Question

PLSSS HELP IF YOU TURLY KNOW THISS

Answer 1

Part I: Determining the common denominator of the terms

Given expression:

`(1)/(3) + (2)/(12)`

To simplify the expression, we need to determine the common denominator of both fractions (1/3 and 2/12). To determine the common denominator of both fractions, we need to determine the LCM of the denominators (12 and 3). Simply write the multiples of (12 and 3) and determine the least common multiple (LCM).

• ⇒ Multiples of three: 3, 6, 9, 12, 15, 18...
• ⇒ Multiples of twelve: 12, 24, 36, 48, 60...

Since the LCM is 12, our common denominator is 12.

Part II: Multiplying both denominators by a number which is equivalent to 12

Now, multiply both denominators by a number such that the denominators are equivalent to 12. Keep in mind that the number you multiply the denominator should also be multiplied to the numerator.

`\implies (x)/(3x) + (2y)/(12y) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \huge\text{[}3x = 12; 12y = 12\huge\text{]}`

`\implies (4)/(3(4)) + (2(1))/(12(1)) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \huge\text{[}x = (12)/(3) = 4; y = (12)/(12) = 1 \huge\text{]}`

`\implies (4)/(12) + (2)/(12)`

Part III: Adding the fractions

Since the denominators are the same, we can now add the fractions;

`\implies (6)/(12)`

Part IV: Simplifying the fraction obtained from the above

Since 6 is divisible by 12, we can further simplify the fraction.

`\implies (6 * 1)/(6 * 2)`

`\implies \boxed{(1)/(2)}`

Answer 2

`(1)/(2)`

Find the least common factors of both numbers.

`1/3~has~4\\2/12~has~1`

Multiply the numerator and denominator.

`(1 * 4)/(3 * 4) = (4)/(12) \\\\(2 * 1)/(12 * 1) = (2)/(12)`

Add both numbers together. That does not mean you have to add the denominators. When the denominators are the same, keep them the same.

`(4)/(12) +(2)/(12) = (6)/(12)`

Simplify.

`(6)/(12) -- > (1)/(2)` because they are both halves.