fraction]
⟹ (72 × 25)/(5 × 36); [Product of numerator and denominator]
⟹ 1800/180
⟹ (1800 ÷ 180)/(180 ÷ 180) [Changing into lowest term]
⟹ 10
Explanation:
The fractions are in mixed form so, in the first step it is changed into improper fraction. Then the first fraction is multiplied with the reciprocal of the second fraction. The next step is both the numerators and denominators are multiplied to get the result. Then the result is reduced into lowest terms to obtain the final answer.
2. (i) 11 1/15 ÷ 1 11/45
⟹ 166/15 ÷ 56/45 [Changing into improper fraction]
⟹ 166/15 × 45/56 [Multiplicative inverse of the second fraction]
⟹ (166 × 45)/(15 × 56) [Product of numerator and denominator]
⟹ 7470/840
⟹ (7470 ÷ 30)/(840 ÷ 30) [Changing into lowest term]
⟹ 249/28
⟹ 8 25/28
Explanation:
The fractions are in mixed form so, in the first step it is changed into improper fraction. Then the first fraction is multiplied with the reciprocal of the second fraction. The next step is both the numerators and denominators are multiplied to get the result. Then the result is reduced into lowest terms and finally into mixed fraction to obtain the final result.
3. (i) 1 1/5 ÷ 12/45
⟹ 6/5 ÷ 12/45; [Changing mixed fraction into improper fraction]
⟹ 6/5 × 45/12; [Multiplicative inverse of the second fraction]
⟹ (6 × 45)/(5 × 12); [Product of numerator and denominator]
⟹ 270/60
⟹ (270 ÷ 30)/(60 ÷ 30); [Changing into lowest term]
⟹ 9/2
⟹ 4 1/2
Explanation:
The first fraction is in mixed form so, in the first step it is changed into improper fraction. Then the first fraction is multiplied with the reciprocal of the second fraction. The next step is both the numerators and denominators are multiplied to get the result. Then the result is reduced into lowest terms and finally into mixed fraction to obtain the final result.
The above examples show the division of fraction by another fraction where the first fraction is multiplied by the reciprocal of the second fraction to obtain the result. After this step the division of fraction is same as multiplication of fractions where numerator and numerator is multiplied and denominator and denominator is multiplied \(\frac{Product of the Numerator}{Product of the Denominator}\) to get the answer. The final answer is expressed in lowest terms and then in proper fraction or mixed fraction (if after changing into lowest terms it is an improper fraction).
You might like these
Worksheet on Divisibility Rules | Questions on Test of Divisibility
This is a worksheet which will provide few problems on the divisibility rule of 2, 3, 4, 5, 6, 7, 8, 9, and 10. 1. Check whether the following numbers are divisible by 2 or 3 or both? (i) 2562 (ii) 5693 (iii) 2201 (iv) 7480 (v) 5296 (vi) 4062 (vii) 4568 (viii) 1425 (ix) 1110
Problems on Divisibility Rules | Rules to Test of Divisibility | Test
Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules. 1. Check whether 3456 is divisible by 2? Solution: The last digit is an even number (i.e. 6) hence 3456 is
Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10
The divisibility rule of 10 states that If the last digit of a number is 0 then the given number is divisible by 10. For eg: Check whether 5400 is divisible by 10 or not? Solution: As the last digit of the number is 0 hence, 5400 is divisible by 10
Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9
This rule states that a number is divisible by 9 if the sum of its digits of the number is divisible by 9 For eg: Check whether 729 is divisible by 9 or not? Sum of the digits = 7 + 2 + 9 = 18 Now 18 is divisible by 9 hence, 729 is also divisible by 9 Here are few examples
Divisible by 8 | Test of Divisibility by 8 |Rules of Divisibility by 8
The most common method to check whether a number is divisible by 8 is to divide and see if the quotient is a whole number or not? If the quotient is a whole number then the given number is divisible by 8. But there is an easier way to check by using the divisibility rule.
Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7
This rule states that if the difference between twice the digit at units place and the number formed from the remaining digits of the given number is divisible by 7 then the whole number is divisible by 7.
