112 Lesson 4.2 ~ Adding and Subtracting Fractions

Sometimes when you add or subtract fractions the denominators are the same. Sometimes you may find that the fractions have different denominators. In this lesson you will learn how to find the sum or difference of fractions whether or not the denominators are equal.

Janice was ordering pizzas for her friends. The table shows the fractions of the pizzas each person said theycould eat.

How much cheese pizza do Lakelynn and Alvaro think they can eat together? Lay out the fraction tiles to represent the amounts of cheese pizza which Lakelynn and Alvaro want. Combine the fraction tiles to find the total. Simplify the fraction, if needed. Draw a picture of the fraction model you used and write the addition equation on paper.

+ = 1 _ 5 + 3 _ 5 = 4 _ 5 step 1: Follow the process shown above to answer the following questions. a. How much cheese pizza will Janice and Jory eat together? b. How much Hawaiian pizza will Jory and Lakelynn eat together? c. How much pepperoni pizza will Lakelynn and Alvaro eat together?

step 2: Look at the equations. What do you notice about the denominators of the fractions being added and the denominator of the answer? What about the numerators? How might you add fractions with common denominators without using fraction tiles?

ExplorE! pizza parTy!

Cheese hawaiian Pepperoni

Janice 3 __ 10 1 _ 6 1 _ 4

lakelynn 1 _ 5 1 _ 3 3 _ 8

Alvaro 3 _ 5 1 _ 2 5 _ 8

Jory 1 __ 10 2 _ 3 1 _ 2

aDDing anD suBTracTing FracTions

lesson 4.2

Lesson 4.2 ~ Adding and Subtracting Fractions 113

How much Hawaiian pizza will Jory and Alvaro eat? Lay out fraction tiles to represent the amount of Hawaiian pizza Jory and Alvaro eat. + = ? 2 _ 3 + 1 _ 2 Find the least common denominator for the two fractions. 2: 2, 4, 6, 8, ... LCD = 6 3: 3, 6, 9, 12, ... Replace the original fraction tiles with equivalent fractions using the LCD. Combine the tiles to find the answer.

+ = 4 _ 6 + 3 _ 6 = 7 _ 6 Simplify the fraction, if needed. All improper fractions should be written as mixed numbers.

7 _ 6 = 1 1 _ 6 step 3: Follow the process shown above to answer the following questions. Draw pictures of the fraction tiles used in the process. Write the addition equation on your paper. a. How much cheese pizza will Janice and Lakelynn eat? b. How much Hawaiian pizza will Lakelynn and Alvaro eat? c. How much Hawaiian pizza will Janice and Jory eat? d. How much pepperoni pizza will Janice and Alvaro eat? e. How much pepperoni pizza will Janice and Jory eat? f. How much pepperoni pizza will Alvaro and Jory eat?

step 4: How might you add fractions with unlike denominators without using fraction tiles?

After adding, subtracting, multiplying or dividing fractions, you must simplify the fraction. This means writing the fraction in simplest form, then changing improper fractions to mixed numbers, if necessary.

ExplorE! conTinuED

114 Lesson 4.2 ~ Adding and Subtracting Fractions

kiley practiced 1 __ 8 of her piano music in the morning. That afternoon she practiced 3 __ 8 of her music. what fraction of her piano music did she practice all together?

Write the problem. 1 _ 8 + 3 _ 8 Add the numerators and write =the sum over the common 1 + 3 ____ 8 = 4 _ 8 denominator. Simplify the fraction. 4 _ 8 = 1 _ 2

Kiley practiced 1 _ 2 of her piano music.

Find the value of 5 __ 6 − 1 __ 6 .

Subtract the numerators. 5 − 1 ____ 6 = 4 _ 6 Write the difference over the common denominator.

Simplify the fraction. 4 _ 6 = 2 _ 3

5 _ 6 − 1 _ 6 = 2 _ 3

mallory made 3 __ 4 gallon of ice cream. logan made 1 _ 2 gallon. how many total gallons of ice cream do they have together?

Write the problem. 3 _ 4 + 1 _ 2 +

Find the least common 2: 2, 4, 6, ...denominator for the set 4: 4, 8, 12, ...of fractions.

