To divide fractions, we need to recognize these 3 an easy parts. Expect we want to division Largea over b by Largec over d, the setup must look like this.

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Dividend – the number being separated or partitioned by the divisor. The is uncovered to the left the the department symbol.Divisor – the number the is separating the dividend. That is located to the right of the division symbol.
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Now, apply the following simple steps to division these fractions.

General actions on exactly how to division Fractions


Step 1: find the reciprocal of the divisor (second fraction)by flipping the upside down. The reciprocal of Large a over b is Large d over c.Step 2: main point the dividend (first fraction) by the reciprocal of the divisor.
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Step 3: simplify the “new” fraction that comes out after multiplication by reducing it to lowest term.

Examples of exactly how to division Fractions

Example 1: divide the fountain below.


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This is our last answer because the resulting fraction is currently in its shortest term!

Example 2: divide the fractions below.


Sometimes you might encounter the phrase “inverse the a fraction”. That’s pretty lot the same once we uncover the reciprocal of afraction. For this reason let’s go ahead and findthe train station of the divisor (second fraction).

The inverse of Large8 over 3 is just Large3 over 8.

Obviously, the next step is to find the product the the dividend and the station of the divisor.


The resulting answer is not simplified yetbecause the numerator and also denominator have actually a typical divisor.Can girlfriend think the the typical divisors of 12 (numerator) and also 48 (denominator)?

If we perform some trial and error, the feasible common divisors the 12 (numerator) and also 48 (denominator) are:


But we desire the greatest typical divisorto reduce our answer to the lowest term, which in this instance is 12.

Divide the top and also bottom by GCF =12 to obtain the final answer.

This time we have actually a fraction being split by a entirety number. An alert that any type of nonzero whole number have the right to be rewritten through a denominator that 1. Therefore, the number 10 is simply large10 = 10 over 1. In this form, it is simple to discover its train station or reciprocal.


The greatest usual divisor between the numerator and also denominator is 2. That means, we can reduce it come the shortest term by splitting both the top and bottom numbers by 2.


Solution:

Before we even divide the fractions, try to view if you have the right to reduce the existing fountain to its lowest term. Observe that the divisor (second number) can be reduced using a typical divisor that 2.


The fractions currently are fairly smaller in size. Proceed with department by multiplying the dividend come the inverse of the divisor.


The final answer is decreased to a totality number. Great!

Example 6: divide the fraction by a whole number.

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Solution:

The divisor deserve to be rewritten through a denominator that 1. Thus, large15 = 15 over 1.

The difficulty becomes


You might also be interested in:

Adding and Subtracting Fractions with the exact same DenominatorAdd and Subtract fractions with different DenominatorsMultiplying FractionsSimplifying FractionsEquivalent FractionsReciprocal that a Fraction


MATH SUBJECTSIntroductory AlgebraIntermediate AlgebraAdvanced AlgebraAlgebra word ProblemsGeometryIntro come Number TheoryBasic mathematics Proofs
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