Find the sum. Write your answer in simplest form.
3/7 + 2/3
To add these fractions, we need a common denominator. The least common multiple of 7 and 3 is 21, so we can write:
3/7 = 9/21 (by multiplying numerator and denominator by 3)
2/3 = 14/21 (by multiplying numerator and denominator by 7)
Now we have:
9/21 + 14/21 = 23/21
To simplify, we can write this as a mixed number:
23/21 = 1 2/21
So the sum of 3/7 and 2/3 is 1 2/21.
To find the sum of 3/7 + 2/3, we need to find a common denominator for both fractions.
The least common multiple (LCM) of 7 and 3 is 21. Therefore, we will rewrite the fractions with the common denominator of 21.
For the first fraction: (3/7) x (3/3) = 9/21
For the second fraction: (2/3) x (7/7) = 14/21
Now that both fractions have the same denominator, we can add them together:
9/21 + 14/21 = 23/21
However, the sum is not in its simplest form because the numerator is greater than the denominator. To simplify, we divide the numerator by the denominator, and express the remaining numerator and denominator as a mixed fraction or an improper fraction.
In this case, 21 evenly divides into 23 once with a remainder of 2. So the simplified form is:
1 (2/21)
Therefore, the sum of 3/7 + 2/3 in simplest form is 1 2/21.
To find the sum of these fractions, we need to have a common denominator. The least common multiple (LCM) of 7 and 3 is 21.
To convert the fractions to have a denominator of 21, we can multiply the first fraction by 3/3 and the second fraction by 7/7. This gives us:
(3/7) * (3/3) + (2/3) * (7/7)
Simplifying this expression, we get:
9/21 + 14/21
Now, we can add the fractions together:
9/21 + 14/21 = 23/21
So, the sum of 3/7 and 2/3 is 23/21.