Dividing Simple and Mixed Fractions

At the end of the lesson, the learners are expected to:

*divide simple fractions and mixed fractions. (M6NS- Ic-96.2)

Unlocking of Difficulties

1. Division- is a simple operation in which a number is divided.

Unlocking of Difficulties

2. Dividend- The number that is being divided (in this case, 15) 15 ÷ 3 = 5.

Unlocking of Difficulties

3. Divisor- The number that it is being divided by (in this case, 3) 15 ÷ 3 = 5.

Unlocking of Difficulties

4. Quotient- The result of the division (in this case, 5)

15 ÷ 3 = 5.

Unlocking of Difficulties

5. Reciprocal- The reciprocal of a fraction is a fraction where the numerator and denominator swap or exchange places. This swapping is called inverting a fraction.

Unlocking of Difficulties

*Reciprocals are pairs of numbers whose product is 1.

*We turn the fraction upside down because division is the inverse or opposite of multiplication.

What part is shaded?

Name the parts of a whole:

What part is shaded?

Give two fractions for the shaded part.

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Have you ever experienced being given a slice of cake and still have to share that slice to someone?

How does it feel sharing the things given to you with someone?

1. How did you arrive with your answer in each one?

2. How do we multiply fractions and mixed numbers? 

3. In what instances do we need to divide fractions and mixed numbers?

In dividing a mixed number by a fraction, change the mixed form into improper fraction, then multiply the dividend by the reciprocal of the divisor. Make sure that the answer is expressed in simplest form.

Think-pair-share: Divide the following fractions. 

1. 8 ÷ 1/2 

2. 5/6 ÷ 3 

3. 4/6 ÷ 1/3 

4. 3 1/2 ÷ 1/3 

5. 1/5 ÷ 2 1/5

Activity 1: Seatwork

Find the quotient. Express the answer in lowest term if possible.

1. 2 ½ ÷3/4

2. 5 ½ ÷ 5/9

3. 6 1/6 ÷ 1/8

4. 2 ¼ ÷ 2/3

5. 1 1/6 ÷ 1/8

Activity 2: Find each quotient. 

1. 5/8 ÷ 2/3 

2. 3 1/3 ÷ 2/5 

3. 5 3/5 ÷ 4 

4. 4 1/2 ÷ 2 1/3 

5. 7/9 ÷ 2 3/4

In your everyday life, how can the concept of dividing fractions be helpful to you? Explain the reason of saying so.

How do we divide a whole number by a fraction? a fraction by another fraction? a mixed number by a fraction? a mixed number by a whole? mixed numbers? a Fraction by a mixed number?

What have you learned?

Read each item carefully then solve. Choose the letter that corresponds to the best answer.

1. If you divide 4/5 by 3/4 , what is the quotient?

A. 1 1/5

B. 1 1/3

C. 1 1/5

D. 2 ¾

What have you learned?

2. The quotient of 3/5 ÷ 2 ½ is ______.

A. 2/10

B. 6/25

C. 4/5

D. 7/5

What have you learned?

3. What is the quotient of 2 3/8 ÷3 ¾?

A. 13/30

B. ½

C. 17/30

D. 19/30

What have you learned?

4. The quotient of 2 numbers is 15/16. If the dividend is 3/8. What is the divisor?

A. 6/5

B. 4/5

C. 2/5

D. 1/5

What have you learned?

5. Teacher has 1 ¾ can of blackboard paint. If 1/8 of a can is enough for one blackboard, how many blackboards can be painted?

A. 12

B. 14

C. 16

D. 18

What have you learned?

In your Math Workbook, answer page 31 (Apply your skills)

What have you learned?

Solving Routine Problems Involving Division Without any of the Other Operations of Simple Fractions and Mixed Fractions Using Appropriate Problem -Solving Strategies and Tools Correctly

At the end of the lesson, the learners are expected to:

*solve routine problems involving division without any of the other operations of fractions and mixed fractions using appropriate problem-solving strategies and tools correctly. (M6NS-Ic-97.2)

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DIVISION CHANT

Dividend in

Divisor stays out

Dividend in

Divisor stays out

DIVISION CHANT

That’s the first step

Do the rest now

That’s the first step

Do the rest now

DIVISION CHANT

Divide, Multiply

Subtract, Bring down

Divide, Multiply

Subtract, Bring down

DIVISION CHANT

Get the quotient

You can check now

Get the quotient

You can check now

Solve for the quotient.

