Question 845926: I have these two problems. Can anyone help please?
6 5/9 - 9 3/4 + 7 1/3 - 1 5/6
3 3/5 x 1 5/9
2/10
Thank you
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: SOLVE linear system by SUBSTITUTION |
Solve:
 We'll use substitution. After moving 1*y to the right, we get:
 , or  . Substitute that
into another equation:
 and simplify: So, we know that y=1. Since , x=1.
Answer:  .
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I am not sure that your problems are displayed correctly, but I will make my best guess at what you meant.
Not knowing your age, your grade, or how much math you have already learned, I do not know how much explanation you need.
Just in case, I will explain a lot, so it may get slow and boring.
To calculate  ,
the first step would be to convert those mixed numbers into improper fractions.
 so the mixed number  can be written as the improper fraction  .
Doing the same with the other numbers,we get
Now the problem is that all the fractions to be added have different denominators.
We need a common denominator, one that is a multiple of all the denominators in those fractions.
We need a number that is a multiple of  ,  ,  and  .
The smallest one we can find is  .
The multiples of 9 are 9, 18, 27, 36, 45, 54, and so on.
Of the multiples of ,
is a multiple of , but not a multiple of the other numbers;
 is a multiple of and , but not a multiple of ,
and  is not a multiple of or either.
The next smallest multiple of is  , and it is a multiple of , , and .
That is the least common multiple of , , and .
So we want to convert all those fractions to fractions with for a denominator.
To convert a fraction into an equivalent fraction, we have to multiply the numerator and denominator times the same number.
Multiplying the numerator and denominator of times we get
 .
Multiplying the numerator and denominator of  times we get
 .
Multiplying the numerator and denominator of  times  we get
 .
Multiplying the numerator and denominator of  times 6 we get
 .
So far we have
Now it is just a question of adding/subtracting the numerators to get
The way I calculate  has 3 steps:
1) I add together all the numbers with a + sign in front, and add together all the numbers with a - sign in front,
2) I figure out which total wins, to use the sign of the winning total, and
3) I calculate the difference of the totals.
I could write that as
Putting all of the above together, I would just write
(The rest of my calculations would be in my head, or on the margin of the paper, or on separate scrap paper).
 cannot be simplified into an equivalent fraction with a denominator smaller than ,
so the last step I could do is converting that  improper fraction into the mixed number  .
I would do that in my head (or pretend I did), but my calculation would be
that  divided by is  with a remainder of  ,
because times is  ,
and is  more than ,
so  .
On my paper, I would only write
,
although a lot of calculating went into that.
I believe your second problem is  x  divided by  .
I would write that as
To begin with,  . It is strange that it was given as ,
because is the same as  and is the simplest way to write that number.
You must also know that dividing by a fraction is the same as multiplying times its reciprocal (the fraction turned upside down), so dividing by is the same as multiplying by the fraction  , which is a fancy way of writing  .
The final  calculation can be done with a calculator,
but it is easy to do in my head if I simplify (cancel out) factors that appear in numerator and denominator.
In my head I see it like this:
 .
Some teachers do not like to see cross-out cancelling,
because sometimes students go cross-out crazy,
and they cross out numbers here and there without rhyme or reason,
ending with a result that is not equal to what they started with.
They think that it should be written as
 ,
That shows that the two s cancel out because they can be rearranged into a factor that equals  , and multiplying times does not change anything.
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