help adding and subtracting mixed fractions!!?

Question

1. 1 1/3 - 5/6 =

2. 3/16 - 5/24 =

3. 2 2/3 + 1 1/4 - 1 3/4 + 2 3/8 =

4. 2 3/4 + 1 1/2 + 7/8 - 2 1/2 + 2 3/8 =

5. 5/6 + 3/8 =

6. 1/6 - 1/8 =

ANYTHING HELPS THANK YOU.

Answer 1

1 1/3 - 5/6 =

4/3 - 5/6

8/6 - 5/6 =

3/6 =

1/2

- - - - - - - - -

3/16 - 5/24

9/48 - 10/48 =

- 1/48

- - - - - - - - - - -

2 2/3 + 1 1/4 -1 3/4 + 2 3/8 =

8/3 + 5/4 - 7/4 + 19/8 =

64/24 + 30/24 - 42/24 + 57/24 =

94/24 - 42/24 + 57/24 =

52/24 + 57/24 =


109/24 =

4 13/24

- - - - - - - - -s-

Answer 2

I'll do a couple... but you probably should do the rest.

#1. 1 1/3 - 5/6
This problem has mixed numbers (whole numbers and fractions), and an answer that needs to be reduced.

1 1/3 really means 1 + 1/3, that is 1x3/3 + 1/3 or 4/3
Similarly 2 3/7 means 2 + 3/7 2x7/7 + 3/7 or 14/7 + 3/7 or 17/7.

So
1 1/3 – 5/6 is the same as 4/3 – 5/6.
But we need to have what is called a “common denominator,” the same denominator in both fractions. A common denominator is a number that both denominators divide into evenly. Sometimes this number can be found simply by multiplying the two numbers. But in this case 3 divides into 6 evenly, and so does 6. So the lowest common denominator is 6. 3 divides into 6 two times. 2/2 = 1, and 1 times anything is that thing (1x5 = 5) so if we multiply 4/3 by 2/2 we get 4x2 on top and 3x2 on the bottom or 8/6

Now we have 8/6 - 5/6.
8/6 – 5/6 = (8-5)/6 = 3/6

But 3/6 = 3x1 / 3x2 = 3/3 x ½
Since 3/3 = 1 and 1 x ½ = ½, the answer is ½ (This process is called “reducing the fraction”)

#5. 5/6 + 3/8

In this one, the common denominator is less trivial, and the answer cannot be reduced.

It was easy to find the common denominator in the first problem. This one is a little more difficult. Neither of the denominators is the common denominator.

Lets look at the multiples of 8. 8x1 = 8. Does 6 divide evenly into 8? No.
How about 2x8 = 16? Does 6 divide evenly into 16? Nope.
How about 3x8 = 24? Does 6 divide evenly into 24? Yes! It goes 4 times.
So multiply 5/6 by 4/4 giving 5x4 / 6x4 = 20/24,
And by multiplying 3/8 by 3/3 we get 3x3 / 3/8 = 9/24

So now the problem becomes
5/6 + 3/8 = 20/24 – 9/24 = (20 – 9)/24 =11/24
Since there are no numbers that divide evenly into11 and 24, this fraction cannot be reduced further.

Note: There is a mathematical way to find the lowest common denominator, but the way presented in problem 5 as shown above will get you there quickly as long as the denominators are small. The mathematical method is to determine the common factors in all the denominators, get their product, and them multiply them by the remaining non-common factors. Suppose you had denominators of 24, 36 and 42.
24 = 2x2x2x3
36 = 2x2x3x3
42 = 2x3x7
The common factors are 2x3= 6
24 = 4x6
36 = 6x6
42 = 7x6
The Lowest Common Denominator in this case would be
6x4x6x7=1008... would have taken some time getting there any other way.

