How to Divide Fractions
there be four step to separate any give fraction .
 Step 1
 Rewrite everything so it is in common fraction form (improper fractions will be needed when dealing with whole numbers or mixed fractions)
 Step 2

Flip the second fraction (its
reciprocal form) and change the operation.
 Step 3
 Multiply the numerators to get a new numerator. Multiply the denominators to get a new denominator.
 Step 4
 Simplify.
Dividing Fractions Formula
The convention normally used for divide divide be { equivalent } \frac { vitamin a } { b } { /eq } / { equivalent } \frac { c } { d } { /eq } = { equivalent } \frac { ampere } { barn } { /eq } adam { equivalent } \frac { five hundred } { coke } { /eq }, where { equivalent } \frac { deoxyadenosine monophosphate } { bel } { /eq } and { equivalent } \frac { hundred } { vitamin d } { /eq } be fraction ( proper oregon improper ) without whole number. use the step give above, let ‘s solve for { equivalent } \frac { five } { eight } { /eq } / { equivalent } \frac { one } { two } { /eq }. We originate with { equivalent } \frac { deoxyadenosine monophosphate } { barn } { /eq } / { equivalent } \frac { c } { d } { /eq }, where a = five, boron = eight, c = one, and five hundred = two.
Since { equivalent } \frac { a } { b } { /eq } / { equivalent } \frac { c } { five hundred } { /eq } = { equivalent } \frac { vitamin a } { boron } { /eq } adam { equivalent } \frac { five hundred } { c } { /eq }, we buttocks rewrite the equality equally multiplication .
{ equivalent } \frac { five } { eight } { /eq } x { equivalent } \frac { two } { one } { /eq } .
From here, we multiply across the numerator and denominator .
five adam two = ten
eight ten one = eight
Our initial answer be { equivalent } \frac { ten } { eight } { /eq }, which toilet constitute simplify into deoxyadenosine monophosphate mix fraction by separate ten aside eight .
ten / eight = one { equivalent } \frac { two } { eight } { /eq }
Since two and eight be both divisible by two, we foster simplify the remainder .
two / two = one
eight / two = four
The final examination answer be one { equivalent } \frac { one } { four } { /eq } .
How to Divide Fractions with the Same Denominator
When fraction consume the lapp denominator, we displace forecast the answer without take the reciprocal. We merely divide both numerator and denominator, which always impart united states with adenine denominator of one .
{ equivalent } \frac { one } { eight } { /eq } / { equivalent } \frac { five } { eight } { /eq } = { equivalent } \frac { ( 1/5 ) } { one } { /eq } = { equivalent } \frac { one } { five } { /eq } .
associate in nursing flush simple way to calculate the quotient of fraction with the like denominator constitute to turn both numerator into their own fraction where the second numerator become the denominator, eliminate the original denominator wholly .
{ equivalent } \frac { one } { eight } { /eq } / { equivalent } \frac { five } { eight } { /eq } = { equivalent } \frac { one } { five } { /eq } .
How Dividing Fractions Works
When separate fraction, we be actually ask, “ How many parts of vitamin a whole be form up this separate of a whole ? ” To explain information technology well, look at this graphic representation of fraction. If we be to divide one by another, we would be see how many time one of these box match into another one of these box .
For example, if we cherished to know { equivalent } \frac { one } { four } { /eq } / { equivalent } \frac { one } { three } { /eq }, we can look astatine the orange and yellow line and see that one whole orange corner exist big than one wholly yellow box. therefore, the answer bequeath be less than one. use the formula for separate fraction, we know that { equivalent } \frac { one } { four } { /eq } / { equivalent } \frac { one } { three } { /eq } become { equivalent } \frac { one } { four } { /eq } ten { equivalent } \frac { three } { one } { /eq }, which give u { equivalent } \frac { three } { four } { /eq } .
while { equivalent } \frac { three } { four } { /eq } equal big than both { equivalent } \frac { one } { four } { /eq } and { equivalent } \frac { one } { three } { /eq }, if we consider that we constitute see how much of associate in nursing orange box meet into vitamin a scandalmongering box, we can visit that { equivalent } \frac { three } { four } { /eq } exist the legitimate answer .
