Answer:
8/9
Explanation:
Step 1: Convert both 4 1/3 and 3 4/9 to improper fractions:
- Both 4 1/3 and 3 4/8 are mixed numbers with a whole number (4 and 3) and a fraction (1/3 and 4/9).
- We can convert them to improper fractions by making a new fraction where the numerator is the product of the whole number and the denominator. We add the original numerator to that product and keep the original denominator.
Converting 4 1/3 to an improper fraction:
For 4 1/3, we'll mutiply 4 by 3, add 1 to that, and keep 3 as the denominator:
((4 * 3) + 1) / 3
((12 + 1) / 3
13/3
Thus, 4 1/3 as an improper fraction is 13/3.
Converting 3 4/9 to an improper fraction:
For 3 4/9, we'll multiply 3 by 9, add 4 to that, and keep 9 as the denominator:
((3 * 9) + 4) / 9
(27 + 4) / 9
31/9
Thus, 3 4/9 as an improper fraction is 31/9.
Finding the difference of 13/3 and 31/9:
- Since 4 1/3 is equivalent to 13/3 and 3 4/9 is equivalent to 31/9, our new equation is 13/3 - 31/9.
- We can subtract straight across by giving the fractions the same denominator.
- We see that one denominator is 3 and the other is 9
- Since 9 is a multiple of 3, we can make 13/3 out of 9 by multiplying the entire fraction by 3/3:
(13/3) * (3/3) = 39/9
Now, we simply subtract 31/9 from 39/9:
39/9 - 31/9
8/9
Thus, 4 1/3 - 3 4/9 = 8/9.