You can
put this solution on YOUR website!g. x/2+2x/3=5
x/2 + 2x/3 = 5
multiply both sides of the equation by 6 to get:
3x + 4x = 30
combine like terms to get:
7x = 30
divide both sides of the equation by 7 to get:
x = 30/7
substitute in original equation to get:
x/2 + 2x/3 = 5 becomes:
(30/7)/2 + (2*(30/7))/3 = 5
multiply both sides of the equation by 6 to get:
3*(30/7) + 2*(2*(30/7)) = 6*5
simplify to get:
90/7 + 120/7 = 30
combine like terms to get:
210/7 = 30
simplify to get:
30 = 30 confirming that x = 30/7 is good.
It's easiest to remove fractions by multiplying both sides of the equation by a number that will eliminate them.
Just be careful to multiply both sides of the equation by the same amount to preserve the equality.
One little slip messes the whole thing up.
----------------------------------------------
t. 5x/6-(3-x)/8=(4x+3)/12
I think this is:
(5x/6) - (3-x)/8 = (4x+3)/12
multiply both sides of the equation by 12 to get:
10x - (12*(3-x))/8 = 4x+3
multiply both sides of the equation by 8 to get:
80x - 12*(3-x) = 8*(4x+3)
simplify by removing parentheses to get:
80x - 36 + 12x = 32x + 24
combine like terms to get:
92x - 36 = 32x + 24
subtract 32x from both sides of the equation to get:
92x - 32x - 36 = 24
add 36 to both sides of the equation to get:
92x - 32x = 24 + 36
combine like terms to get:
60x = 60
divide both sides of the equation by 60 to get:
x = 1
substitute in the original equation to get:
(5x/6) - (3-x)/8 = (4x+3)/12 becomes:
(5/6) - (2/8) = (7/12)
multiply both sides of the equation by 12 to get:
10 - (24/8) = 7
simplify to get:
10 - 3 = 7
combine like terms to get:
7 = 7 confirming the value of x = 1 is good.
---------------------------------------
s. 1/3(a+5)=7/2
multiply both sides of the equation by 3 to get:
a + 5 = 21/2
multiply both sides of the equation by 2 to get:
2a + 10 = 21
subtract 10 from both sides of the equation to get:
2a = 11
divide both sides of the equation by 2 to get:
a = 11/2
substitute in the original equation to get:
1/3(a+5)=7/2 becomes:
(1/3)*((11/2) + 5) = 7/2
Multiply both sides of the equation by 6 to get:
6*(1/3)*((11/2)+5) = 6*7/2
simplify to get:
2*((11/2+5) = 3*7
simplify further to get:
11 + 10 = 21
combine like terms to get:
21 = 21 confirming the value of a = 11/2 is good.
---------------------------------
b. (3k-8)/14+5/7=(k+1)/2
I think this is:
((3k-8)/14) + (5/7) = (k+1)/2
assuming that it is, then the equation would be solved as follows:
multiply both sides of the equation by 14 to get:
(3k-8) + 10 = 7*(k+1)
simplify by removing parentheses to get:
3k-8+10 = 7k+7
combine like terms to get:
3k+2 = 7k+7
subtract 3k from both sides of the equation to get:
2 = 7k+7-3k
subtract 7 from both sides of the equation to get:
2-7 = 7k-3k
combine like terms to get:
-5 = 4k
this is the same as:
4k = -5
divide both sides of the equation by 4 to get:
k = -5/4
substitute in the original equation to get:
(3k-8)/14) + (5/7) = (k+1)/2 becomes:
(3*(-5/4) -8)/14 + (5/7) = ((-5/4)+1)/2
Simplify to get:
((-15/4)-8)/14 + (5/7) = (-1/4)/2
multiply both sides of the equation by 14 to get:
((-15/4) -8) + 10 = 7*(-1/4)
remove parentheses to get:
(-15/4) - 8 + 10 = (-7/4)
Multiply both sides of the equation by 4 to get:
-15 - 32 + 40 = -7
combine like terms to get:
-7 = -7 confirming that x = -5/4 is a good answer.
