9/10 +2/3= need to show all work to lowest terms

9/10 +2/3

We must change these to equivalent fractions with the same denominator.

9/10 = 27/30
2/3 = 20/30

27/30 + 20/30 = 47/30 = 1 17/30

thank you!

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To add the fractions 9/10 and 2/3 and express the result in lowest terms, you need to find a common denominator for the two fractions.

Step 1: Finding a Common Denominator
The common denominator is the least common multiple of the denominators, which in this case is 30. To get to this, you can list the multiples of 10 and 3:
Multiples of 10: 10, 20, 30, 40, 50, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

From this list, we can see that the smallest multiple common to both 10 and 3 is 30.

Step 2: Converting the Fractions
Now that we have a common denominator of 30, we need to convert both fractions to have a denominator of 30.

For 9/10:
To achieve a denominator of 30, multiply both the numerator and denominator by 3:
(9/10) x (3/3) = 27/30

For 2/3:
To achieve a denominator of 30, multiply both the numerator and denominator by 10:
(2/3) x (10/10) = 20/30

Step 3: Adding the Fractions
Now that both fractions have a common denominator, we can add them:
27/30 + 20/30 = 47/30

Step 4: Simplifying the Result to Lowest Terms
To express the fraction 47/30 in lowest terms, we need to reduce it to its simplest form.

To do this, find the greatest common divisor (GCD) of the numerator and denominator, which is 1 in this case.

Divide both the numerator and denominator by the GCD:
47/1 ÷ 30/1 = 47/30

Therefore, the final result, in lowest terms, is 47/30.