Question

Compute. show your work. (5 2/3)^2 -(4 1/3)^2

Answer 1

Add: 1/3 + 2/4 = 1 · 4/3 · 4 + 2 · 3/4 · 3 = 4/12 + 6/12 = 4 + 6/12 = 10/12 = 2 · 5/2 · 6 = 5/6

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, cancel by a common factor of 2 gives 5/
6
.
In other words - one third plus two quarters = five sixths.
Add:1 + 1/2 = 5/6 + 1/2 = 5/6 + 1 · 3/2 · 3 = 5/6 + 3/6 = 5 + 3/6 =8/6 = 2 · 4/2 · 3 = 4/3

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 2) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 2 = 12. In the following intermediate step, cancel by a common factor of 2 gives 4/3. In other words - five sixths plus one half = four thirds.

Answer 2

Explanation:

First convert the mixed fractions to improper fractions.

`(5(2)/(3))^(2)-(4(1)/(3))^(2) = ((17)/(3))^(2) - ((13)/(3))^(2)`

We can use the identity a² - b² = (a +b)(a - b)

Here a = 17/3 and b = 13/3

`= ((17)/(3)+(13)/(3))((17)/(3)-(13)/(3))`

We can add & subtract as they have common denominators.

`=(30)/(3)*(14)/(3)\\\\= 10*(14)/(3)\\\\\\=(140)/(3)\\\\\\= 46(2)/(3)`