Subtracting Mixed Numbers: 4 1/5 - 1 1/4 Explained!
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To subtract mixed numbers effectively, it's essential to grasp the concept of mixed numbers themselves. A mixed number combines a whole number and a fraction, making them particularly useful in everyday calculations, such as cooking or carpentry. In this article, we'll break down the process of subtracting mixed numbers step by step, using the example of (4 \frac{1}{5} - 1 \frac{1}{4}). Let's dive into it!
Understanding Mixed Numbers
What is a Mixed Number?
A mixed number consists of a whole part and a fractional part. For example, in (4 \frac{1}{5}), the whole number is 4, and the fraction is (\frac{1}{5}). This representation makes it easier to handle quantities that are greater than 1 while still accounting for fractional amounts.
Converting Mixed Numbers to Improper Fractions
Before performing any operations with mixed numbers, it often helps to convert them into improper fractions. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). The formula to convert a mixed number to an improper fraction is:
[ \text{Improper Fraction} = ( \text{Whole Number} \times \text{Denominator} ) + \text{Numerator} \div \text{Denominator} ]
Example: Converting (4 \frac{1}{5}) and (1 \frac{1}{4})
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For (4 \frac{1}{5}):
- Whole Number: 4
- Fraction: (\frac{1}{5})
- Conversion: [ (4 \times 5) + 1 = 20 + 1 = 21 ]
- So, (4 \frac{1}{5} = \frac{21}{5})
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For (1 \frac{1}{4}):
- Whole Number: 1
- Fraction: (\frac{1}{4})
- Conversion: [ (1 \times 4) + 1 = 4 + 1 = 5 ]
- So, (1 \frac{1}{4} = \frac{5}{4})
Table of Mixed Numbers to Improper Fractions
Here’s a handy table for converting mixed numbers to improper fractions:
<table> <tr> <th>Mixed Number</th> <th>Improper Fraction</th> </tr> <tr> <td>2 1/3</td> <td>7/3</td> </tr> <tr> <td>3 2/5</td> <td>17/5</td> </tr> <tr> <td>4 1/5</td> <td>21/5</td> </tr> <tr> <td>1 1/4</td> <td>5/4</td> </tr> </table>
Subtracting Improper Fractions
Now that we have converted the mixed numbers to improper fractions, we can perform the subtraction:
[ \frac{21}{5} - \frac{5}{4} ]
Finding a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 4 is 20. Therefore, we must convert both fractions to have a denominator of 20.
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Convert (\frac{21}{5}): [ \frac{21 \times 4}{5 \times 4} = \frac{84}{20} ]
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Convert (\frac{5}{4}): [ \frac{5 \times 5}{4 \times 5} = \frac{25}{20} ]
Performing the Subtraction
Now, we can subtract the two fractions:
[ \frac{84}{20} - \frac{25}{20} = \frac{84 - 25}{20} = \frac{59}{20} ]
Converting Back to a Mixed Number
The result, (\frac{59}{20}), is an improper fraction, so we will convert it back to a mixed number:
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Divide the numerator by the denominator: [ 59 \div 20 = 2 \quad \text{(whole number)} ]
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Find the remainder: [ 59 - (20 \times 2) = 19 \quad \text{(remainder)} ]
Therefore, we can express (\frac{59}{20}) as:
[ 2 \frac{19}{20} ]
Summary
To summarize the process of subtracting mixed numbers:
- Convert mixed numbers to improper fractions.
- Find a common denominator.
- Subtract the fractions.
- Convert the result back to a mixed number if necessary.
So, the final answer to (4 \frac{1}{5} - 1 \frac{1}{4}) is:
(2 \frac{19}{20}) 🎉
Understanding these concepts of mixed numbers and fractions not only simplifies arithmetic but also helps in practical situations like cooking, budgeting, and measuring. Keep practicing, and soon enough, subtracting mixed numbers will become second nature!