Adding and Subtracting Fractions with Regrouping

Mathematics 5

Quarter 1 - Week 5

​How are you?

​Let us recall our past lesson.

​READY?!?

Multiple Choice

Factors are numbers we multiply together to get another number.

Multiple Choice

When we find the factors of two or more numbers and found some factors that are the same, they are called common factors.

Multiple Choice

The common factors of 12 and 16 are 2 and 3.

Multiple Choice

We can get a multiple of a number when we multiply it by another number. The list of multiples of a set of numbers are called common multiples.

Multiple Choice

The Least Common Multiple is simply the largest common multiple of a number.

Multiple Choice

The Least Common Multiple (LCM) of 4 and 5 is 20.

Multiple Choice

In finding the GCF, we will use continuous division through composite numbers.

Multiple Choice

In finding the GCF, we will use continuous division through prime numbers. The GCF is the product of all the prime divisors.

Multiple Choice

In finding the LCM, we use again the continuous division.

Multiple Choice

The Greatest Common Factor (GCF) of two or more numbers is the largest number that is a factor or divisor of each number, while the Least Common Multiple (LCM) of two or more numbers is the smallest number that is divisible by each of the given number or set of numbers.

​Lesson 1

Add and Subtract Fractions and Mixed Fractions with and without Regrouping

​Lesson 2

Solves Routine and Non-routine Problems Involving Addition or Subtraction of Fractions

​Addition and Subtraction

of Fractions

(With or Without Regrouping)

​- Similar Fractions

​- Dissimilar Fractions

​- Mixed Numbers

​Addition and Subtraction of Similar Fractions Without Regrouping

 1. Add or subtract the numerator.

2. Copy the denominator.

3. Change the answer to simplest form/lowest term if possible.

​ALWAYS FOLLOW THESE when adding or subtracting fractions WITHOUT regrouping:

​1) ADD or SUBTRACT

2) COPY

3) SIMPLIFY

Ang halimbawa natin ay similar fractions (pareho ang digits sa ibaba). Sa example, i-classify muna natin kung alin ang numerator at denominator. Ang mga numerator ay 3 at 1, samantalang ang mga denominator naman ay parehong 8. Kapag similar fractions, i-add o i-subtract ang numerator, tapos kopyahin lang ang denominator. I-express ito sa simplest form kung kailangan.

1) ​Add or subtract the numerator.

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2) Copy the denominator.

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3) Simplify the answer if possible. (lowest term)

Do not forget to Box your final answer. ü

Addition / Subtraction of Similar Fractions Without Regrouping

​ADDITION:

SUBTRACTION:

​ALWAYS FOLLOW THESE when adding or subtracting fractions WITH regrouping:

​1) RENAME

2) REGROUP

3) SUBTRACT

4) SIMPLIFY

​1) RENAME

2) ADD

3) SIMPLIFY

​ADDITION

SUBTRACTION

Addition / Subtraction of Dissimilar Fractions With Regrouping

​1) Rename with common denominator.

​Ginagawa ito kung dissimilar ang fractions tulad ng nasa given. Find the LCD.

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​2) Regroup the first fraction.

​Kapag mas maliit ang numerator ng naunang fraction sa ikalawa, kuhanin ang 1 mula sa unang mixed number at gawing fraction.

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Addition / Subtraction of Dissimilar Fractions With Regrouping

​1) Rename with common denominator.

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​2) Regroup the first fraction.

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\__________/

\_____/

Mula sa ganito↑, magiging ganito↑.

​3) Subtract.

​Sa puntong ito, maaari nang i-subtract dahil similar fractions na ang dalawa. Same procedures din naman sa addition.

Addition / Subtraction of Dissimilar Fractions With Regrouping

​1) Rename with common denominator.

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​2) Regroup the first fraction.

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​3) Subtract.

4) Simplify the answer if possible.

​Ang sagot na 5/6 ay nasa simplest form na kaya ito na ang final answer. Always box your final answer.

​Ulitin natin.

Addition / Subtraction of Dissimilar Fractions With Regrouping

​1) Rename with common denominator.

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​2) Regroup the first fraction.

}

​3) Subtract.

​4) Simplify the answer if possible.

​Box your final answer.

Ganyan ang steps at maayos na pagsusulat ng sagot sa operations on fractions. Pareho rin lang ng gagawin sa addition, maliban lang sa pag-subtract.

