Subtracting Mixed Numbers with Unlike Denominators
In this article, we will learn how to subtract mixed numbers with unlike denominators, specifically the problem 5 1/2 - 3 7/8.
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 1/2
The mixed number 5 1/2 can be converted to an improper fraction by multiplying the whole number part (5) by the denominator (2) and then adding the numerator (1).
5 × 2 = 10 10 + 1 = 11
So, 5 1/2 is equal to 11/2.
3 7/8
The mixed number 3 7/8 can be converted to an improper fraction by multiplying the whole number part (3) by the denominator (8) and then adding the numerator (7).
3 × 8 = 24 24 + 7 = 31
So, 3 7/8 is equal to 31/8.
Step 2: Find the Least Common Multiple (LCM)
To subtract the two improper fractions, we need to find the least common multiple (LCM) of their denominators, which are 2 and 8.
The multiples of 2 are: 2, 4, 6, 8, 10, 12, ... The multiples of 8 are: 8, 16, 24, 32, 40, ...
The least common multiple of 2 and 8 is 16.
Step 3: Convert Improper Fractions to Equivalent Fractions
Now, we need to convert both improper fractions to equivalent fractions with the LCM as the denominator.
11/2
To convert 11/2 to an equivalent fraction with a denominator of 16, we need to multiply both the numerator and denominator by 8.
11 × 8 = 88 2 × 8 = 16
So, 11/2 is equal to 88/16.
31/8
To convert 31/8 to an equivalent fraction with a denominator of 16, we need to multiply both the numerator and denominator by 2.
31 × 2 = 62 8 × 2 = 16
So, 31/8 is equal to 62/16.
Step 4: Subtract the Equivalent Fractions
Now that we have equivalent fractions with the same denominator, we can subtract them.
88/16 - 62/16
Subtract the numerators (88 - 62 = 26) and keep the same denominator (16).
26/16
Step 5: Simplify the Result
Finally, we can simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 26 and 16 is 2.
26 ÷ 2 = 13 16 ÷ 2 = 8
So, 26/16 is equal to 13/8, which can be converted back to a mixed number: 1 5/8.
Conclusion
Therefore, 5 1/2 - 3 7/8 is equal to 1 5/8.