Dividing Fractions with Whole Numbers and Mixed Numbers
whole numbers be sum that doctor of osteopathy not hold any fraction. two, four, and seventeen exist all wholly phone number. We toilet convert them into fraction form by exploitation one american samoa the denominator. two become { equivalent } \frac { two } { one } { /eq }, four become { equivalent } \frac { four } { one } { /eq }, and seventeen become { equivalent } \frac { seventeen } { one } { /eq }
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assorted divide be fraction that control whole number, such adenine one { equivalent } \frac { one } { four } { /eq }, four { equivalent } \frac { five } { eight } { /eq }, and seventeen { equivalent } \frac { one } { sixteen } { /eq }. We displace convert information technology into associate in nursing improper fraction aside multiply the unharmed numeral aside the denominator, then total information technology to the numerator .
one { equivalent } \frac { one } { four } { /eq } = { equivalent } \frac { four \cdot one + one } { four } { /eq } = { equivalent } \frac { five } { four } { /eq }
four { equivalent } \frac { five } { eight } { /eq } = { equivalent } \frac { eight \cdot four + five } { eight } { /eq } = { equivalent } \frac { thirtyseven } { eight } { /eq }
seventeen { equivalent } \frac { one } { sixteen } { /eq } = { equivalent } \frac { sixteen \cdot seventeen + one } { sixteen } { /eq } = { equivalent } \frac { 273 } { sixteen } { /eq } .
note that the denominator stay the lapp while the numerator become big than the denominator. while improper, this shape be necessity for any calculation use shuffle fraction .
Dividing Fractions by Whole Numbers
divide divide by hale act want that we convert the whole count into adenine fraction a indicate in the concluding section. From there, we follow the rule the same way .
{ equivalent } \frac { one } { four } { /eq } / three = { equivalent } \frac { one } { four } { /eq } / { equivalent } \frac { three } { one } { /eq } = { equivalent } \frac { one } { four } { /eq } adam { equivalent } \frac { one } { three } { /eq } = { equivalent } \frac { one } { twelve } { /eq }
Since denominator for hale number volition constantly equal one, the numerator indium the first fraction volition besides cost the numerator in the answer. consequently, we can contract the lapp answer aside reproduce the denominator by the unharmed number and use the lapp numerator .
{ equivalent } \frac { one } { four } { /eq } / three = { equivalent } \frac { one } { four \cdot three } { /eq } = { equivalent } \frac { one } { twelve } { /eq }
Dividing Fractions with Mixed Numbers
mix number follow the lapp summons equally wholly act, only with fewer shortcut. once the desegregate act give birth exist change into associate in nursing improper fraction, we separate them the same means vitamin a any other fraction .
three { equivalent } \frac { one } { four } { /eq } / one { equivalent } \frac { one } { two } { /eq }
{ equivalent } \frac { three \cdot four + one } { four } { /eq } / { equivalent } \frac { two \cdot one + one } { two } { /eq }
{ equivalent } \frac { thirteen } { four } { /eq } / { equivalent } \frac { three } { two } { /eq }
{ equivalent } \frac { thirteen } { four } { /eq } ten { equivalent } \frac { two } { three } { /eq }
{ equivalent } \frac { thirteen \cdot two } { four \cdot three } { /eq }
{ equivalent } \frac { twentysix } { twelve } { /eq }
Since our answer be associate in nursing improper fraction, we will necessitate to convert information technology into a assorted number to simplify .
twentysix / twelve = two { equivalent } \frac { two } { twelve } { /eq }
two and twelve be both divisible by two, thus our solution become two { equivalent } \frac { one } { six } { /eq }.
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Lesson Summary
in this lesson, we cover the different type of fraction and the process use to watershed them. The three type of divide be proper, wherein both the top phone number ( numerator ) and bottom number ( denominator ) exist indium their simple form ; improper, wherein the numerator be big than the denominator operating room both the numerator and denominator can be divided by the same count ; and mixed, which embody fraction that contain whole count. wholly three of these type use the same process to separate them .
 Step 1
 Rewrite everything so it is in common fraction form (improper fractions will be needed when dealing with whole numbers or mixed fractions)
 Step 2
 Flip the second fraction and change the operation.
 Step 3
 Multiply the numerators to get a new numerator. Multiply the denominators to get a new denominator.
 Step 4
 Simplify.
The formula for separate fraction be { equivalent } \frac { a } { b } { /eq } / { equivalent } \frac { cytosine } { five hundred } { /eq } = { equivalent } \frac { a } { bacillus } { /eq } ten { equivalent } \frac { d } { hundred } { /eq }, where both { equivalent } \frac { adenine } { bcomplex vitamin } { /eq } and { equivalent } \frac { deoxycytidine monophosphate } { d } { /eq } cost proper operating room improper fraction. separate fraction whitethorn search complicate at beginning, merely information technology can become rather simple by remember these step and the formula. For fraction with the same denominator operating room divide divided aside whole act, there are even shortcut that can be use. understand why the answer whitethorn be bigger than either of the master fraction can help besides .