3 years ago

First, write out the prime factorization of each number

#10 = 2 xx 5# #15 = 3 xx 5# #20 = 2^2 xx 5# #30 = 2 xx 3 xx 5#

We can rewrite the above with more clarity as

#10 = 2^1 xx 3^0 xx 5^color(blue)(1)# #15 = 2^0 xx 3^color(blue)(1) xx 5^color(blue)(1)# #20 = 2^color(blue)(2) xx 3^0 xx 5^color(blue)(1)# #30 = 2^1 xx 3^color(blue)(1) xx 5^color(blue)(1)#

For each prime factor, take the one with the highest exponent. 2 is raised to the power of 2 in 20. 3 and 5 have both a maximum exponent of 1. Refer to the

Therefore,

#"LCM" = 2^2 xx 3^1 xx 5^1#

#= 60#

This algorithm is guaranteed to generate the least common multiple.

3 years ago

**B.E.D.M.A.S. (brackets, exponents, division, multiplication, addition, subtraction)**, work on the exponents first, since the given problem does not contain any brackets. Recall that any number to the power of

#6.73-2*color(teal)(5^0)-:2#

#=6.73-2*color(teal)1-:2#

#=6.73-color(darkorange)(2*1)-:2#

#=6.73-color(darkorange)2-:2#

#=6.73-color(violet)(2-:2)#

#=6.73-color(violet)1#

#=color(green)(|bar(ul(color(white)(a/a)color(black)(5.73)color(white)(a/a)|)))#

3 years ago

**Given:**

- Craig's older brother's shirts take up

- Craig's younger brother's shirts take up

**You are trying to find:**

- how much of the basket belongs to Craig's older or younger brother

Thus, add

#1/6+3/6#

#=(1+3)/6#

#=4/6#

Since the numerator and denominator have a common factor of

#(4color(red)(-:2))/(6color(red)(-:2))#

#=color(green)(|bar(ul(color(white)(a/a)2/3color(white)(a/a)|)))#

3 years ago

The numbers to remember are 5, 9 and 32

Fahrenheit are the lager number when comparing like temperature for like. So to convert Centigrade to Fahrenheit, you need to make the numbers bigger. Thus you multiply by

All you need to remember now is that freezing point for each is different.

Centigrade freezing point is

Fahrenheit freezing point is

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We are going from Centigrade to Fahrenheit so it is small number to large. So we have

We are changing freezing point from 0 on 1 scale to 32 on a different scale so we now have:

Thus the full conversion is:

3 years ago

Bob's training can be broken down into three steps:

#1# . ran#14.6# milesawayfrom home

#2# . ran#9.8# milestowardshis home

#3# . ran#5.3# milesawayfrom his home

Since Bob starts running from his home, he is

If he starts running from his home for **add** the distance he travels. In contrast, when he travels towards his home, you subtract the distance he travels.

#0color(white)(i)"miles"+14.6color(white)(i)"miles"#

When Bob runs towards his home at a distance of

#0color(white)(i)"miles"+14.6color(white)(i)"miles"-9.8color(white)(i)"miles"#

Finally, when Bob runs

#0color(white)(i)"miles"+14.6color(white)(i)"miles"-9.8color(white)(i)"miles"+5.3color(white)(i)"miles"#

If you solve the addition problem, you get

Please see below.

**Divisibility Rule for #11#**

Divide the alternate digits in two different groups. Take the sum of alternate digits separately and find the difference of the two numbers. If the difference is

Example:

**Divisibility Rule for #12#**

If the number is divisible by both

Example: In

**Divisibility Rule for #13#**

Recall the divisibility rule of

Starting from right mark off the digits in groups of threes (just as we do when we put commas in large numbers).

Now add up alternate group of numbers and find the difference between the two. If the difference is divisible by

For example

and

As difference between

As

3 years ago

See explanation...

If it is a terminating decimal, then multiply it by a power of

For example:

#0.16 = 16/100 = (color(red)(cancel(color(black)(4)))*4)/(color(red)(cancel(color(black)(4)))*25) = 4/25#

If it is a repeating decimal, then multiply by a power of

For example:

#0.2345345345... = 0.2bar(345)#

Multiply by

#(10000-10)0.2bar(345) = 2345.bar(345) - 2.bar(345) = 2343#

So, dividing by

#0.2bar(345) = 2343/(10000-10) = 2343/9990 = (color(red)(cancel(color(black)(3)))*781)/(color(red)(cancel(color(black)(3)))*3330) = 781/3330#

3 years ago

25% of 90 is 22.5.

A percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:

Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:

Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.

**---------------------------**

**The Fractional Method**

So we have a fraction:

and

so that means,

or

This means that we need four 25's to get 100.

or,

(we could also divide both numerator and denominator by 5 to get the same result:

Now that we know 25% is equal to **divide 90 by 4**, its easiest (for me anyway) to just divide 90 by 4.

**---------------------**

**The Decimal Method**

As we found out above 25% equals 0.25 so we can solve this problem using decimals too! All we need to do is multiply 90 by 0.25, which gives us the same answer as above.

**---------------------**

Despite the fact that that mathematics seemed to be a lot more involved in the fractional method, the calculations were a lot easier and personally I found it to be faster than the decimal method. The decimal method is great when you're working with fractions that aren't equal to 100 (For example:

Sorry this is so long, I hope it helped though!

3 years ago

So lets first operate with positive numbers. We should go about this by thinking about a pie, like this:

**Courtesy of: http://etc.usf.edu/clipart/40600/40610/pie_01-10a_40610.htm (ClipArt ETC Free Classroom License)**

Lets say that the circle above is an apple pie. The apple pie has 10 slices, or parts. If no one takes a piece of the pie then we have all 10 slices of the pie. Since we have all ten slices of pie we can say that we have "10 of the 10 slices" or

...or a full pie (this is sweet potato pie):

**Courtesy of: http://culinaryphysics.blogspot.com/2015/11/patti-labelle-sweet-potato-pie-recipe-soul-food.html (Public Domain)**

Or this (key lime):

**My own photo (and baking), feel free to reuse, if you want the recipe shoot me a message**

Okay, now lets say that 9 people enter the room and they all take a slice of the pie. That means there is only on piece of pie left

We know this because

There's an underlying tend here, which looks like this:

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

*_**_**_*** _**___

This exact same trend exists for negative fractions we just have to put a negative sign in front of the decimal. This means that:

I hoped this helped!

3 years ago

First you have to multiply

When talking about order of operation the PEDMAS rule applies. According to this rule first you have to calculate everything which is in the most inner brackets.

In this expression you have 2 kinds of brackets, but it makes no difference how they look like because you only have to look at those which contain no other brackets, and they are

In those brackets you have 2 operations: addition and multiplication. According to PEDMAS rule you have to do multiplication first, then the addition, so you get:

In every line the next operation is marked with the red color exept last line with only one operation (substraction