[tex]\frac{2}{9}+\frac{2}{6}=[/tex]
Answer (1)
Find a common denominator for 9 2 and 6 2 , which is 18. Convert the fractions: 9 2 = 18 4 and 6 2 = 18 6 .
Add the fractions: 18 4 + 18 6 = 18 10 . Simplify the result: 18 10 = 9 5 .
Add the integers: 6 + 3 = 9 .
The final answers are 9 5 and 9 .
Explanation
Problem Analysis We have two separate math problems to solve:
Adding two fractions: 9 2 + 6 2
Adding two integers: 6 + 3
Let's solve them one by one!
Adding Fractions To add the fractions 9 2 and 6 2 , we need to find a common denominator. The least common multiple (LCM) of 9 and 6 is 18. So, we will convert both fractions to have a denominator of 18.
9 2 = 9 × 2 2 × 2 = 18 4
6 2 = 6 × 3 2 × 3 = 18 6
Now we can add the fractions:
18 4 + 18 6 = 18 4 + 6 = 18 10
We can simplify the fraction 18 10 by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
18 10 = 18 ÷ 2 10 ÷ 2 = 9 5
Adding Integers Now, let's add the two integers:
6 + 3 = 9
Final Answer So, we have:
9 2 + 6 2 = 9 5
6 + 3 = 9
Therefore, the answers are 9 5 and 9 .
Examples
Fractions and integer additions are fundamental arithmetic operations that we use every day. For example, if you are baking a cake and the recipe calls for 9 2 cup of flour and 6 2 cup of sugar, you need to add these fractions to know the total amount of dry ingredients. Similarly, if you have 6 apples and you buy 3 more, you need to add these integers to find the total number of apples you have. These basic math skills are essential for everyday tasks.
