Fraction Calculation: 1-3/4 + 9/16
In this article, we will explore the calculation of a mixed fraction addition problem: 1-3/4 + 9/16.
Step 1: Convert Mixed Fractions to Improper Fractions
To add these fractions, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.
1-3/4
To convert 1-3/4 to an improper fraction, we need to multiply the whole number part (1) by the denominator (4) and then add the numerator (3).
(1 × 4) + 3 = 7
So, the improper fraction equivalent of 1-3/4 is **7/4**.
**9/16**
The fraction 9/16 is already in its simplest form, so we can use it as is.
Step 2: Find the Least Common Multiple (LCM)
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 4 and 16.
The multiples of 4 are: 4, 8, 12, 16, 20, ...
The multiples of 16 are: 16, 32, 48, ...
The first number that appears in both lists is 16, so the LCM of 4 and 16 is 16.
Step 3: Convert Fractions to Have the LCM as the Denominator
7/4
To convert 7/4 to have a denominator of 16, we need to multiply the numerator and denominator by 4.
(7 × 4) / (4 × 4) = 28/16
**9/16**
The fraction 9/16 already has a denominator of 16, so we can use it as is.
Step 4: Add the Fractions
Now that we have both fractions with the same denominator, we can add them.
28/16 + 9/16 = (28 + 9)/16 = 37/16
Conclusion
The result of the addition problem 1-3/4 + 9/16 is 37/16.
