Question
How is adding and subtracting mixed numbers similar to adding and subtracting fractions? How is adding and subtracting mixed numbers different than adding and subtracting fractions? Give examples to explain your answer. make it look like a 4th grader
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Answer
you have to make the hole ting 4 sentenis
Answered by
GPT-4o mini
Adding and subtracting mixed numbers is similar to adding and subtracting fractions in a few ways, but there are also some differences. Let’s break it down!
### Similarities:
1. **Common Denominator**: Just like with fractions, when you add or subtract mixed numbers, you need a common denominator if the fractions have different denominators.
**Example**:
If you are adding \( \frac{1}{4} \) and \( \frac{1}{2} \), you would need to find a common denominator (which is 4).
\( \frac{1}{2} = \frac{2}{4} \)
So, \( \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \).
In mixed numbers:
\( 2 \frac{1}{4} + 3 \frac{1}{2} \) becomes \( 2 \frac{1}{4} + 3 \frac{2}{4} = 2 \frac{3}{4} \).
2. **Adding or Subtracting**: In both cases, whether you're working with regular fractions or mixed numbers, you add or subtract the fractions in the same way.
### Differences:
1. **Whole Numbers**: Mixed numbers have a whole number part and a fraction part, while regular fractions do not.
**Example**:
For \( 2 \frac{1}{3} + 1 \frac{2}{3} \), you would first add the whole numbers:
\( 2 + 1 = 3 \).
Then, you add the fractions:
\( \frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 \).
Now, you put that together:
\( 3 + 1 = 4 \).
So, \( 2 \frac{1}{3} + 1 \frac{2}{3} = 4 \).
2. **Converting**: Sometimes, when adding or subtracting mixed numbers, you might need to convert them to improper fractions first.
**Example**:
If you wanted to add \( 3 \frac{1}{2} + 2 \frac{2}{5} \), you would first convert them to improper fractions:
\( 3 \frac{1}{2} = \frac{7}{2} \) and \( 2 \frac{2}{5} = \frac{12}{5} \).
Now you need a common denominator (which is 10):
\( \frac{7}{2} = \frac{35}{10} \) and \( \frac{12}{5} = \frac{24}{10} \).
Add them:
\( \frac{35}{10} + \frac{24}{10} = \frac{59}{10} \).
To change it back to a mixed number, you would divide 59 by 10. That’s 5 with a remainder of 9, so it becomes \( 5 \frac{9}{10} \).
### Summary:
So, adding and subtracting mixed numbers is similar to adding and subtracting fractions because you deal with fractions and need common denominators. The difference is that mixed numbers have a whole number part, and sometimes you need to convert to improper fractions.
I hope this helps you understand how to work with mixed numbers and fractions!
### Similarities:
1. **Common Denominator**: Just like with fractions, when you add or subtract mixed numbers, you need a common denominator if the fractions have different denominators.
**Example**:
If you are adding \( \frac{1}{4} \) and \( \frac{1}{2} \), you would need to find a common denominator (which is 4).
\( \frac{1}{2} = \frac{2}{4} \)
So, \( \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \).
In mixed numbers:
\( 2 \frac{1}{4} + 3 \frac{1}{2} \) becomes \( 2 \frac{1}{4} + 3 \frac{2}{4} = 2 \frac{3}{4} \).
2. **Adding or Subtracting**: In both cases, whether you're working with regular fractions or mixed numbers, you add or subtract the fractions in the same way.
### Differences:
1. **Whole Numbers**: Mixed numbers have a whole number part and a fraction part, while regular fractions do not.
**Example**:
For \( 2 \frac{1}{3} + 1 \frac{2}{3} \), you would first add the whole numbers:
\( 2 + 1 = 3 \).
Then, you add the fractions:
\( \frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 \).
Now, you put that together:
\( 3 + 1 = 4 \).
So, \( 2 \frac{1}{3} + 1 \frac{2}{3} = 4 \).
2. **Converting**: Sometimes, when adding or subtracting mixed numbers, you might need to convert them to improper fractions first.
**Example**:
If you wanted to add \( 3 \frac{1}{2} + 2 \frac{2}{5} \), you would first convert them to improper fractions:
\( 3 \frac{1}{2} = \frac{7}{2} \) and \( 2 \frac{2}{5} = \frac{12}{5} \).
Now you need a common denominator (which is 10):
\( \frac{7}{2} = \frac{35}{10} \) and \( \frac{12}{5} = \frac{24}{10} \).
Add them:
\( \frac{35}{10} + \frac{24}{10} = \frac{59}{10} \).
To change it back to a mixed number, you would divide 59 by 10. That’s 5 with a remainder of 9, so it becomes \( 5 \frac{9}{10} \).
### Summary:
So, adding and subtracting mixed numbers is similar to adding and subtracting fractions because you deal with fractions and need common denominators. The difference is that mixed numbers have a whole number part, and sometimes you need to convert to improper fractions.
I hope this helps you understand how to work with mixed numbers and fractions!
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