-----------------------------------------
Answer by checkley77(7052)
(Show Source):
You can
put this solution on YOUR website!7x-3y=6?
-3y=-7x+6
y=-7x/-3+6/-3
y=7x/3-2 the slope of this line=7/3.
Therefore a perpendicular line would have a slope=-3/7(the negative reciprical).
Answer by solver91311(5072) 
(Show Source):
Question 238075: how do you solve improper fractions ex.49 6/7+64 5/14
Answer by Theo(675)
(Show Source):
You can
put this solution on YOUR website!your equation is:
49 and 6/7 added to 64 and 5/14
this can be looked upon as:
49 + 6/7 + 64 + 5/14
set y = to this equation.
you get:
y = 49 + 6/7 + 64 + 5/14
multiply both sides of this equation by 14 to get
14y = 14*49 + 2*6 + 14*64 + 5
simplify and combine terms on the right side of this equation to get:
14y = 1599
divide both sides of this equation by 14 to get:
y = 1599/14 = 114.2142857
I confirmed this with the original equation so I know the answer is good.
The other way to solve this is to make the improper fractions into proper fractions and then solve.
your original equation is once again:
49 and 6/7 added to 64 and 5/14
take 49 and 6/7 and make a proper fraction out of it.
you multiply 49 by 7 and divide it by 7 to get 49*7/7
you add 49*7/7 to 6/7 to get (49*7+6)/7
this becomes 349/7
do the same with 64 and 5/14
multiply 64 by 14 and divide it by 14 to get 64*14/14.
this becomes 896/14.
add this to 5/14 to get 901/14
your problem becomes adding 349/7 to 901/14
you still need to get a common denominator so take 349/7 and multiply it by 2 and divide it by 2 to get 698/14.
your problem is now to add 698/14 to 901/14
this becomes (698 + 901)/14 which becomes 1599/14
divide 1599 by 14 to get 114.2142857
this is the same as 114 + 3/14
that's the same answer we got before so we're good.
the third alternative is to simply take the fractional part and turn it into a decimal and add it to the whole number part.
this works best if you have a calculator.
49 + 6/7 becomes 49.857142857
64 and 5/14 becomes 64.357142857
49.857142857 and 64.357142857 = 114.2142857 which is the same answer you got before using the two other methods.
when you multiply a number and divide a number by the same number, the number remains the same.
2 * 7/7 is still 2.
it just looks different.
it looks like 14/7 rather than 2.
if you divide 14 by 7 though, you still get 2.
Question 232306: what are reciprocals fraction
Answer by College Student(210)
(Show Source):
You can
put this solution on YOUR website!The numerator (# on top of the fraction) turns into the denominator (# on the bottom of the fraction)... and the denominator turns into the numerator.
.
Example:
The reciprocal of:
is
Question 238065: 225 + 4*3
----------
64 + 27 - 4
Answer by checkley77(7052) (Show Source):
Question 237966: Please help me with this fraction problem. The equation is -2/7x = 1/5
what is x? the answer i got when i tried to figure it out was x = -1/5 but that's not right... Thank you!
Answer by unlockmath(117) 
(Show Source):
You can
put this solution on YOUR website!Hello,
What you want to do is multiply both sides by -7/2 which looks like this:
(-7/2)-2/7x = (-7/2)1/5 Then do the multiplying to look like this:
x = -7/10
There you go. Now plug the answer into the original equation and it should work out fine.
RJ Toftness
www.math-unlock.com
Question 237893: what is the answer to 7 1/4 minus 2 3/4. Please show work so I can complete my homework
Answer by vleith(1977)
(Show Source):
You can
put this solution on YOUR website!First, get each term as a single fraction
Since the two terms are both over the same denominator (4), you can combine them
Now simplify
Question 21197: Seven more than 3 times a number is -5. find the number.
