Explore

Engage

Elicit

Lesson 1: Adding and Subtracting Fractions

A. Find the sum of the fractions and mixed numbers.

1.13+ 1

22. 2

56+ 2

33. 1

34+2

712

+ 13

B. Find the difference of the two fractions or mixed numbers.

1.56−1

32. 1

14−7

83. 3

512

−134

Reflect: How do we add or subtract fractions or mixed numbers?

Antonia mixed 314

cups of flour and 178

cups of water for her recipe. Unfortunately, 12

cups of the mixture spilled while she was stirring it. How many cups of the mixture remained?

Pause & Reflect: What do you know about addition and subtraction of fractions and mixed numbers?

Exploration 1: Addition and Subtraction of Fractions without Regrouping

1. Find 114+5

8−1

2.

2. Change the fractions and mixed fractions to similar fractions using the least common denominator.

3. Add and subtract the fractions.

328+1

48−1

8 Do the operations from left to right. First, add 3

58

and 148

.

178− 4

8 Then, subtract

1

78∧4

8.

8

314+1

12−1

83

28+1

48−1

8

Explain

138

Express the answer in lowest form if necessary.

4. Is 138

already in lowest form?

Exploration 2: Addition and Subtraction of Fractions with Regrouping

1. What is 316−3

4+ 11

12?

2. Change the fractions and mixed fractions to similar fractions using the least common denominator.

3. Add and subtract the fractions.

32

12− 9

12+ 11

12 Firstly, regroup3

212

as 21212

+ 212

∨21412

.

21412

− 912

+ 1112

Do the operations from left to right. Subtract2

1412

∧9

12.

25

12+ 11

12 Add

2

512

∧11

12.

21612

Change 1612

to a mixed number.

2+14

12 Add the whole numbers and express

412

to lowest form.

313

Do you have a shorter way to add and subtract fractions and mixed numbers?

Go back to the questions in ENGAGE. In groups of five, explain on how you will answer them. Below are the ideas you should have learned in this lesson.1. In adding and subtracting fractions and mixed numbers without/with regrouping:

a. Change the fractions and mixed numbers to similar fractions.b. Regroup the mixed numbers or fractions if neededc. Add or subtract the fractions depending on the first operation to appear from left

to right. d. Express the final answer to lowest form.

9

316−3

4+ 11

123

212

− 912

+ 1112

Evaluate

Elaborate‘

Do you know how to bake biko or rice cake? The table below shows the amount of ingredients that you can use to make a delicious one. Use the given information to answer the questions below. Ingredients glutinous

ricewater brown

sugarcoconut

milksalt

Number of cups 323

58

412

814

112

1. How many cups is the mixture of coconut milk and water? 2. How much more is brown sugar than salt? 3. By how much is the coconut milk greater than the mixture of water and brown sugar?

A. Add and subtract the fractions and mixed numbers. Express the answers in lowest form.

1. 256+ 1

22. 5

712

−234

3. 913−(4

16+2

89 )

B. Find the missing term in each mathematical sentence.

4. 4712

−¿334

5. +238−1

516

=39

166. (3 3

8–

12 )+¿

C. Explain whether each statement is either true or false. 7. Add or Subtract fractions when they are already similar. 8. Change the fractions and mixed numbers to dissimilar fractions.9. Add the fractions all the time before subtraction. 10. Reduce the sum or difference in lowest form

D. How do you add and/or subtract fractions? Use fraction bars to illustrate your explanation.

E. Create a mathematical sentence with an answer of234

. The number sentence should have

at least 3 dissimilar fractions and mixed numbers. It should also use both addition and subtraction as its operation.

Pause & Reflect

Are you happy with the result of your evaluation? Why?What concepts are clear to you?What concepts are still not clear to you?What is the most desirable value or attitude that you have developed in this lesson?

10

Extend

534−1

13+2

512

59

12−1

412

+2512

59

12−3

912

I. Use the digits 1, 2, 6 and 9 once to form two fractions.

a. What is the least sum that you can have?b. What is the largest difference that you can have?

Hint: List all the possible fractions that can be formed and get their sums or differences.

II. A friend shows you his solutions to a math problem. Study his solutions in the box.Is he correct or not? Why? What will you tell him to correct his solution?

11

Example:16+ 2

9=N

318

+ 418

= 718

718

can be a sum of the

fractions.