Math and Fractions?

Question

Can someone explain how I get the answers to the following:

2/3+1/6+5/9=
1 1/6+ 3 1/4=

11/15+7/10-2/5=

find the decimal equivalent of the mixed number

8 7/8

Answer 1

okay well to add or subtract fractions you have to have common denominators

so you have

2/3+1/6+5/9

all of the denominators can go into 18

so to get 3 to 18 you multiply by six which means you must multiply the 2 by 6 also and same with all the other fractions

2/3*6+1/6*3+5/9*2
12/18+3/18+10/18

now read left to right and add the numerators

12+3+10=25

25/18=1 7/18

the second one

change to mixed numbers first

1*6+1=7
4*3+1 (you take the denominator times the whole number then add the numerator)
=13

so now you have 7/6+13/4 they can both go into 12 so you have

14/12+39/12

so now add 14+39=53 so now you have 53/12 change back into a mixed number and you get
4 5/12


the third one

you have 11/15+7/10-2/5

they can all go into 30 so you have

22/30+21/30-12/30

now read left to right and follow the signs

22+21=43
43-12=31

31/30=1 1/30

now to find the decimal equivalent you already know that 8 is going to be the whole number before the decimal so all you need to look at is 7/8 now just divide 7 by 8 and you get .875

so the decimal is 8.875

check ya later ♥

Answer 2

You need to use what's called a "common denominator," which is just a piece-size which everything breaks down to. For example, take your first problem
2/3+1/6+5/9=?
The fraction 2/3 means that, having split 1 into 3 pieces, you have 2 of them. 1/6 means that, having split 1 into 6 pieces, you have 1 of them. 5/9 means that, having cut up 1 into 9 pieces, you have 5 of them. You need to figure out how to compare all of these different piece sizes. The common denominator is how. Imagine cutting 1 up into 18 pieces. 6 of these pieces is going to be the same as 1/3, because 3*6=18. So 6/18=1/3, which you should read as "six of the 1/18 size pieces is 1/3." Since 6*3=18, 3/18 is the same amount as 1/6. So by cutting everything up into 1/18 size pieces, you have managed to compare 1/6 and 1/3.

This means that 2/3 is twice 1/3, which is 12/18, while 1/6 is still 1/6 which is 3/18, so that 2/3+1/6=15/18. Meanwhile 9*2=18, so that 1/9 is 2/18, and 5/9 is 10/18, so the grand total becomes 25/18, or 1 +7/18.

You need to find a piece size (the common denominator) which all of the other numbers fit into. Then everything gets simpler because the pieces are all the same size.

Answer 3

To add and subtract fractions, you need a common denominator. For the first problem, you can rewrite all the fractions in terms of 18ths, so you get:

12/18 + 3/18 + 10/18 = 25/18 = 1 7/18

For the second one you can turn them both into improper fractions and then put them in terms of 12ths, so you get:
7/6 + 13/4 = 14/12 + 39/12 = 53/12 = 4 5/12

The lowest common denominator for the third one 30, so you get:

22/30 + 21/30 - 12/30 = 31/30 = 1 1/30

To find the decimal equivalent of a fraction, you divide the numerator by the denominator either by hand or with a calculator. 7 divided by 8 is .875, so the decimal equivalent of 8 7/8 is 8.875

Answer 4

I'll do the first one for you only:

Convert all the fractions to the same base:

2/3 * 6/6 = 12/18
1/6 * 3/3 = 3/18
5/9 * 2/2 = 10/18

Now add numerators: (12+3+10)/18 = 25/18
So, 2/3+1/6+5/9 = 25/18

8 7/8 = 71/8 = 8.875

Answer 5

2/3 + 1/6 + 5/9 = 12/18 + 3/18 + 10/18 = 1 7/18
you have to find the common denominator
8.875 just multiply the 8 by the denominator (the other 8) add the 7 to the result then divide by 8 .

Answer 6

(2/3) + (1/6) + (5/9)
Multiply everything by 18
(12/18) + (3/18) + (10/18)
(12 + 3 + 10)/18
(25/18)
ANS : 1 7/18

------------------------------------

(1 1/6) + (3 1/4)
(7/6) + (13/4)
Multiply everything by 12
(14/12) + (39/12)
(14 + 39)/12
(53)/12
4 5/12

-----------------------------------------

(11/15) + (7/10) - (2/5)
Multiply everything by 30
(22/30) + (21/30) - (12/30)
(22 + 21 - 12)/30
(43 - 12)/30
(31/30)
1 1/30

-----------------------------------------

8 7/8 = 8 + .875 = 8.875

Answer 7

The general rule for fractional operations are:

(a / b) + (c / d) = ( ad + bc) / bd


(a / b) - (c / d) = ( ad - bc) / bd


(a / b) x (c / d) = ab / cd


(a / b) / (c / d) = ad / bc


a,b,c,d can be integers or fractional numbers or entire functions - the operating rules remain consistent.

These rules can be chained together for a series of fractions starting with the first two.

If the fractional result needs to be reduced to lowest terms, it only needs to be done once at the end of the process.

Answer 8

first one answer is 25/18
12+3+10/8 = 25/18
secone one answer is 53/12
14+39/12
third one is 13/30
22+21-30/30

last one is 8.875
well hope this is right