Here's one of my own:
2 1/2 - 1 1/3 + 1/5
2 1/2 means 2 + 1/2. Just as in the first problem 2 = 2x2/2 = 4/2. so 2 1/2 means 4/2 + 1/2 = (4+1)/2 = 5/2

Similarly, 1 1/3 = 1 + 1/3. 1 = 1x3 / 3 = 3/3, so 1 1/3 = 3/3 + 1/3 = (3+1)/3 = 4/3.

Now
2 1/2 - 1 1/3 + 2/5 has become
5/2 - 4/3 + 2/5... but we have the denominator problem again.
Look at the largest denominator, 5, and start checking the multiples of 5. We're looking for a multiple of 5 that BOTH 2 and 3 divide into evenly.
Clearly 2 does not divide evenly into 5.
2 x 5 = 10. 2 divides evenly into 10, but does 3? No.
3 x 5 = 15. 3 divides evenly, but does 2? No.
4 x 5 = 20. Again 2 divides evenly, but 3 does not.
5 x 5 = 25. Neither 2 nor 3 divide evenly into 25
6 x 5 = 30. 2 divides evenly 15 times. 3 divides evenly 10 times. So 30 is our common denominator.
Looking at 5/2, 2 divides evenly into 30 15 times. 15/15 = 1 (remember this procedure?) so 5/2 = 5x15 / 2x15 = 75/30
Similarly, 3 divides evenly 30 10 times. 10/10 = 1 so 4/3 = 4x10 / 3x10 = 40/30
Finally, 5 divides into 30 6 times. 6/6 = 1 so 2/5 = 2x6 / 5/6 = 12/30.

So
5/2 - 4/3 + 2/5 becomes
75/30 - 40/30 + 12/30 = (75 - 40 + 12)/30 = 47/30
But we're not done. While we can't reduce 47/30, 47 is greater than 30. So we have a mixed number for an answer.
47/30 = 30/30 + 17/30. 30/30 = 1. So the answer is 1 17/30.

Answer 3

First you have to make all the mixed numbers improper fractions by taking the bottom number times the whole number then adding the top number example 2 3/5 (2*5+3 over 5) = 13/5

Once you have all fractions…. Make sure you have a common denominator.
13/5 – 3/10 (Change the 13/5 to 26/10)

Answers to your questions

1. 1 1/3 - 5/6 = 8/6 – 5/6 = 3/6 or 1/2

2. 3/16 - 5/24 = 9/48 – 10/48 = -1/48 (This one came out to be a negative… are you sure it’s the right problem?

3. 2 2/3 + 1 1/4 - 1 3/4 + 2 3/8 = 64/24+30/24-42/24+57/24= 109/24

4. 2 3/4 + 1 1/2 + 7/8 - 2 1/2 + 2 3/8 = 22/8+12/8+7/8-20/8+19/8=40/8 = 5

5. 5/6 + 3/8 = 20/24+9/24 = 29/24 or 1 5/24

6. 1/6 - 1/8 = 4/24-3/24 = 1/24

Answer 4

1. 1 1/3 -5/6 =4/3 - 5/6 =8/6 -5/6= 3/6 = 1/2

2. 3/16 -5/24= 9/48 -10/48 = -1/48

3. 2 2/3 +1 1/4 -1 3/4 +2 3/8 = 8/3 +5/4 -7/4 +19/8 =
64/24 +30/24 -42/24 + 57/24 = 109/24= 4 13/24

4. 2 3/4 + 1 1/2 +7/8 - 2 1/2 + 2 3/8 = 11/4 + 3/2 +7/8 -5/2 +
19/8 = 22/8 +12/8+7/8-20/8+19/8 = 40/8 = 5

