How do you divide #\frac { 3} { 4} \div \frac { 5} { 4} #?

Answer 1

#3/4div5/4=color(green)(3/5)#

Dividing is the same as multiplying by the inverse.

So #color(white)("XXX")3/4div5/4# is the same as #color(white)("XXX")3/4xx4/5#
#color(white)("XXX")=3/5#
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Answer 2

Use the complex fraction method. A fraction is a division problem so set one fraction divided by the second fraction.

The complex fraction method makes sense of the rule of invert and multiply.

#3/4-:5/4# can be written as
#(3/4) / ( 5/4) # This is a complex fraction

To simplify the fraction multiply both the numerator ( top fraction) and the denominator ( bottom fraction) by the inverse of the denominator .

The inverse of # 5/4 = 4/5# Now multiply both fractions by # 4/5#
#{ ( 3/4) xx (4/5)} / {(5/4) xx ( 4/5)} #
# ( 5/4) xx ( 4/5) = 1 # This causes the bottom fraction to disappear. This leaves only the top fraction which gives.
# ( 3/4) xx ( 4/5) = ( 12/20) # Now factor out the common factor of 4
#( 4 xx 3)/ (4 xx 5)# This leaves
# 3/5#

After the bottom fraction divides out it leaves the invert and multiply method. Using the complex fraction makes mathematical sense of the method and avoids reliance on memory.

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Answer 3

If the denominators are the same just divide the numerators.

#3-:5->3/5#

A fraction consists of #("count")/("size indicators of what you are counting")#

Using the allocated names we have:

#("count")/("size indicator")->("numerator")/("denominator")#

Consider whole numbers. For example 6 and 3

These can, and may, be written as #6/1 and 3/1# They are rational numbers. It is not normally done but never the less it is correct.
Now consider # 6-:3->6/1-:3/1#
#color(blue)("You just divide the counts as the 'size indicators' are the same")#
#6-:3->6/1-:3/1->6/3=2#
#color(magenta)("You have been applying this principle for a long time without even realizing that you were.")#
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Answer 4

To divide (\frac{3}{4}) by (\frac{5}{4}), you multiply the first fraction by the reciprocal of the second fraction:

[ \frac{3}{4} \div \frac{5}{4} = \frac{3}{4} \times \frac{4}{5} ]

Simplify the expression:

[ = \frac{3 \times 4}{4 \times 5} ]

[ = \frac{12}{20} ]

This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

[ = \frac{3}{5} ]

So, (\frac{3}{4} \div \frac{5}{4} = \frac{3}{5}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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