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Featured 1 month ago

Multiply

An equivalent fraction is equal to 1 such as

An equivalent fraction is the same as multiplying by

so the ratio does not change.

This fraction would be equal to

Hence an example would be that

Featured 2 months ago

If the denominators are the same just divide the numerators.

A fraction consists of

Using the allocated names we have:

Consider whole numbers. For example 6 and 3

These can, and may, be written as

Now consider

Featured 2 weeks ago

It depends...

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:

**Possible interpretation 1 - "Historical"**

Historically the obelus

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

**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#

**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#

**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.

Featured 2 weeks ago

The numbers 'between'

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

Prime numbers have exactly

Composite numbers have more than

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

Featured 1 week ago

33

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.

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

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.

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

DONE!!

Featured 3 days ago

The equivalent fractions below all simplify to

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.

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