Divisible by 6 | Test of divisibility by 6 |Rules of Divisibility by 6
This topic on divisible by 6 will discuss about the divisibility rule of 6 and few example on the same. Divisibility rule of 6: A number is divisible by 6 if the prime factor of that is 2 & 3 is divisible by 6. For Example: 216 216 is divisible by 2 as the last digit 6 is
Divisible by 5 | Test of divisibility by 5 |Rules of Divisibility by 5
This topic on divisible by 5 will discuss on the divisibility rule of 5 and illustrate few example on the same. Divisibility Rule of 5: If a number ends with 0 or 5 then the number is divisible by 5. For Example: 550 Since the number ends with 0 hence the number is divisible
Divisible by 4 | Rules of Divisibility by 4|Divisibility Rules & Tests
This topic i on divisibility rule of 4 and will provide examples on the same. Divisibility Rule of 4: If the last two digits of the number is divisible by 4 then the whole number is divisible by 4 For eg: 524 The last two digit of the number is 24 which is divisible by 4.
Divisible by 3 | Rules of Divisibility by 3|Divisibility Rules & Tests
This topic is on the divisibility rule of 3 and few examples based on the topic. If the sum of the digits is divisible by 3 then the whole number is divisible by 3. For example 519 The sum of the digits = 5 + 1 + 9 = 15 15 is divisible by 3 hence 519 is also divisible by 3
Divisible by 2 | Divisibility Rule of 2 | Test of Divisibility by 2
This topic would deal with the divisibility rule of 2 and few sums on divisibility rule of 2. Numbers that are ending with 0, 2, 4, 6, and 8 are divisible by 2. That means numbers ending with 0 or multiples of 2 are divisible by 2. We know that numbers which are multiples of
Properties of Divisibility | Divisibility Property |Divisibility Rules
This topic deals with the properties of divisibility which will help us in doing our multiplication and division easy. These rules will help us to determine quickly the factors of certain number, the divisibility criteria of certain number and helps in overall strengthening
Worksheet on Multiples and Factors | List the First Five Multiples
1. List the first five multiples of the following numbers: 2. Choose the numbers that are factors of 24. 3. 3. Choose the numbers that are multiples of 15. 4. Choose the numbers which are multiple of 3 as well as factor of 36
Divisibility Rules | Divisibility Rules from 2 to 12|Divisibility Test
This topic would deal with divisibility rules. There are certain divisibility rules of certain numbers which help in determining that by which number the given number is divisible. Divisibility rules are an effective tool for determining with which numbers a given number
From Division of a Fractional Number to HOME PAGE
Recent Articles
-
Respiratory Balance Sheet | TCA Cycle | ATP Consumption Process
Feb 18, 24 01:56 PM
The major component that produced during the photosynthesis is Glucose which is further metabolised by the different metabolic pathways like glycolysis, Krebs cycle, TCA cycle and produces energy whic… -
Electron Transport System and Oxidative Phosphorylation | ETC |Diagram
Feb 04, 24 01:57 PM
It is also called ETC. Electron transfer means the process where one electron relocates from one atom to the other atom. Definition of electron transport chain - The biological process where a chains… -
Tricarboxylic Acid Cycle | Krebs Cycle | Steps | End Products |Diagram
Jan 28, 24 12:39 PM
This is a type of process which execute in a cyclical form and final common pathway for oxidation of Carbohydrates fat protein through which acetyl coenzyme a or acetyl CoA is completely oxidised to c… -
Aerobic Respiration | Definition of Aerobic Respiration | Glycolysis
Dec 15, 23 08:42 AM
This is a type of respiration where molecular free oxygen is used as the final acceptor and it is observed in cell. Site of Aerobic Respiration - Aerobic respiration is observed in most of the eukaryo… -
Fermentation | Definition | Types of Fermentation | Application
Nov 29, 23 10:27 PM
Definition of fermentation- It is a process that is energy yielding process of anaerobic oxidation of organic compounds which are carried out by the enzyme action of micro organisms where neither gase…
New! Comments
Have your say about what you just read! Leave me a comment in the box below.