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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:

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:

It depends...

Explanation:

Given:

#15-:5(8-6+3)xx5#

I think we are all agreed that the content of the parentheses should be evaluated first. Subtraction and addition are given the same priority, so the expression in parentheses is to be evaluated from left to right:

#8-6+3 = 2+3 = 5#

Now we have:

#15-:5(5)xx5#

This is where it gets interesting. Here are three possibilities, in no particular order:

#color(white)()#
Possible interpretation 1 - "Historical"

Historically the obelus #-:# was used to express a division of everything on the left by everything on the right. In our example, that means that we have:

#15-:5(5)xx5 = 15/(5(5)xx5) = 15/(5xx5xx5) = 15/125 = 3/25#

#color(white)()#
Possible interpretation 2 - "Pure PEMDAS"

PEMDAS does not distinguish multiplication by juxtaposition from any other kind of multiplication. So in full we can write:

#15-:5(5)xx5 = 15-:5xx5xx5#

This is then evaluated from left to right (multiplication and division having the same priority). So we get:

#15-:5xx5xx5 = 3xx5xx5 = 15xx5 = 75#

#color(white)()#
Possible interpretation 3 - "Skewed PEMDAS"

This common practice gives higher priority to multiplication by juxtaposition. This is sometimes "justified" by people who claim that the "Parentheses first" includes any multiplier outside the parentheses. Such a justification seems spurious to me, but the visual proximity does suggest a higher priority.

Following this interpretation, we get:

#15-:5(5)xx5 = 15-:25xx5 = 3/5xx5 = 3#

#color(white)()#
Which is right?

They are all "right" or "wrong" or neither. The fact is that the given expression is ambiguous. Operator precedence rules are intended to clarify communication by providing agreed rules of interpretation.

They do not work well all of the time - especially if the particular rule set is not shared between the writer and reader.

It is best to use extra parentheses to make the meaning clear.

Answer:

#12," "14," "15," "16," "18," "#

Explanation:

The numbers 'between' #11 and 19# are:

#12," "13," "14," "15," "16," "17," "18," "#

All numbers (except 1) are either prime or composite.

Prime numbers have exactly #2# factors while
Composite numbers have more than #2# factors.

There are more composite numbers than prime numbers, so the quickest way to find the composite numbers in a given set, is to simply exclude the primes.

The prime numbers between #11 and 19# are:

#color(blue)(13 and 17)#, so all the rest are composite.

#12," "cancelcolor(blue)(13)," "14," "15," "16," "cancelcolor(blue)(17)," "18," "#

Answer:

33

Explanation:

Remember your order of operations:

First work in the parenthesis. Since you have two operations inside the parenthesis you need to again follow the order of operations and do your multiplication before you add.

#4 xx 5 = 20#
#8+20 =28#

Now rewrite your equation replacing the 28 for the terms in the parenthesis.

#28 \div 7+ 29#

After parenthesis come multiplication and division. If you have both, you do them from left to right. In this case, we just need to do the division 28 divided by 7.

#28 \div 7 = 4#

Replace the 28 divided by 7 in your equations with 4, then do the last of the math by add 29.

#4 +29 =33#

DONE!!

Answer:

The equivalent fractions below all simplify to #3/5#

Explanation:

Equivalent fractions are those which have the same size, but they look different because they have different numerators and denominators. However, they all simplify to the same fraction in simplest form.

You can find equivalent fractions by multiplying the top and bottom by the same number.

#9/15 xx 2/2 = 18/30#

#9/15 xx 5/5 = 45/75#

#9/15 xx 10/10 = 90/150#

#9/15 xx11/11 = 99/165#

#9/15 div 3/3 = 3/5#

#9/10 xx (2/3)/(2/3) = 6/10#

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