Sarah has 1 2/9 of flour and 2 1/3 bags of rice in her shop. How many bags of flour and rice does Sarah have in all?
1 2/9 + 2 3/9 = ____
To find out how many bags of flour and rice Sarah has in total, we need to add the fractions together and then simplify the result.
Let's start by finding the sum of the fractions for the flour:
1 + 2/9
To add the whole number 1 and the fraction 2/9, we need to find a common denominator, which in this case is 9.
1 is the same as 9/9, so we can rewrite the sum as:
9/9 + 2/9 = 11/9
Now, let's find the sum of the fractions for the rice:
2 + 2/3
To add the whole number 2 and the fraction 2/3, we need to find a common denominator, which in this case is 3.
2 is the same as 6/3, so we can rewrite the sum as:
6/3 + 2/3 = 8/3
Now, to find the total number of bags of flour and rice that Sarah has, we need to add the two fractions together:
11/9 + 8/3
To add these fractions, we need to find a common denominator, which in this case is 9.
Multiplying the numerator and denominator of the second fraction by 3 to make the denominators equal:
11/9 + (8/3) * (3/3) = 11/9 + 24/9 = 35/9
So, Sarah has a total of 35/9 bags of flour and rice in her shop. This fraction cannot be simplified further, so the answer is 35/9 bags.
To find out how many bags of flour and rice Sarah has in total, we first need to add the fraction of flour and the number of bags of rice.
Given that Sarah has 1 2/9 of flour, we need to convert the mixed number into an improper fraction. To do this, multiply the whole number (1) by the denominator (9), and then add the numerator (2). This gives us (1 * 9) + 2 = 11. The numerator of the fraction portion remains the same, so we have 11/9.
Now, we can add this fraction to the fraction representing the bags of rice. We have 2 1/3 of rice, which can be written as an improper fraction as (2 * 3) + 1 = 7/3.
So, we add 11/9 + 7/3. To do this, we need to find a common denominator. The least common multiple of 9 and 3 is 9. We can convert both fractions so that they have a denominator of 9.
For the first fraction, multiply both the numerator and denominator by 1 equating to the common denominator (9/9). This gives us 11/9 * 1/1 = 11/9.
For the second fraction, multiply both the numerator and denominator by 3/3, which is equivalent to 1, equating to the common denominator (3/3). This gives us 7/3 * 3/3 = 21/9.
Now that both fractions have a denominator of 9, we can add them together: 11/9 + 21/9 = (11 + 21)/9 = 32/9.
So, Sarah has a total of 32/9 bags of flour and rice in her shop.