Subtract And Answer As A Mixed Number In Simplest Form:$\[ 2 \frac{9}{10} - \frac{2}{5} \\]Enter The Whole Number.
Introduction
Mixed numbers are a combination of a whole number and a fraction. They are commonly used in mathematics to represent quantities that have both a whole and a part. In this article, we will focus on subtracting mixed numbers and provide a step-by-step guide on how to do it.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It is written in the form of:
a b/c
Where 'a' is the whole number, 'b' is the numerator, and 'c' is the denominator.
Example of a Mixed Number
Let's consider an example of a mixed number:
2 9/10
In this example, the whole number is 2, and the fraction is 9/10.
Subtracting Mixed Numbers
To subtract a mixed number from another mixed number, we need to follow these steps:
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Convert the mixed numbers to improper fractions: To subtract mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.
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Find a common denominator: Once we have converted the mixed numbers to improper fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.
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Subtract the numerators: Once we have found the common denominator, we can subtract the numerators. The numerator is the top number in the fraction.
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Simplify the result: After subtracting the numerators, we need to simplify the result. This involves dividing the numerator by the denominator and writing the result as a mixed number.
Step-by-Step Example
Let's consider an example of subtracting mixed numbers:
2 9/10 - 2/5
Step 1: Convert the mixed numbers to improper fractions
To convert the mixed number 2 9/10 to an improper fraction, we need to multiply the whole number by the denominator and add the numerator:
2 x 10 = 20 20 + 9 = 29
So, the improper fraction is 29/10.
To convert the mixed number 2/5 to an improper fraction, we don't need to do anything because it is already an improper fraction.
Step 2: Find a common denominator
The common denominator is the least common multiple (LCM) of the two denominators. In this case, the LCM of 10 and 5 is 10.
Step 3: Subtract the numerators
Now that we have found the common denominator, we can subtract the numerators:
29/10 - 2/10 = 27/10
Step 4: Simplify the result
To simplify the result, we need to divide the numerator by the denominator and write the result as a mixed number:
27 ÷ 10 = 2 with a remainder of 7
So, the result is 2 7/10.
Conclusion
Subtracting mixed numbers can be a bit tricky, but with these steps, you should be able to do it easily. Remember to convert the mixed numbers to improper fractions, find a common denominator, subtract the numerators, and simplify the result. With practice, you will become more comfortable with subtracting mixed numbers.
Final Answer
Q: What is the difference between a mixed number and an improper fraction?
A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than the denominator. For example, 2 3/4 is a mixed number, while 11/4 is an improper fraction.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. For example, to convert 2 3/4 to an improper fraction, you would multiply 2 by 4 and add 3, which gives you 11/4.
Q: What is the common denominator?
A: The common denominator is the least common multiple (LCM) of the two denominators. For example, if you are subtracting 1/2 and 1/4, the common denominator would be 4.
Q: How do I find the common denominator?
A: To find the common denominator, you need to list the multiples of each denominator and find the smallest multiple that they both have in common. For example, the multiples of 2 are 2, 4, 6, 8, 10, etc. The multiples of 4 are 4, 8, 12, 16, etc. The smallest multiple that they both have in common is 4.
Q: What is the difference between subtracting mixed numbers and subtracting fractions?
A: Subtracting mixed numbers is similar to subtracting fractions, but you need to convert the mixed numbers to improper fractions first. Once you have converted the mixed numbers to improper fractions, you can subtract them just like you would subtract fractions.
Q: Can I subtract a mixed number from a whole number?
A: Yes, you can subtract a mixed number from a whole number. To do this, you need to convert the mixed number to an improper fraction and then subtract it from the whole number. For example, if you want to subtract 3 1/2 from 5, you would convert 3 1/2 to an improper fraction (7/2) and then subtract it from 5.
Q: What if the denominators are different?
A: If the denominators are different, you need to find a common denominator before you can subtract the fractions. Once you have found the common denominator, you can subtract the fractions just like you would subtract fractions with the same denominator.
Q: Can I use a calculator to subtract mixed numbers?
A: Yes, you can use a calculator to subtract mixed numbers. However, it's always a good idea to check your work by converting the mixed numbers to improper fractions and then subtracting them.
Q: What if I get a negative result when subtracting mixed numbers?
A: If you get a negative result when subtracting mixed numbers, it means that the second mixed number is larger than the first mixed number. To write the result as a mixed number, you need to convert the improper fraction to a mixed number by dividing the numerator by the denominator and writing the result as a mixed number.
Q: Can I add and subtract mixed numbers with different signs?
A: Yes, you can add and subtract mixed numbers with different signs. To do this, you need to follow the rules of addition and subtraction, just like you would with whole numbers. For example, if you want to subtract 3 1/2 from -2 3/4, you would convert both mixed numbers to improper fractions, find a common denominator, and then subtract the numerators.
Q: What if I'm not sure how to subtract mixed numbers?
A: If you're not sure how to subtract mixed numbers, don't worry! You can always ask a teacher or tutor for help. You can also practice subtracting mixed numbers by working through examples and exercises. With practice, you'll become more comfortable with subtracting mixed numbers.