A number divided by 3, then increased by -2 is 10. What is the number.
Answer by lmk1213(1)
(Show Source):
Question 237592: -1/6+2/3
Answer by College Student(210) (Show Source):
You can
put this solution on YOUR website!In order to solve this, you must find the LCD. Now, there are a few different ways to explain this. Here is the way I do it.
Now, bear with me for a second.
- We know that any number multiplied by 1 equals the same number you started with, right? Ex. 3 x 1 = 3 So this would not change our equation.
- We also know that when you divide a number by itself, the result is 1, right? Ex. 3 / 3 = 1
.
Following this logic, we can multiply any equation by 1 and still not alter the final result. So, in order to find a common denominator, I'm going to multiply both fractions by a value equal to 1. Look carefully:
I used the denominator of the second fraction, 3, to multiply the first fraction's numerator and denominator.
For the second fraction, I used the denominator from the first fraction, 6.
This operation will give us a common denominator.
Now you can combine the fractions since they have common denominators.
Can you reduce the fraction to a simpler fraction? Yes.
Since it's the last step, I'll let you do it.
Hint: How many times 9 fits in 18?
Question 237528: what is the key to solving multiple fractional factors such as
12
105 x
14
30 x
15
14
Answer by checkley77(7052) (Show Source):
You can
put this solution on YOUR website!12/105*14/30*15/14 MULTIPLY THE NUMERATORS & THE DENOMINATORS.
(12*14*15)/(105*30*14) CANCEL OUT THE 14 FROM THE NUMERATOR & DENOMINATOR.
REDUCE 15/30=1/2
12/105*1/2 MULTIPLY THE NUMERATORS
12/210 REDUCE BY DIVIDING NUMERATOR & DENOMINATOR BY 6.
2/35 ANS.
Question 237595: 6 2/3 x 2 3/4
Found 2 solutions by College Student, checkley77:
Answer by College Student(210) (Show Source):
You can
put this solution on YOUR website!6 x 2/3 is the same as to say 6/1 x 2/3.
Therefore, you may multiply the numerators and denominator to obtain a new fraction. Do the same to both terms.
Now you have two fractions.
Can you simplify either or both of them?
Yes.
Can you see what I did here?
12/3=4; 6/4=3/2 when you divide the numerator & denominator by 2
Now, remember that:
4*(3/2) is the same as to say (4/1)*(3/2), so...
Now simplify (12/2)...
I'll let you figure this one out. :) That would be your final result.
Answer by checkley77(7052) (Show Source):
Question 237593: -1/3 -(-3/5)
Answer by checkley77(7052) (Show Source):
Question 237398: Is not a fraction nouthing more than a division problem-
Thank you---Thor
Answer by solver91311(5072) (Show Source):
You can
put this solution on YOUR website!
Though technically correct, saying that a fraction is nothing more than a division problem limits the scope of one's understanding. Rather say a fraction is one possible way, and sometimes a more convenient way, of representing a division operation. Also, using the concept of fractions, you never actually have to divide again! You can always multiply by the reciprocal. Something divided by 5, for example, is exactly the same thing as saying that same something multiplied by one-fifth. That's why "Invert and Multiply" works for dividing by a fraction.
John
Question 237351: Answer is $60,000. How to write it as a 'numeric answer'?
Answer by solver91311(5072) (Show Source):
You can
put this solution on YOUR website!
"Numeric" means "of or relating to numbers" I don't see how you can get much more "numeric" than $60,000 unless it would be 60000 eliminating the dollar sign and the comma. Perhaps your instructor has a different definition of the term "numeric answer" than I understand. You should ask.
John
Question 237340: Please help me understand how to solve the following problem?
Three tired and hungry people had a big bag of apples. While the other two were asleep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second person awoke, ate one-third of the remaining apples and went back to sleep. Finally, the third person awoke and ate one-third of the remaining apples, leaving 8 apples in the bag. How many apples were in the bag originally?
