Adding Mixed Numbers: 1 1/2 + 1 6/7 as a Fraction
When working with mixed numbers, it's essential to understand how to add them correctly. In this article, we'll explore how to add 1 1/2 and 1 6/7 as a fraction.
Step 1: Convert Mixed Numbers to Improper Fractions
To add these mixed numbers, we need to convert them into improper fractions.
1 1/2 = ?
To convert 1 1/2 to an improper fraction, we multiply the whole number part (1) by the denominator (2) and then add the numerator (1).
1 × 2 + 1 = 3
So, 1 1/2 as an improper fraction is 3/2.
1 6/7 = ?
Similarly, to convert 1 6/7 to an improper fraction, we multiply the whole number part (1) by the denominator (7) and then add the numerator (6).
1 × 7 + 6 = 13
So, 1 6/7 as an improper fraction is 13/7.
Step 2: Add the Improper Fractions
Now that we have the improper fractions, we can add them.
3/2 + 13/7 = ?
To add these fractions, we need a common denominator. The least common multiple (LCM) of 2 and 7 is 14. So, we'll convert both fractions to have a denominator of 14.
3/2 = 21/14 13/7 = 26/14
Now, we can add the fractions:
21/14 + 26/14 = 47/14
Step 3: Simplify the Fraction (Optional)
If we want to simplify the resulting fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 47 and 14 is 1, so the fraction is already in its simplest form.
The Result
Therefore, 1 1/2 + 1 6/7 as a fraction is 47/14.