Solves Routine and Non-routine Problems Involving Addition or Subtraction of Fractions

ROUTINE PROBLEM - It involves using at least one of the four arithmetic operations and/or ratio to solve problems.

NON-ROUTINE PROBLEM - Also referred to as creative problem solving, this can be solved in multiple ways and with a variety of strategies.

​POLYA's STEP

​1) Understand ----

​2) Plan -------------

​

​

​3) Solve ------------

​4) Check -----------

AGONSA

​1) Asked, Given

​2) Operation, Number Sentence

​3) Solution

​4) Answer

​STEPS IN SOLVING WORD PROBLEMS

​Josie needs 1/4 cup of oil for a plain cake and 3/8 cup of oil for pineapple sponge cake. How many cups of oil are needed?

​Josie needs 1/4 cup of oil for a plain cake and 3/8 cup of oil for pineapple sponge cake. How many cups of oil are needed?

Understand:

​- What is asked in the problem?

​The total cups of oil needed. ( Ang pagsagot sa "what is asked" ay sa paraan nang pasalaysay o declarative sentence na.)

- What are the given facts?

1/4 cup of oil for plain cake, 3/8 cup of oil for pineapple sponge cake (Always put label. Ang ibig sabihin ng label ay kung anong bagay ang given. Dito ay oil for...)

​Josie needs 1/4 cup of oil for a plain cake and 3/8 cup of oil for pineapple sponge cake. How many cups of oil are needed?

​Josie needs 1/4 cup of oil for a plain cake and 3/8 cup of oil for pineapple sponge cake. How many cups of oil are needed?

​Josie needs 1/4 cup of oil for a plain cake and 3/8 cup of oil for pineapple sponge cake. How many cups of oil are needed?

​Let's practice.

​READY?!?

Multiple Choice

$$\frac{3}{8}+\ \frac{2}{8}=N$$  

• $$\frac{5}{8}$$  

• $$\frac{7}{8}$$  

Multiple Choice

$$\frac{3}{8}+\ 3\frac{4}{8}=N$$  

• $$4\frac{7}{8}$$  

• $$3\frac{7}{8}$$  

Multiple Choice

$$\frac{2}{5}+\frac{2}{3}=N$$  

• $$\frac{4}{8}\ or\ \frac{1}{2}$$  

• $$1\ \frac{1}{15}$$  

Multiple Choice

$$\frac{5}{7}-\frac{3}{7}=N$$  

• $$\frac{2}{7}$$  

• $$\frac{2}{0}$$  

Multiple Choice

$$6-\frac{3}{7}=N$$  

• $$5\frac{4}{7}$$  

• $$6\frac{3}{7}$$  

Multiple Choice

$$3\ \frac{2}{7}-\frac{3}{7}=N$$  

• $$2\frac{6}{7}$$  

• $$3\frac{6}{7}$$  

Multiple Choice

WHAT IS ASKED IN THIS PROBLEM?

$$\frac{5}{8}$$   of the staff are male. $$\frac{5}{12}$$   of the staff works part time at the aquarium. What fraction of the staff is female?

• The total fraction of female staffs

• The total fraction of male staffs

Multiple Choice

WHAT ARE THE GIVEN FACTS?

$$\frac{5}{8}$$   of the staff are male. $$\frac{5}{12}$$   of the staff works part time at the aquarium. What fraction of the staff is female?

• $$\frac{5}{8}$$  male staffs,  $$\frac{5}{12}$$   part-timers

• The total fraction of male staffs

Multiple Choice

WHAT IS THE NUMBER SENTENCE?

$$\frac{5}{8}$$   of the staff are male. $$\frac{5}{12}$$   of the staff works part time at the aquarium. What fraction of the staff is female?

• $$\left(\frac{5}{8}+\frac{5}{12}\ \right)\ -\ \frac{5}{8}\ =\ N$$  

• 12 + 16 = N

Multiple Choice

WHAT IS THE ANSWER?

$$\frac{5}{8}$$   of the staff are male. $$\frac{5}{12}$$   of the staff works part time at the aquarium. What fraction of the staff is female?

• $$1\ \frac{1}{24}$$  

• $$\frac{10}{20}or\ \frac{1}{2}$$   

​Magsagot na po ng worksheet!!!

​Thank you!!!