Have you ever found yourself wondering what the sum of 2/3 + 2/3 cups equals? Well, you’re not alone! Many people are perplexed by this seemingly simple arithmetic problem. In order to find the answer, we need to add the two fractions together.
When we have two fractions with the same denominator (in this case, cups), like 2/3 and 2/3, we can simply add their numerators (the numbers on top) together while keeping the denominator unchanged. So, 2/3 + 2/3 equals 4/3 cups.
Now you might be thinking, “What does that mean in terms of measurements?” Well, since a whole cup is divided into three equal parts (denominator), four-thirds of a cup is equivalent to one and one-third cups or 1 1/3 cups.
So, there you have it! The sum of 2/3 + 2/3 cups is equal to 4/3 cups or 1 1/3 cups. It’s always fascinating how fractions can come into play when dealing with measurements.
What is 2/3 + 2/3 cups equal
Adding Fractions with Like Denominators
When it comes to adding fractions, like denominators make the process much simpler. In this case, we have two fractions with the same denominator of cups. To find what 2/3 + 2/3 cups equals, we can add the numerators and keep the denominator the same. So, in this case:
2/3 + 2/3 = (2 + 2) / 3
= 4 / 3
Finding a Common Denominator
However, what if we encounter fractions with different denominators? We need to find a common denominator before performing addition. Let’s say we have to add something like 1/4 cup and 1/8 cup. The first step is finding a common denominator for these fractions.
To do this, we look for a number that both denominators (4 and 8) can evenly divide into. In this case, that number is none other than their least common multiple (LCM), which happens to be 8.
Now that we have our common denominator of 8, let’s rewrite our original fractions using this new denominator:
1/4 = (1 * 2) / (4 * 2) = **2/8**
1/8 = (1 * 1) / (8 * 1) = **1/8**
Converting Fractions to Have a Common Denominator
Another approach to finding a common denominator is by converting each fraction so that they share the same base.
Let’s consider adding two fractions: 5/6 cup and 7/12 cup.
Firstly, note that both denominators are multiples of each other: 6 and 12. To find their LCM, we can simply use the larger denominator, which is 12.
Now let’s convert each fraction to have a common denominator of 12:
5/6 = (5 * 2) / (6 * 2) = **10/12**
7/12 = (7 * 1) / (12 * 1) = **7/12**
With both fractions having a denominator of 12, we can proceed to add them together:
10/12 + 7/12 = (10 + 7) / 12
= 17 / 12
Converting Mixed Numbers to Improper Fractions
When it comes to solving mathematical equations involving fractions, converting mixed numbers to improper fractions can be a helpful technique. In this section, I’ll explain how to convert mixed numbers to improper fractions and show you how it applies to the calculation of “what is 2/3 + 2/3 cups equal”.
To convert a mixed number to an improper fraction, follow these steps:
- Multiply the whole number by the denominator of the fraction.
- For example, if we have the mixed number 2 2/3, we multiply 2 (whole number) by 3 (denominator) which gives us 6.
- Add the result from step 1 to the numerator of the fraction.
- Continuing with our example, we add 6 (result from step 1) and 2 (numerator), resulting in a new numerator of 8.
- Keep the denominator unchanged.
- Our original denominator was already 3 in this case.
- Write down the new fraction using the updated numerator and denominator.
- The converted improper fraction for our example is now 8/3.
Now that we’ve converted our mixed numbers into improper fractions, let’s calculate “what is 2/3 + 2/3 cups equal”. Since both fractions have a common denominator of three, we can simply add their numerators together while keeping the denominator unchanged:
[
begin{tabular}{|c c|}
hline
& \
$frac{2}{3}$ + $frac{2}{3}$ & = \
& \
hline
& \
$frac{4}{3}$ & \
& \
hline
end{tabular}
]
Therefore, when adding two-thirds plus two-thirds cups together, the result is four-thirds.
Converting mixed numbers to improper fractions can be a useful technique in various mathematical calculations. By following these steps, you’ll be able to simplify equations and work with fractions more easily.
