Respuesta :
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.
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:
Step-by-step explanation:
First convert the mixed fractions to improper fractions.
[tex](5\dfrac{2}{3})^{2}-(4\dfrac{1}{3})^{2} = (\dfrac{17}{3})^{2} - (\dfrac{13}{3})^{2}[/tex]
We can use the identity a² - b² = (a +b)(a - b)
Here a = 17/3 and b = 13/3
[tex]= (\dfrac{17}{3}+\dfrac{13}{3})(\dfrac{17}{3}-\dfrac{13}{3})[/tex]
We can add & subtract as they have common denominators.
[tex]=\dfrac{30}{3}*\dfrac{14}{3}\\\\= 10*\dfrac{14}{3}\\\\\\=\dfrac{140}{3}\\\\\\= 46\dfrac{2}{3}[/tex]