Found 2 solutions by rapaljer, edjones:
Answer by rapaljer(3620) (Show Source):
You can
put this solution on YOUR website!Let x = original number of apples in the bag
x-1/3x= 2/3x = number of apples left after the first person
The second person ate 1/3 of those that were left, so
1/3*2/3x= 2/9x apples = number of apples eaten by the second person.
This leaves (2/3)x-(2/9)x which is (6/9)x - (2/9)x or 4/9x apples left after the second person.
The third person ate 1/3 of the 4/9x apples, which is 4/27x apples.
This leaves (4/9)x-(4/27)x apples after the third person, which is
(12/27)x-(4/27)x or (8/27)x.
So the equation is, based upon the number of apples left being equal to 8:
Multiply both sides of the equation by the reciprocal of (8/27) which is (27/8), and you have
x= 27 apples.
Check:
The first person eats 1/3 of 27 which is 9 apples, leaving 18 apples.
The second person eats 1/3 of 18 which is 6 apples, leaving 12.
The third person eats 1/3 of 12 which is 4 apples, leaving 8 apples.
VERY NICE PROBLEM!!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by edjones(3296) 
(Show Source):
Question 237314: 
, two over three x -7 = 5
or 
Answer by eggsarecool(32)
(Show Source):
You can
put this solution on YOUR website!Not sure which you wanted so I will solve both.
For
we will multiply both sides by
Giving us
When we distribute the 5
Now add 35 to both sides.
and divide both sides by 15.
Now the other interpretation of your problem.
For this one you would need to get a common denominator first.
So
With the common denominator we have.
Now we will multiply both sides by 3x.
Giving us
Add 21x to both sides.
Divide both sides by 36.
Question 237312: How do you simplify r squared minus 5r minus 6 over r plus 1
Answer by solver91311(5072) (Show Source):
Question 236205: Find al numbers for which the raional expression is undefined. (n^3-3n) / (n^2-4)
Answer by Alan3354(6082) 
(Show Source):
Question 235462: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
Answer by Alan3354(6082) (Show Source):
You can
put this solution on YOUR website!If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
------------
S does 1/4 house per hour
J does 1/6 house per hour
Together, they do 1/4 + 1/6 per hour
= 3/12 + 2/12 = 5/12 house per hour
--> 12/5 hours per house
= 2.4 hours
---------------
Use the shortcut for these, product/sum
4*6/(4+6) = 24/10
= 2.4
Question 234686: perform the indicated arithmetic operation. Express the answer in the same unit as the units used in the questions.
3yd2ft4in divided by 2
Answer by ankor@dixie-net.com(6693) 
(Show Source):
You can
put this solution on YOUR website!3yd 2ft 4in divided by 2
Convert everything to inches then divide by 2
= 68 inches
:
68 - 36 = 32 inches: 1 yd
32 - 24 = 8 inches: 2 ft
:
1 yd, 2 ft, 8 inches
:
:
Check: 36 + 24 + 8 = 68
Question 235036: why when we do numeric fractions we always come out with difffrent numbers
Answer by solver91311(5072) (Show Source):
Question 234914: This is a sample equation in my practice exercises in my math book
the answer is 4/3 the problem is 4x-5=1/3 can you show me how to solve this problem in laymans' terms??
Answer by JenniferTutors(46) 
(Show Source):
You can
put this solution on YOUR website!For the problem:
First, get 4x by itself by adding the -5 to the right side of the equation:
Next, to combine the terms you need to make 5 into a fraction by having the same denominator as the other term, 3.
Now you can combine the fractions,
Next, you want to get x by itself, so you would multiply the reciprocal of 4 on both sides of the equation:
Now, you're left with x by itself and you simplify the fraction:
Question 234460: Desiree drove north for 30 min at 50 miles per hr. Then she drove south for 60 min at 20 miles per hr. How far and in what direction is Desiree from where she started
Answer by edjones(3296) (Show Source):