5. 5/6 + 3/8 = 20/24 +9/24 = 29/24 = 1 5/24

6. 1/6 - 1/8 = 4/24 - 3/24 = 1/24

Answer 5

1. 1 1/3 is the same as 8/6 therefore 8/6 - 5/6 = 3/6 = 1/2
2. 3/16 is the same as 9/46 and 5/24 is the same as 10/48 there fore the answer is 9/49 - 10/48 = -1/48
3. 2 2/3 is the same as 64/24 and 1 1/4 is the same as 30/24 and 1 3/4 is the same as 42/24 and 2 3/8 is the same as 57/24 therefore the sum is 64/24 + 30/24 - 42/24 + 57/24 = 109/24 = 4 13/24
4. 66/24 + 36/24 + 21/24 - 60/24 + 57/24 = 120/24 = 5
5. 20/24 + 9/24 = 1 5/24
6. 4/24 - 3/24 = 1/24

that was harder then i thought :P

Answer 6

1. 1 1/3 - 5/6
= 4/3 - 5/6
= 8/6 - 5/6
= 3/6
= 1/2

2. 3/16 - 5/24
= 9/48 - 10/48
= -1/48

3. 2 2/3 + 1 1/4 - 1 3/4 + 2 3/8
= 8/3 + 5/4 - 7/4 + 19/8
= 64/24 + 30/24 - 42/24 + 57/24
= 109/24

4. 2 3/4 + 1 1/2 + 7/8 - 2 1/2 + 2 3/8
= 11/4 + 3/2 + 7/8 - 5/2 + 19/8
= 11/4 - 2/2 + 26/8
= 22/8 - 8/8 + 26/8
= 40/8
= 5

5. 5/6 + 3/8
= 20/24 + 9/24
= 29/24

6. 1/6 - 1/8
= 4/24 - 3/24
= 1/24

Answer 7

All you need to do is to make the bottom number the same. So you times the specific fraction to get the same bottom number.

1. 1 1/3 - 5/6 = 1 2/6 - 5/6 = 8/6 - 5/6 = 3/6 = 1/2

2. 3/16 - 5/24 = 9/48 - 10/48 = -1/48

3. 2 2/3 + 1 1/4 - 1 3/4 + 2 3/8 = 2 16/24 + 1 6/24 - 1 18/24 + 2 9/24 = 2 + 1 - 1 + 2 + 16/24 + 6/24 - 18/24 + 9/24 = 4 13/24

4. 2 3/4 + 1 1/2 + 7/8 - 2 1/2 + 2 3/8 = 2 + 1 - 2 + 2 + 6/8 + 4/8 - 4/8 + 3/8 = 3 17/8 = 5 1/8

5. 5/6 + 3/8 = 20/24 + 9/24 = 29/24 = 1 5/24

6. 1/6 - 1/8 = 4/24 - 3/24 = 1/24

I hope I didn't make any mistakes (done them in my head)

Answer 8

This isn't too hard. Just follow these steps (we'll use #1 for an example)

1) Convert the mixed fraction into a regular fraction.
a) Take the denominator (the "bottom" number in a fraction) times the whole number.In this case its 3 x 1 = 3
b) Add the numerator ("top" number) to the number you just got. In this case 1 + 3 = 4
c) The denominator stays the same for your new number, so the new regular fraction is b/a, or 4/3
2) Find your lowest common denominator. (In this case, the lowest common denominator is 6 because the smallest number that both 3 (from the denominator of the first fraction) and 6 (the denominator of the second fraction) will go into is 6.
3) Find what you would have to multiply each original denominator by in order to get your new denominator. In this case, you'd need to multiply the first denominator (3) by 2 in order to get 6. You'd have to multiply 6 (the second denominator) by 1 to get 6.
4) Multiply the each fraction by the number you found in the last step. (4x2)/(3x2) = 8/6 and (5x1)/(6x1) = 5/6
5) Subtract the numerators (top numbers) 8-5=3.
6) Keep your original lowest common denominator. The answer is 3/6.
7) Reduce if possible. In this case, 3/6 is the same as 1/2.

Good luck!

Answer 9

3 1/3 = 10/3 2 2/5 = 12/5 Since the denominators are different ( 3 & 5) bring both to the same denominator 15 10/3 = 50/15 12/5 = 36/15 50/15 - 36/15 = 14/15 ANSWER

Answer 10

Buy a Texas Instruments calculator that does fractions...it saved my life.