Operations on Mixed Operations on Mixed NumbersNumbers

Section 4.7

2

Recall that aRecall that a mixed number mixed number is a sum of a is a sum of a whole number and a whole number and a properproper fraction. fraction.

19

53

4

5

34

53

4

5

00 11 22 554433

Martin-Gay, Prealgebra, 5ed

Multiplying or Dividing with Mixed Multiplying or Dividing with Mixed Numbers or Whole NumbersNumbers or Whole Numbers

To multiply or divide with mixed numbers or whole To multiply or divide with mixed numbers or whole numbers, first write each mixed number as an numbers, first write each mixed number as an improper fraction.improper fraction.

Multiply: Multiply: 3 215

14

3 215

14 16

594

4 45

94

365

7 15

Write the solutionas a mixed number

if possible.

Remove common factorsand multiply.

Change mixed numbersto improper fractions.

3Martin-Gay, Prealgebra, 5ed

We can add or subtract mixed We can add or subtract mixed numbers by first writing each mixed numbers by first writing each mixed number as an improper fraction. But number as an improper fraction. But it is often easier to add or subtract it is often easier to add or subtract the whole-number parts and add or the whole-number parts and add or subtract the proper-fraction parts subtract the proper-fraction parts vertically.vertically.

Adding or Subtracting Mixed NumbersAdding or Subtracting Mixed Numbers

4Martin-Gay, Prealgebra, 5ed

Add: 2 5514

67

The LCD of 14 and 7 is 14.

2 2

5 5

514

514

67

1214

71714

1714

1 314Since is , write the sum as

71714

7 1 314

8 314

Write equivalent fractions with the LCD of 14.

Notice that the fractional part is improper.

Add the fractions, then add the whole numbers.

Make sure the fractionalpart is always proper.

5Martin-Gay, Prealgebra, 5ed

When subtracting mixed numbers, When subtracting mixed numbers, borrowing may be needed.borrowing may be needed.

313

00 11 22 554433

313

2 113 2 1

13 2

33

13 2

43

Borrow 1 from 3. 6Martin-Gay, Prealgebra, 5ed

Subtract: 5 3314

67

The LCD of 14 and 7 is 14.

5 5

3 3

314

314

67

1214

Write equivalent fractions with the LCD of 14.

To subtract the fractions, we have to borrow.

Notice that the fractionalpart is proper.

4 1714

4 1714

Subtract the fractions, then subtract the whole numbers.

5 5 4

3 3 3

314

314

1714

67

1214

1214

1 514

5 4 1314

314

7