To divide fractions, we need to know these 3 basic parts. Expect we want to divide Largea over b by Largec over d, the setup need to look like this.

You are watching: How do you find the quotient of a fraction

Dividend – the number being divided or partitioned by the divisor. That is uncovered to the left of the department symbol.Divisor – the number that is splitting the dividend. That is located to the right the the division symbol.
*

Now, apply the following simple steps to division these fractions.

General procedures on exactly how to divide Fractions


Step 1: uncover the mutual of the divisor (second fraction)by flipping that upside down. The reciprocal of Large a over b is Large d over c.Step 2: main point the dividend (first fraction) through the mutual of the divisor.
*

Step 3: simplify the “new” portion that comes the end after multiplication through reducing it to shortest term.

Examples of exactly how to division Fractions

Example 1: divide the fountain below.


*

*

*

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

Example 2: division the fractions below.


Sometimes you may encounter the expression “inverse of a fraction”. That’s pretty much the same as soon as we discover the mutual of afraction. Therefore let’s walk ahead and findthe inverse of the divisor (second fraction).

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

Obviously, the following step is to discover the product of the dividend and also the inverse of the divisor.


The result answer is not simplified yetbecause the numerator and denominator have actually a usual divisor.Can friend think of the usual divisors the 12 (numerator) and 48 (denominator)?

If we execute some trial and error, the possible common divisors that 12 (numerator) and also 48 (denominator) are:


But we desire the greatest usual divisorto alleviate our answer to the shortest term, i m sorry in this case is 12.

Divide the top and bottom by GCF =12 to gain the last answer.

This time we have a portion being separated by a totality number. Notification that any type of nonzero whole number have the right to be rewritten v a denominator that 1. Therefore, the number 10 is simply large10 = 10 over 1. In this form, the is straightforward to uncover its station or reciprocal.


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


Solution:

Before we even divide the fractions, try to watch if you deserve to reduce the existing fountain to its shortest term. Observe the the divisor (second number) deserve to be decreased using a common divisor the 2.


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


The last answer is reduced to a entirety number. Great!

Example 6: division the portion by a totality number.

See more: How Much Does A 3/4 Plywood Weigh ? What Does 1/2 Cdx Plywood Weigh


Solution:

The divisor have the right to be rewritten v a denominator of 1. Thus, large15 = 15 over 1.

The problem becomes


You might likewise be interested in:

Adding and also Subtracting Fractions with the very same DenominatorAdd and also Subtract fractions with various DenominatorsMultiplying FractionsSimplifying FractionsEquivalent FractionsReciprocal the a Fraction


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