Featured 3 weeks ago

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of

Note that moving decimal

Hence, we should either divide the number by

In other words, it is written as

To write

Hence in scientific notation

Featured 3 weeks ago

We want to follow order of operations. The first thing to check is parentheses. There's a (1/2) in there, but that's as far as that can go. So, we check the next thing, which is exponents.

We must square both the numerator and denominator.

We are adding everything now, and that operation is communitive (we can do it in any order), but we have a fraction. Let's take care of the simple addition first.

With that out of the way, we need to make the 5 compatible by multiplying it by a factor of 1. Since our fraction is in fourths, we will multiply by

This can be written as

19 is prime, so we cannot do anything else. If we are not allowed to leave it as an improper fraction (larger numerator than denominator), we must convert to a mixed fraction.

To do this, we divide the numerator by the denominator to get the whole number, and the remainder is under the denominator unchanged.

Featured 3 weeks ago

To add 2 fractions we require the

#color(blue)"denominators"# to be the same value.In this case they are, both 8

We can therefore

#color(blue)"add the numerators"# while leaving the denominator as it is.

#rArr5/8+7/8#

#=(5+7)/8#

#=12/8# We can

#color(blue)"simplify"# the fraction by dividing the numerator/denominator by the#color(blue)"highest common factor"# of 12 and 8, which is 4

#rArr12/8=(12÷4)/(8÷4)=3/2larrcolor(red)" in simplest form"# This process is normally done using

#color(blue)"cancelling"#

#rArr12/8=cancel(12)^3/cancel(8)^2=3/2larrcolor(red)" in simplest form"# A fraction is in

#color(blue)"simplest form"# when no other factor but 1 divides into the numerator/denominator.

Featured 3 weeks ago

See the explanation

Let one of the common factors be

let a numeric count be

As the numbers to be tested I chose:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As the process is based on subtraction then the starting point of

This will be true of every subtraction in that the difference will a factor.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Set the following

The subtraction process

This system is stating that the

.......................................................................................................

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Featured 2 weeks ago

3

So we can write:

Another way of writing this is:

Which is the same as

but

so

Featured 2 weeks ago

There are 2 possible approaches to evaluating this product.

#• color(red)" Simplify then multiply"larr" preferable method"# To simplify consider

#color(blue)"common factors"# of the values on the numerators with values on the denominators and#color(blue)"cancel"# In this case 7 and 14 can be divided by 7 and 3 and 15 by 3

#rArrcancelcolor(red)(7)^1/cancelcolor(magenta)(3)^1xxcancelcolor(magenta)(15)^5/cancelcolor(red)(14)^2larr" cancelling"#

#=(1xx5)/(1xx2)#

#=5/2larrcolor(purple)" in simplest form"#

#• color(red)" Multiply then simplify"#

#7/3xx15/14=(7xx15)/(3xx14)=105/42# If you see that 21 is the

#color(blue)"highest common factor"# then straight to the simplification.

#105/42=cancel(105)^5/cancel(42)^2=5/2# If not then simplify in steps using 3 then 7, for example.

#rArrcancel(105)^(35)/cancel(42)^(14)=cancel(35)^5/cancel(14)^2=5/2larrcolor(purple)" in simplest form"# A fraction is in

#color(purple)"simplest form"# when no other factor but 1 will divide into the numerator/denominator.

Featured 1 week ago

2 points of note.

#• 9(-2)^2=9xx(-2)^2#

#• -5(6)=-5xx6# When evaluating expressions with

#color(blue)"mixed operations"# there is a particular order that must be followed.Follow the order as set out in the acronym PEMDAS

[Parenthesis (brackets), Exponents (powers), Multiplication, Division, Addition, Subtraction ]

#rArr9(-2)^2-5(6)-11#

#=(9xx4)-5(6)-11larrcolor(red)"Exponents"#

#=36-30-11larrcolor(red)"Multiplication"# Subtract from left to right.

#=-5larrcolor(red)"Subtraction"#

Featured 1 week ago

There are 2 possible approaches to this calculation, both made fairly 'awkward' due to the values on the denominators of the fractions.

#color(red)"Approach 1"# Change the

#color(blue)"mixed numbers " "to "color(blue)"improper fractions"#

#rArr5 1/16=81/16" and "1 13/18=31/18# The calculation is now.

#81/16-31/18# Before we can subtract the fractions we require them to have a

#color(blue)"common denominator"# We have to find the

#color(blue)"lowest common multiple"# ( LCM) of 16 and 18The LCM of 16 and 18 is 144

#rArr81/16xx9/9=729/144" and "31/18xx8/8=248/144#

#rArr729/144-248/144larrcolor(red)" is now the calculation"# Since the denominators are now common we can subtract the numerators, leaving the denominator as it is.

#rArr729/144-248/144=(729-248)/144#

#=481/144=3 49/144larrcolor(red)" returning a mixed number"#

#color(red)"Approach 2"#

#"Using the fact that "5 1/16=5+1/16;1 13/18=1+13/18#

#"Then "5 1/16-1 13/18#

#=5+1/16-(1+13/18)=5+1/16-1-13/18# We can now subtract the numbers and subtract the fractions separately.

#rArr5+1/16-1-13/18=(5-1)+1/16-13/18#

#=4+(1/16xx9/9-13/18xx8/8)#

#=4+(9/144-104/144)#

#=4+(-95/144)#

#=4-95/144#

#=576/144-95/144#

#=481/144#

#=3 49/144larrcolor(red)" as a mixed number"#

Featured 1 week ago

The reciprocal is

The reciprocal of a number is also called its multiplicative inverse.

To find the reciprocal you flip the number.

The reciprocal is

When you multiply a number by its reciprocal the answer is always

Featured 4 days ago

check: