Education.com
Try
Brainzy
Try
Plus

Operations with Mixed Numbers Study Guide (page 3)

By
Updated on Aug 24, 2011

Example

Work with the whole numbers first: 5 – 1 = 4. Now look at the fractions. We can't subtract from , because is greater than . We need to borrow 1 from the whole number part of our answer: 4 – 1 = 3. The whole number part of our answer is now 3. What do we do with the 1 we just borrowed? We write it as and add it to the fraction that we already have, . Now we can subtract the fractions: . The fractional part of our answer is . Therefore, .

Instead of subtracting from , we subtracted from , because and are equal. When we borrow 1 from the whole number part of the mixed number, we write that 1 as a number over the denominator of the mixed number. Because the denominator of the mixed number was 3, we wrote the borrowed 1 as .

Let's look at another example just to be sure we've got it down!

Example

Again, work with the whole numbers first: 15 – 12 = 3. Now look at the fractions. The least common denominator of 7 and 8 is 56; and . We can't subtract from , because is greater than . We need to borrow 1 from the whole number part of our answer: 3 – 1 = 2. We write the borrowed 1 as and add it to the fraction that we already have: . Now we can subtract the fractions: . The fractional part of our answer is . Therefore, .

Caution!

When you borrow, be sure to subtract 1 from the whole number part of your answer, and be sure that you add that borrowed 1 to the correct fraction. In a subtraction sentence, the number that you are subtracting is called the subtrahend, and the number from which you are subtracting is called the minuend. In the subtraction sentence 5 – 4 = 1, 5 is the minuend and 4 is the subtrahend. When you borrow, be sure to add 1 to the fraction part of the minuend. In the last example we saw, was the minuend. After borrowing 1 from the whole number part of our answer, we added 1 in the form of to , the fractional part of the minuend.

Some people prefer to convert both mixed numbers to improper fractions before subtracting. If you do this, you won't have to worry about borrowing at all. Converting mixed numbers to improper fractions is good practice, and as we'll soon see, it's the only way to multiply and divide mixed numbers. Let's look at a subtraction example first.

Example

First, convert each number to an improper fraction. 3 × 2 = 6, 6 + 1 = 7, so . 2 × 5 = 10, 10 + 4 = 14, so . The least common denominator of 2 and 5 is 10; and . Now we can subtract: .

Inside Track

If you can see that a subtraction problem involving mixed numbers will NOT require borrowing, the easiest method is to subtract whole numbers and subtract fractions. If you can see that the problem will require borrowing, the easiest method is to convert each mixed number to an improper fraction before subtracting. However, either method will work in either case. If you find one method easier than the other, use it all the time!

Multiplying Mixed Numbers

There is only one method for multiplying mixed numbers: Convert each mixed number to an improper fraction, and then multiply the numerators and multiply the denominators. No common denominators needed—once we have two improper fractions, we're ready to go!

Example

Convert each number to an improper fraction. 2 × 6 = 12, 12 + 1 = 13, so ; 6 × 3 = 18, 18 + 2 = 20, so . Now that we have two improper fractions, multiply the numerators and multiply the denominators: 13 × 20 = 260 and 6 × 3 = 18, so . The greatest common factor of 260 and 18 is 2, so reduces to . 130 divided by 9 is 14 with 4 left over, so .

Inside Track

There are three places in which you can simplify a multiplication problem involving mixed numbers. After converting the mixed numbers to fractions, you can divide a numerator and denominator by the same number. In the last example, we could have simplified by dividing the 6 in the first fraction and the 20 in the second fraction by 2. Or, we could have reduced to before converting to a mixed number (which is what we did). Finally, we can reduce the fraction part of a mixed number after converting the improper fraction into a mixed number. You can simplify at any—or all three—places. Often, if you reduce the improper fractions first, you'll have an easier time multiplying—and you may not have to simplify at all later.

Let's look at one more example.

View Full Article
Add your own comment