Make the internet a better place to learn

2

Answer:

#56,700,000=5.67xx10^7#

Explanation:

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 #10#.

Note that moving decimal #p# digits to right is equivalent to multiplying by #10^p# and moving decimal #q# digits to left is equivalent to dividing by #10^q#.

Hence, we should either divide the number by #10^p# i.e. multiply by #10^(-p)# (if moving decimal to right) or multiply the number by #10^q# (if moving decimal to left).

In other words, it is written as #axx10^n#, where #1<=a<10# and #n# is an integer.

To write #56,700,000# in scientific notation, we will have to move the decimal point seven points to the left, which literally means dividing by #10^7#.

Hence in scientific notation #56,700,000=5.67xx10^7# (note that as we have moved decimal seven points to the left we are multiplying by #10^7#.

1

Answer:

#19/4#

Explanation:

#-(1/2)^2+3+2#

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.

#-1^2/2^2+3+2#

#-1/4+3+2#

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.

#-1/4+5#

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 #4/4#

#-1/4+5*4/4#

#-1/4+20/4#

This can be written as

#20/4-1/4#

#19/4#

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.

#19/4=4 r3#

#4 3/4#

2

What is 5/8 +7/8 ?

Jim G.
Jim G.
Featured 3 weeks ago

Answer:

#12/8=3/2#

Explanation:

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.

2

Answer:

See the explanation

Explanation:

#color(blue)("The numeric reference")#

Let one of the common factors be #f=8#
let a numeric count be #n#

As the numbers to be tested I chose:

#8xx20=160#
#8xx15=120#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The underlying principle")#

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

#160-120# has to have a difference that is related to one of the factors. In that: #" "120+nxx"some factor of 160"=160#

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The demonstration of process")#

Set the following
#8xx20=160 = 20f#
#8xx15=120=15f#

The subtraction process

#20f-15f=color(white)(1)5flarr" largest - smallest: next use the 15 & 5"#

#15f-color(white)(1)5f=10flarr" largest - smallest: next use the 10 & 5"#

#10f-color(white)(1)5f=color(white)(1)5flarr" largest - smallest: next use the 5 & 5"#

#5f-5f=0 larr" we have to stop at this point"#

This system is stating that the #GCF = 5f = 5xx8=40#
.......................................................................................................
#color(brown)("Numeric equivalent")#

#160-120=40" ......." ->color(white)(.) 5f->color(white)(.)5xx8=40#
#120-40=80" ........." ->10f->10xx8=80#
#80-40=40" ..........."->color(white)(.) 5f->color(white)(.)5xx8=40#
#40-40=0#

#GCF = 40#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Using prime factor trees")#

Tony B

#GCF=2xx2xx2xx5=40#

1

Answer:

3

Explanation:

#1/(27^(1/3))# is the same as #27^(-1/3)#

So we can write: #27^(2/3)xx27^(-1/3)#

Another way of writing this is:

#27^(2/3-1/3)" "=" "27^(1/3)#

Which is the same as #root(3)(27)#

but #3xx3xx3=27#

so #27^(1/3)=root(3)(27)=3#

1

Answer:

#5/2#

Explanation:

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.

1

Answer:

#-5#

Explanation:

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"#

1

Answer:

#3 49/144#

Explanation:

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 18

The 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"#

1

Answer:

The reciprocal is #1/5#

Explanation:

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

To find the reciprocal you flip the number.

#5 = 5/1# as a fraction

The reciprocal is #1/5#

When you multiply a number by its reciprocal the answer is always #1# which is the identity element for multiplication and division.

#5/1 xx 1/5 = 1#

#a/1 xx 1/a = 1" "# assuming that #a !=0#

1

Answer:

#8/49#

Explanation:

#1/(6+1/8)#

#:.=1/(6 1/8)#

#:.=1/(49/8)#

#:.=1/1 xx 8/49#

#:.=8/49#

check:

#1/8=0.125+6=6.125#

#1-:6.125=0.163265306#

#8/49=0.163265306#