Download 4-3 Adding and Subtracting Mixed numbers

4-3 Adding and Subtracting
Mixed numbers
What You’ll Learn
To
add mixed numbers
To subtract mixed numbers
Example 1: Adding Mixed Numbers
Solve 3 1/5 + 6 4/9 = ?
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Step 1: Rewrite horizontal problems vertically. (This step is not necessary,
but many students find it easier to add fractions when the problems are
written vertically.)
Step 2: Separate the problem into addition of whole numbers and addition
of fractions.
Step 3: Find a common denominator (a common multiple of the
denominators of two or more fractions) for the fractions. The common
denominator is 45 (because both 5 and 9 will divide into 45). Multiply 1/5 by
9/9. Multiply 4/9 by 5/5.
Step 4: Add the whole numbers (3 + 6 = 9). Add the numerators (9 + 20 =
29). The denominator remains the same (45).
Step 5: Combine the whole number and fraction to produce the answer.
Example 2: Subtracting Mixed Numbers
Solve. 7 4/5 - 3 2/9 = ?
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Step 1: Write the problem vertically.
Step 2: Separate the problem into subtraction of whole numbers and
subtraction of fractions.
Step 3: Find a common denominator (a common multiple of the
denominators of two or more fractions) for the fractions. For this
problem, the common denominator is 45. Multiply 4/5 by 9/9 to get
36/45. Multiply 2/9 by 5/5 to get 10/45.
Step 4: Subtract the whole numbers (7 - 3 = 4). Subtract the
numerators (36 - 10 = 26). The denominator remains the same (45).
Example 3 : Subtracting Mixed Numbers
Solve. 5 2/3 - 2 3/4
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Step 1: Write the problem vertically.
Step 2: Separate the problem into subtraction of whole
numbers and subtraction of fractions.
Step 3: Find a common denominator for the fractions.
For this problem, the lowest common denominator is 12.
Multiply 2/3 by 4/4 to get 8/12. Multiply 3/4 by 3/3 to get
9/12.
Step 4: Rewrite the problem with the fractions having
common denominators.
Step 5: Since the top fraction (8/12) is smaller than the
bottom fraction (9/12), trade one from the 5 and add
12/12 to the 8/12 to get 20/12.
Step 6: Subtract the whole numbers (4 - 2 = 2). Subtract
the numerators of the fractions (20 - 9 = 11). The
denominator (12) remains the same.
Example 3 : Subtracting Mixed Numbers
Solve. 5 2/3 - 2 3/4
Let’s Try a Few Problems
1¾+4¾=
 2 ¼ + 1 2/3 =
 3 1/6 + 8 7/8 =
5½-3¾=
 4 1/3 – 2 5/8 =
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