Simplifying the Subtraction of Mixed Numbers: 5 4/7 - 2 1/2 as a Fraction
When working with mixed numbers, subtraction can be a bit challenging. In this article, we will explore how to subtract 2 1/2 from 5 4/7 and express the result as a fraction.
Step 1: Convert Mixed Numbers to Improper Fractions
To subtract mixed numbers, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
- 5 4/7 = (5 × 7) + 4 / 7 = 39/7
- 2 1/2 = (2 × 2) + 1 / 2 = 5/2
Step 2: Find the Least Common Multiple (LCM) of the Denominators
To add or subtract fractions, we need to find the least common multiple (LCM) of the denominators. In this case, the LCM of 7 and 2 is 14.
Step 3: Convert Improper Fractions to Equivalent Fractions with the LCM
Now, we need to convert the improper fractions to equivalent fractions with the LCM as the denominator.
- 39/7 = (39 × 2) / (7 × 2) = 78/14
- 5/2 = (5 × 7) / (2 × 7) = 35/14
Step 4: Subtract the Fractions
Now that we have equivalent fractions with the same denominator, we can subtract them.
78/14 - 35/14 = 43/14
Result
Therefore, 5 4/7 - 2 1/2 as a fraction is equal to 43/14.
