Adding and subtracting fractions with unlike denominators word problems

Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?

Analysis: To solve this problem, we will add two fractions with like denominators.

Solution: 

Answer: Rachel rode her bike for three-fifths of a mile altogether.

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Solution: 

Answer: Stefanie swam one-third of a lap farther in the morning.

Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.

Solution:

Answer: It took Nick three and one-fourth hours to complete his homework altogether.

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Solution: 

Answer:

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.

Solution:

Answer: Diego and his friends ate six pizzas in all.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.

Solution: 

Answer: The Cocozzelli family took one-half more days to drive home.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.

Solution: 

Answer: The warehouse has 21 and one-half meters of tape in all.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.

Solution: 

Answer: The electrician needs to cut 13 sixteenths cm of wire.

Analysis: To solve this problem, we will subtract a mixed number from a whole number.

Solution:

Answer: The carpenter needs to cut four and seven-twelfths feet of wood.

Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: 

1. Add fractions with like denominators.
2. Subtract fractions with like denominators.
3. Find the LCD.
4. Add fractions with unlike denominators.
5. Subtract fractions with unlike denominators.
6. Add mixed numbers with like denominators.
7. Subtract mixed numbers with like denominators.
8. Add mixed numbers with unlike denominators.
9. Subtract mixed numbers with unlike denominators.

Exercises

Directions: Subtract 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 fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.