Need a little help in subtracting fractions.?

Question

Directions: Choose the best estimate

26 25/49 - 24 19/81 is approximately

a. 2 1/2
b. 2 3/4
c. 2 1/4
d. 1 1/2

Now the answer is C, but I need to know how to get this answer.

Answer 1

Start by looking at the fractions. 25/49 is close to 25/50, which is 1/2. 19/81 is close to 20/80, which is 1/4. You can subtract 1/4 from 1/2, and the answer is 1/4, no borrowing needed. Now you can just subtract the whole numbers, 26-24=2. So your final estimate would be 2 1/4, which is C.

Answer 2

An estimate is an "in your head" approximate solution. Notice that 25/49 is about 1/2 (thought not exactly) since 25 is nearly half of 49, and 19/81 is about 1/4 (thought not exactly) since 19 is nearly a fourth of 81. So using those values for the fractions, you would have

26 and 1/2 minus 24 and 1/4, which is 2 and 1/4.

Answer 3

25/49 is very close to 25/50 which is 1/2 (or 2/4)
19/81 is pretty close to 20/80 which is 1/4
so 26 25/49 - 24 19/81 ~ 26 2/4 - 24 1/4 = 2 ¼
.
The trick is to see if you can make a small change in the numerator (preferably) or denominator (if necessary) to make the numerator a factor of the denominator. By small I mean a fraction of the value. if the numerator is 1 then changing it to 2 is huge, but if its 1000 changing it to 1005 ain't so bad...
..
the second fraction 19/81 could have gone to 18/81 which you might recognize as 2/9. So why did I go to 20/80 ?
Easy! The answers were in 1/4ths (or multiples of).
If I had gone with 9s I'd have to have used 4/18ths since
the first fraction is roughly one half and would have given 4.5/9 as a fraction - which isn't simplifying...
ANother way of putting it is that since I started with the 25/49 fraction and got it to ½, I preferred to keep with even denominators. But I should have evaluated both fractions TOGETHER to see where I wanted to go with both of them...a little mental juggling... which wasn't necessary since the multiple choice answers provided the clear preference of 1/4s.

Answer 4

estimate the fraction before you subtract
ie: 25/49 is about 1/2 also 19/81 is about 1/4
26-24= 2
1/2 - 1/4= 1/4
leaving you with your answer 2 1/4

Answer 5

To estimate, you have to think of what a fraction is close to.
25/49 is almost 1/2 since 1/2 would be 25/50. So use 1/2 to estimate this fraction.

19/81 is almost 1/4 since it's close to 20/80.

26 1/2 - 24 1/4 = 2 1/4

Answer 6

26 25/49 = [26(49)+25]/49 =1299/49 = 26.51
24 19/81 =[24(81)+19]/81 = 1963/81 = 24.23
The difference is 2.28 which is close to 2 1/4
2 1/4 is [4(2)+1]/4 = 9/4 = 2.25

Answer 7

26 25/49 is approx 26 1/2
24 19/81 is approx 24 1/4

26 1/2 - 24 1/4
26 2/4 - 24 1/4
2 1/4
c

Answer 8

First, take 26-24. now you've got 2.

Second, look at the fractions. 25/49 is about 1/2. 19/81 is about 1/4.

1/2 minus 1/4 = 1/4. (think of 50 cents minus 25 cents)

so, 2 1/4 would be C.

Answer 9

approx 26 1/2 = 24 1/4 = 2 1/4
OPTION c.