Example 1: Martha added four and one-fifth packages of soil to her garden on Monday and three and two-fifths packages of soil on Friday. How many packages of soil did she add in all?
Analysis: This problem is asking us to add mixed numbers.
The fractions have like denominators. We will add the whole numbers and add the fractions separately.
Solution:
In example 1, we arranged the work vertically to make it easier to add the mixed numbers.
To add mixed numbers, add the whole numbers and add the fractions separately: (whole + whole) + (fraction + fraction)
Let's look at some more examples.
Example 2:
Analysis: The fractions have like denominators. Add the whole numbers and add the fractions separately.
Solution:
In example 2, it was necessary to simplify the result.
Example 3:
Analysis: We are adding a whole number and a mixed number. Think of ten as "ten and zero-sixteenths."
Solution:
Example 4:
Analysis: The fractions have unlike denominators. We will write equivalent fractions using the LCD, 8.
Solution:
Example 5:
Analysis: The fractions have unlike denominators. We will write equivalent fractions using the LCD, 20.
Solution:
Example 6:
Analysis: The fractions have unlike denominators. We will write equivalent fractions using the LCD, 36.
Solution:
Example 7: An ice cream vendor sold eighteen and five-sixths liters of ice cream on Friday, and nineteen and one-half liters of ice cream on Saturday. How many liters did he sell in all?
Analysis: The fractions have unlike denominators. We will write equivalent fractions using the LCD, 6.
Solution:
Summary: To add mixed numbers:
- Examine the fractional part of each mixed number to determine whether the denominators are like or unlike.
- If the denominators are unlike, use the LCD to rewrite them as equivalent fractions.
- Add the whole numbers and add the fractions separately: (whole + whole) + (fraction + fraction)
- Simplify the result, if necessary.
Exercises
Directions: Add the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.
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In one week, the Glosser family drank one and seven-twelfths cartons of regular milk and four and one-twelfth cartons of soy milk. How much milk did they drink in all? |