What’s division of fractions?
Dividing fractions is a mathematical course of through which it’s decided what number of instances a fraction (known as a divisor) suits into one other fraction (known as a dividend).
To divide fractions, the rule of multiplication of fractions is used however with a small variation: the inverse (reciprocal) fraction of the divisor is taken and a multiplication of fractions is carried out.
For instance, if we wish to divide 3/4 by 1/2, we invert the fraction 1/2, acquiring 2/1. Then, we multiply the fractions: (3/4) x (2/1) = 6/4.
As soon as the multiplication is obtained, the fraction is simplified if potential. On this case, we are able to simplify the fraction 6/4 by dividing each phrases by the best widespread divisor (GCD), which is 2. Thus, we now have 6 ÷ 2 / 4 ÷ 2 = 3/2.
The ultimate reply is 3/2, which is equal to 1 1/2 in combined quantity kind.
You will need to do not forget that, as in multiplying fractions, it’s advisable to simplify the ensuing fraction to acquire an easier and extra comprehensible reply.
Guidelines for dividing fractions
In arithmetic, dividing fractions is an operation that consists of calculating the quotient between two fractions. This operation is quite common and has some vital guidelines that we should keep in mind.
Rule 1: To divide fractions, multiply the primary fraction by the inverse of the second fraction.
This rule is key. To divide two fractions, multiply the primary fraction by the inverse of the second fraction. The inverse of a fraction is obtained by exchanging the numerator and the denominator. For instance:
- As an alternative of dividing 1/2 by 3/4, we multiply 1/2 by 4/3.
- As an alternative of dividing 2/5 by 7/8, we multiply 2/5 by 8/7.
Keep in mind: By multiplying the primary fraction by the inverse of the second fraction, the widespread phrases within the numerator and denominator will cancel, simplifying the consequence.
Rule 2: If any of the fractions is an entire quantity, it may be expressed as a fraction.
If one of many fractions is an entire quantity, it may be expressed as a fraction with denominator 1. For instance:
- As an alternative of dividing 2 by 3/4, we are able to specific 2 because the fraction 2/1 and multiply 2/1 by 4/3.
- As an alternative of dividing 5/6 by 2, we are able to specific 2 because the fraction 2/1 and multiply 5/6 by 1/2.
Keep in mind: Simplify fractions earlier than multiplying them.
Rule 3: If there are greater than two fractions to divide, rule 1 is utilized iteratively.
If we now have greater than two fractions to divide, we are able to apply rule 1 iteratively. That’s, divide the primary fraction by the second, after which divide the consequence by the third, and so forth. For instance:
- To divide 1/2 by 3/4 after which divide the consequence by 5/6, we are able to multiply 1/2 by 4/3 after which multiply the consequence by 6/5.
Keep in mind: Simplify fractions earlier than multiplying them.
These are the fundamental guidelines for dividing fractions. By following these guidelines, it is possible for you to to unravel fraction division issues accurately and simply.
Examples of fraction division workout routines
Dividing fractions is a mathematical operation that consists of dividing a fraction by one other fraction. To resolve fraction division workout routines, it’s essential to comply with some steps:
Step 1: Invert the fraction divisor
Step one is to invert the fraction divisor. That’s, if we now have the fraction 3/4 divided by 2/5we’ll invert the divisor fraction and it’ll turn into 5/2.
Step 2: Multiply the fractions
Subsequent, we multiply the dividend fraction (the fraction above) by the divisor fraction (the inverted fraction). Following the earlier instance, we multiply 3/4 by 5/2 and we’ll receive the results of the division.
Step 3: Simplify the ensuing fraction
Lastly, we simplify the ensuing fraction if potential. To simplify a fraction, discover the best widespread divisor between the numerator and the denominator and divide each numbers by that worth. On this approach, we receive the fraction in its most simplified kind.
Under are some examples of fraction division workout routines:
Instance 1:
Break up: 2/3 ÷ 1/4
Invert the divisor: 1/4 → 4/1
Multiply the fractions: 2/3 × 4/1 = 8/3
Simplify the fraction: 8/3 (Can’t be simplified)
Instance 2:
Break up: 3/8 ÷ 5/6
Invert the divisor: 5/6 → 6/5
Multiply the fractions: 3/8 × 6/5 = 18/40
Simplify the fraction: 18/40 → 9/20
Instance 3:
Break up: 4/5 ÷ 3/10
Invert the divisor: 3/10 → 10/3
Multiply the fractions: 4/5 × 10/3 = 40/15
Simplify the fraction: 40/15 → 8/3
Keep in mind to observe these workout routines to strengthen your information and abilities in dividing fractions.
Suggestions for fixing fraction division workout routines
Fraction division workout routines could appear sophisticated at first, however with a couple of ideas and methods, it is possible for you to to unravel them shortly and successfully. Listed below are some helpful ideas: