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Multiply #3/8# by an equivalent fraction that equals #1#.

An equivalent fraction is equal to 1 such as #2/2# or #3/3#

An equivalent fraction is the same as multiplying by #1#
so the ratio does not change.

This fraction would be equal to #a/a=1# where a is an integer.

Hence an example would be that

#2/2 * 3/8 = 6/16#

Answer:

#4#

Explanation:

The key to division of fractions is to reciprocate the divisor (what comes after the division sign) and change the division sign to multiplication.

In this case, we have a mixed fraction so we change it to an improper fraction first.

How do we do that?

Simple!

Take the denominator of the mixed fraction, multiply it by the whole number and add the numerator.

Whatever value you get becomes the numerator of the improper fraction over the denominator of the mixed fraction.

So for #1(2)/6#, we multiply #6# by #1# and add the product to #2#

#(6*1)+2#

#6+2#

#8#

So our numerator is #8# over our denominator which is #6#

#:.#Our improper fraction is #8/6=4/3#

Back to our question;

#1(2)/6-:1/3#

#4/3-:1/3#

Reciprocate #1/3# and change the division sign to multiplication.

#4/3xx3/1#

Multiply the numerators and the denominators.

#12/3#

Reduce the fraction if possible

#=(4xxcancel(3))/cancel3#

#rArr4#

Answer:

If the denominators are the same just divide the numerators.

#3-:5->3/5#

Explanation:

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.")#

Answer:

8

Explanation:

The lowest common multiple is the lowest number which is a multiple of both numbers.

Since 8 * 1 = 8 and 2 * 4 = 8, 8 is the lowest common multiple.

An easy way to find the LCM is to list all multiples of each number, up to the product of both numbers (in this case, 16).

For 2:
- 2, 4, 6, 8, 10, 12, 14, 16

For 8:
- 8, 16,

8 is the lowest number they both have in common.

The highest possible value of an LCM is both numbers multiplied by each other. This is why for both lists i stopped at 16, because
2*8 = 16

Answer:

Please see below.

Explanation:

A fraction, say #a/b#, where #a# is called as numerator and #b# is called denominator, assuming #a < b#, represents a part of a whole object, wherein the object is divided in #b# equal parts, of whom #a# are chosen.

For example, in the figure below, shows a full bar divided into #12# parts of which #9# parts (coloured blue) have been chosen and they represent #9/12# of the whole bar.

enter image source here

Let us consider a simple example, say #1/2#, which is say object divided in two equal parts of which one is chosen, like in the figure below and this blue portion represents #1/2# of whole.

enter image source here

What if we had divided the object in #4# parts and then chosen #2# parts. It would have appeared as shown below.

enter image source here

Although it is #2/4#, it is quite obvious that whether one gets #1/2# of a whole or gets #2/4# of the whole, there is no difference i.e. #1/2=2/4#.

What if we had divided the same in #6# parts and for getting equivalent amount, one would have to choose #3# parts (i.e. #3/6#) as is obvious from following figure.

enter image source here

Hence one can say that #3/6=2/4=1/2#.

Similarly dividing by #8# and choosing #4# out of it i.e. #4/8# appears as below.

enter image source here

It is quite obvious that #1/2=2/4=3/6=4/8#

Also observe that in this case we are just multiplying numerator and denominator same number (in above case #2#, #3# and #4#) and

#1/2=(1xx2)/(2xx2)=(1xx3)/(2xx3)=(1xx4)/(2xx4)#.

Now without actually drawing these figures consider #9/12# shown in the first figure. Observe that had we divided the figure in #4# parts, for equivalent portion, we would have selected #3/4#. Why?

Because #9/12=(9-:3)/(12-:3)=3/4#

Hence multiplying or dividing both numerator and denominator, make an equivalent fraction.

The greatest common factor (GCF) is the largest number by which both numbers are divisible, and the least common multiple is the smallest number that is equal to either number multiplied by an integer.

The GCF must divide both numbers, so it must be a product of two or more factors belonging to both numbers at the same time. It turns out that these factors are all prime numbers.

The prime factorization of #84# is #color(green)(2 xx 2 xx 3) xx 7#.
The prime factorization of #48# is #color(green)(2 xx 2) xx 2 xx 2 xx color(green)(3)#.

I've highlighted the common factors. Therefore, the GCF is #2 xx 2 xx 3 = color(blue)(12)#.

The LCM can be found by looking at the above prime factorization and multiplying together the factors unique to each number.

#2 xx 2 " "color(white)(........) xx 3 xx color(green)(7)#
#color(green)(2 xx 2 xx 2 xx 2 xx 3)#

Since the #7# from the prime factors of #84# is not in the prime factorization of #48#...

#2 xx 2 xx 2 xx 2 xx 3 xx 7 = 336#

The LCM of #84# and #48# is #color(blue)(336)#. But is this really the LCM? Let's check...

#336/84 = 4#

#336/48 = 7#

Yeah, it's a multiple of both numbers. Also, neither factor after dividing by #48# or #84# is a multiple or factor of the other factor.

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