A mixed number is an integer that coexists with a fraction, such as 5, and can be difficult to add.
Step
Method 1 of 2: Adding Integers and Fractions Separately
Step 1. Add the integers together
The integers are 1 and 2, so 1 + 2 = 3.
Step 2. Find the smallest denominator (BPT) of the two fractions
BPT is the smallest number that is divisible by both numbers. Since the denominators of the fraction are 2 and 4, the BPT is 4, because 4 is the smallest number that is divisible by 2 and 4.
Step 3. Convert the fraction to have BPT as the denominator
Before you can add fractions together, they must have 4 as the denominator, so you have to make the fractions still have the same value even though they have a new base. Here's how to do it:
- Since the denominator of the fraction 1/2 must be multiplied by 2 to get 4 as the new base, you must also multiply the numerator of 1 by 2. 1 * 2 = 2, so the new fraction is 2/4. The fraction 2/4 = 1/2, but has been translated into larger ratios to get a larger base. This means that the numbers are fractions that have the same value. Both have different bases, but the value remains the same.
- Since the fraction 3/4 already has a base of 4, you don't need to change it.
Step 4. Add up the fractions
Once you have a denominator, you can add the fractions by adding up the numerators.
2/4 + 3/4 = 5/4
Step 5. Convert improper fractions to mixed numbers
An improper fraction is a fraction whose numerator is equal to or greater than the denominator. You must convert improper fractions to mixed numbers before you can add them to the sum of whole numbers. Since the original problem used mixed numbers, your answer must be mixed numbers as well. Here's how to do it:
- First, divide the numerator by the denominator. Do long divisions to divide 5 by 4. The number 4 must be multiplied by 1 to get closer to 5. This means that the quotient is 1. The remainder, or the remaining numbers, is 1.
- Turn the quotient into a new integer. Take the remaining number and place it over the original denominator to complete the conversion of the improper fraction to a mixed number. The quotient is 1, the remainder is 1, and the original denominator is 4, so the final answer is 1 1/4.
Step 6. Add the sum of the integers to the sum of the fractions
To get your final answer, you must add up the two sums you find. 1 + 2 = 3 and 1/2 + 3/4 = 1 1/4, so 3 + 1 1/4 = 4 1/4.
Method 2 of 2: Converting Mixed Fractions To Improper Fractions and Adding Them
Step 1. Convert mixed fractions to improper fractions
You can do this by multiplying the denominator by the whole number of a mixed number, then adding it by the numerator of the fraction in the mixed number. Your answer will be the new numerator while the denominator remains the same.
-
To convert 1 1/2 to a mixed number, multiply the integer 1 by the denominator 2, then add it by the numerator. Put your new answer on top of the original base.
1 * 2 = 2, and 2 + 1 = 3. Put 3 above the original denominator and you get 3/2
-
To convert 2 3/4 to a mixed number, multiply the integer 2 by the denominator 4. 2 * 4 = 8.
Next, add this number to the original numerator and place it above the original denominator. 8 + 3 = 11. Put 11 on top of 4 to get 11/4
Step 2. Find the least common multiple (LCM) of the two divisors
LCM is the smallest number that can be divisible by both numbers. If the denominators are the same, skip this step.
If one of the denominators is divisible by the other, the larger divisor is the LCM. LCM of 2 and 4 is 4 because 4 is divisible by 2
Step 3. Make the denominators the same
You can do this by looking for equal fractions. Multiply the denominator by a number to get the LCM. Multiply the numerator by the same number. Do this for both shards.
- Since the denominator of 3/2 must be multiplied by 2 to get a new denominator of 4, you must multiply the numerator by 2 to find a fraction equal to 3/2. 3 * 2 = 6, so the new fraction is 6/4.
- Since 11/4 already has a denominator of 4, you're in luck. You don't need to change it.
Step 4. Add the two fractions together
Now that the denominators are the same, just add up the numerators to get your answer while keeping the base the same.
6/4 + 11/4 = 17/4
Step 5. Convert the improper fraction back into a mixed number
Since the original problem is in mixed number form, you can convert it back to mixed number. Here's how to do it:
- First, divide the numerator by the denominator. Divide 17 by 4. In order for 4 to be 17 it must be multiplied four times, so the quotient is 4. The remainder, or the remaining number, is 1.
- Turn the quotient into a new integer. Take the remaining numbers and place them over the original denominators to complete the conversion of improper fractions to mixed numbers. The quotient is 4, the remaining number is 1, and the original denominator is 4, so the final answer is 4 1/4.