Rewrite the fractions using 3 _ 4 = 3 _ 4 1 _ 2 = 2 _ 4 the LCD. Add the numerators. 3 _ 4 + 2 _ 4 = 3 + 2 ____ 4 = 5 _ 4

Change the improper fraction 5 __ 4 = 1 1 _ 4 to a mixed number.

Mallory and Logan made a total of 1 1 _ 4 gallons of ice cream.

ExamplE 1

solution

ExamplE 2

solution−

=

ExamplE 3

solution

+

× 2

× 2

+

Lesson 4.2 ~ Adding and Subtracting Fractions 115

Find the value of 2 __ 3 − 1 __ 4 .

Find the LCD. 3: 3, 6, 9, 12, ... 4: 4, 8, 12, 16, ...

Rewrite the fraction 2 _ 3 = 8 __ 12 using the LCD.

1 _ 4 = 3 __ 12

Subtract the numerators. 8 __ 12 − 3 __ 12 = 8 − 3 ____ 12 = 5 __ 12

2 _ 3 − 1 _ 4 = 5 __ 12

ExErcisEs

Find each sum or difference. write in simplest form. 1. 1 __ 4 + 1 __ 4 2. 3 __ 5 + 1 __ 5 3. 1 __ 8 + 5 __ 8

4. 1 ___ 10 + 5 ___ 10 5. 7 __ 9 + 5 __ 9 6. 5 __ 6 − 3 __ 6

7. 7 __ 8 − 5 __ 8 8. 9 ___ 15 − 4 ___ 15 9. 9 ___ 11 − 3 ___ 11

10. Isaiah surveyed his class to see whether they thought the beaver was an appropriate mascot for their school. Four-eighths of the class thought it was a good choice. Three-eighths of the class thought another animal should be chosen as the mascot. One-eighth of his class did not want to answer the survey. What fraction of his class answered the survey? Show all work necessary to justify your answer.

11. Jace ran 3 __ 10 mile on Monday. On Tuesday he ran 5 __ 10 mile. How much further did he run on Tuesday than Monday? Use mathematics to justify your reasoning.

12. Draw a model to show 1 __ 10 + 3 __ 10 and write the answer in simplest form.

13. Draw a model to show 3 _ 4 − 1 _ 8 and write the answer in simplest form.

ExamplE 4

solution

× 4

× 4 × 3

× 3

116 Lesson 4.2 ~ Adding and Subtracting Fractions

Find each sum or difference. write in simplest form.

14. 1 __ 8 + 1 __ 2 15. 5 ___ 12 + 4 __ 6 16. 3 ___ 10 + 2 __ 5

17. 1 __ 2 + 2 __ 6 18. 3 __ 4 + 2 __ 3 19. 2 __ 3 − 1 __ 2

20. 5 __ 6 − 2 __ 8 21. 5 __ 9 − 1 __ 3 22. 11 ___ 12 − 3 __ 4

23. Natasha’s desk measured 3 _ 4 meter wide. Neil’s desk was 2 _ 3 meter wide. How much wider was Natasha’s desk than Neil’s desk? Show all work necessary to justify your answer.

24. Lara ate 1 _ 2 of a sub sandwich. Lucas ate 3 _ 4 of a sub sandwich. How much did they eat altogether? Use mathematics to justify your reasoning.

25. One-third of the students Ms. Jarrett teaches are sixth graders. Five-twelfths of the students she teaches are seventh graders. The rest are eighth graders. a. What fraction of her students are 6th and 7th graders? b. What fraction of her students are 8th graders?

26. Aaron rode his bike off a jump 7 __ 12 yard tall. The next day he rode his bike off a jump 8 _ 9 yard tall. How much taller was the second jump than the first jump?

rEviEw

draw a line with the given measure.

27. 2 1 _ 8 in 28. 4 3 _ 4 in 29. 1 1 _ 2 in estimate each difference.

30. 9 __ 10 − 3 _ 8 31. 11 __ 12 − 1 _ 5 32. 5 1 _ 8 − 2 1 _ 4

tic-tAc-toe ~ mode l s

Write directions about how to add and subtract fractions using fraction tiles.

Have a parent or classmate follow your directions to see if they work. Make any needed changes to your directions so they are clear and useful.

Create a brochure using your directions to teach students how to use fraction tiles to show addition or subtraction of fractions.