7 3/5 + 11 4/9 =
5 2/5 - 2 7/10
18 8/45
7 3/5 + 11 4/9 = 38/5 + 103/9 = (38*9)/45 + (103*5)/45
= 342/45 + 515/45
= 857/45
= 855/45 + 2/45 = 19 2/45
or
18 + 3/5 + 4/9 = 18 + 27/45 + 20/45 = 18+47/45 = 19 2/45
To add or subtract mixed numbers like these, you need to first convert them into improper fractions. Here's how you can do it:
For 7 3/5:
To convert the whole number 7 into a fraction, multiply it by the denominator of the fraction (5), and add the numerator (3) to get the numerator of the new fraction. So, 7 becomes (7 * 5) + 3 = 38. The denominator remains the same, so it becomes 38/5.
For 11 4/9:
Following the same process, convert 11 into a fraction: (11 * 9) + 4 = 103. So it becomes 103/9.
Now, you can add or subtract them:
7 3/5 + 11 4/9 = 38/5 + 103/9
To add fractions with different denominators, you need to find a common denominator. In this case, the least common multiple (LCM) of 5 and 9 is 45.
Now, you need to rewrite the fractions with the new common denominator:
(38/5) * (9/9) = 342/45
(103/9) * (5/5) = 515/45
Now you can add them:
342/45 + 515/45 = (342 + 515)/45 = 857/45
So, 7 3/5 + 11 4/9 = 857/45.
Now, let's move on to the subtraction:
For 5 2/5:
Convert 5 into a fraction: (5 * 5) + 2 = 27/5.
For 2 7/10:
Convert 2 into a fraction: (2 * 10) + 7 = 27/10.
Now, you can subtract them:
5 2/5 - 2 7/10 = 27/5 - 27/10
To subtract fractions with different denominators, you also need a common denominator, which in this case is 10.
Now, rewrite the fractions with the new common denominator:
(27/5) * (2/2) = 54/10
(27/10) * (1/1) = 27/10
Now you can subtract them:
54/10 - 27/10 = (54 - 27)/10 = 27/10
So, 5 2/5 - 2 7/10 = 27/10.