Hint: Change the mixed numbers to improper fractions.
To do this, multiply the denominator times the whole number, and then add the numerator as shown below.
Write the 8 as the numerator and leave the 3 as the denominator to create an improper fraction.
Do the same for the second mixed number.
Multiply as usual.
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This section will cover the fundamentals and rules of adding, subtracting, multiplying, and dividing fractions.
Adding Fractions
Below is a quick review of the parts of a fraction:
Example 2: Fractions with answers that are improper, must be rewritten as a mixed number.
Example 1: When adding fractions with like denominators, simply add the numerators.
Example 3: Fractions with different denominators will require finding their least common denominator. In this case, their least common denominator is 12.
Hint: Divide the numerator by the denominator. Then place the remainder on top of the divisor to create a mixed number.
Hint: How many times will 3 go into 12? 4 Multiply 4 x 1. The answer is 4. The first numerator is 4.
Find the second numerator, using the same method.
Add both numerators together. Place that number over the denominator.
Example 4: Mixed numbers can be added together.
Step 1:
Step 2:
Step 1:
Step 2:
Step 1:
Step 2:
Step 3:
Step 2 requires finding a common denominator for both 3 and 5. Since 3 cannot go into 5, multiply the two numbers together. The common denominator is 15.
Step 3 requires changing an improper fraction to a mixed number, and then adding the whole numbers together as shown below.
Subtracting Fractions
Example 1: When subtracting fractions with like denominators, simply subtract the numerators.
Example 2: Fractions with different denominators will require finding a denominator that both fractions have in common. Then subtract the numerators.
Example 3: Subtract a mixed number from a fraction.
Since our answer is not in its lowest term, we will have to reduce. To do this, find the greatest common factor.
Hint: Since we know that our denominator in our mixed number is 5, we will turn our whole number 5 into a mixed number.
To do this, take 1 away from 5, and then turn
Now we're ready to subtract as usual.
Example 4: Subtract a larger numerator from a smaller numerator.
Hint: Since we can't take 4 from 2, we will borrow 1 from our whole number 6, which we will use to create a mixed number.
Add the mixed number to the original fraction, to make the numerator larger.
Subtact as usual.
Multiplying Fractions
Example 1: To multiply fractions, follow the steps below:
- Reduce to lowest terms if possible.
- Multiply the numerators.
- Multiply the denominators.
Step 1:
Step 2:
Step 3:
Step 3 shows how to reduce our answer to lowest terms.
To avoid reducing at the end, see if any reducing can be done in Step 1.
For example:
Hint: Since 2 can go into both 2 and 4, we can divide both numbers by 2.
Then multiply as usual.
Example 2: Multiply the following.
Example 3: Multiply two fractions and reduce diagonally both ways.
Note: Reducing a fraction to lowest terms when multiplying can only be done diagonally.
Example 4: Multiply multiple fractions
Note: Whichever way we reduce, the answer is the same.
Example 5: Multiply mixed numbers.
Step 1:
Step 2:
Dividing Fractions
Example 1: Divide fractions:
- Change the division sign to a mutliplication sign. (Step 2)
- Write the reciprocal of the second fraction. (Step 2)
- Reduce fractions to lowest terms. (Step 3)
- Multiply as usual. (Step 3)
Step 1:
Step 2:
Step 3:
Example 2: Divide mixed numbers:
- Change the mixed numbers to improper fractions. (Step 2)
- Write the reciprocal of the second fraction. (Step 3)
- Reduce fractions to lowest terms if possible.
- Multiply as usual. (Step 4)
Step 1:
Step 2:
Step 3:
Step 4:
Example 3: Divide a mixed number by a whole number:
- Change the mixed number to improper fractions. (Step 2)
- Change the whole number to an improper fraction. (Step 2)
- Write the reciprocal of the second fraction. (Step 3)
- Reduce fractions to lowest terms if possible.
- Multiply as usual. (Step 3)
Step 1:
Step 2:
Step 3:
1st mixed number
2nd mixed number
Math: Operations with Fractions - Tutorial