1. 6/8 ÷ 2/5 

2. 5 7/8 ÷ 3/5

3. 9 1/6 ÷ 5

4. 10 / 2 ÷ 4 1/4 

5. 7/15 ÷ 3 1/5

Have you seen street children?

How did you feel about them?

As a pupil, can you do something that would make them happy? How?

Solve the problem using any method.

*There were 10 1/2 loaves of bread which were equally shared with 21 street children. What part of the bread did each child get?

Steps in solving word problems. 

1. Understand the problem 

2. Devise a plan 

3. Carry out the plan/Solve

4. Look back and evaluate the solution/Check

Think-pair-share: Divide the following fractions. 

1. Teresita has 20 meters of cloth. If she used 1 ½ meters per blouse, how many pieces of blouse can she make?

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Think-pair-share: Divide the following fractions. 

2. A baker bought 10 ½ kilogram of butter. He used 5/8 of it in baking cakes and 1/5 of it in baking cookies. How much butter was left?

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Activity 2: Solve the following. 

1. Shane has a piece of rope that is 7 4/5 meters long. If he cuts it into pieces that are each 3/5 of a unit long, how many pieces does he have?

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Activity 2: Solve the following. 

2. Dawn is making pan cakes for her friends. Each pan cake requires 4 1/3 tablespoon of flour. If she has 10 friends, do you think 43 1/2 spoons of flour is enough? Explain.

Are the problems you encounter during the lesson really happen in real-life.

What are the steps in solving routine problems involving division of fractions?

What have you learned?

A. For each problem, check the correct division equation. Choose the letter of the correct answer.

1. How many pieces of string 5/6 dm long each be cut from a roll 3 2/3 dm?

a. 5/6 ÷ 3 2/3 =n

b. 3 2/3 ÷ 5/6 =n

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What have you learned?

2. How many benches 2 ½ m long each can be placed end to end in the hallway 13 1/3 m long?

a. 2 ½ ÷ 13 1/3 =n

b. 13 1/3 ÷2 ½=n

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What have you learned?

B. Solve the following using steps in problem-solving.

3. Some cakes were sold out in the store. One cake was cut into 10 slices. A girl bought 1 slice and her friend bought 5 slices. What fractional part of the cake was left?

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What have you learned?

Make a journal stating what you have learned and how you will apply the concept of division of fraction inside your home.

What have you learned?

Solving Routine Problems Involving Division With any of the Other Operations of Simple Fractions and Mixed Fractions Using Appropriate Problem-Solving Strategies and Tools Correctly

At the end of the lesson, the learners are expected to:

*solve routine problems involving division with any of the other operations of fractions and mixed fractions using appropriate problem-solving strategies and tools correctly. (M6NS-Ic-97.2)

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FRACTION RHYME

You start with a whole, with everything there

Someone comes along and they want to share

It’s split into two, that’s two groups

It could be pizza or fruit loops.

You each get one-half

And that is fair

It’s the same on both sides

It’s like a pair.

What are the steps in solving routine problems involving Dividing Fractions?

To have an abundant harvest from your garden, what are the needs of your plants that you should consider or provide?

You have three-fourths yard of water pipe to be used in your garden? How many pieces can you cut the pipe into if each piece is one-eight yard?

SOLUTION:

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¾ ÷ 1/8 = ¾ x 8/1 =24/4

= 6

Steps in solving word problems. 

1. Understand the problem 

2. Devise a plan 

3. Carry out the plan/Solve

4. Look back and evaluate the solution/Check

Think-pair-share: Solve the problem presented in the Task Card.

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Think-pair-share: Solve the problem presented in the Task Card.

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Think-pair-share: Solve the problem presented in the Task Card.

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1. Margarita solicited 10 2/3 litres of paint for the Brigada Eskwela. Their City Mayor gave their school another 7 2/5 litres of paint. If each classroom needs 2 3/7 litres, how many classrooms can be painted? 

2. Rona has 20 1/2 meters of cloth, she uses 2/3 of it for a girls’ dress. The remaining cloth will be used for a baby dress. If each dress needs 4/5 meters, how many baby dress can Rona make?

From all the activities that we had, aside from the concept of dividing fractions, what other ideas do you think are useful in our daily lives?

Aside from using the steps that I shared to you, what are the techniques you used in solving problems?

What have you learned?

Solve the following.

1. A fruit vendor weighed 5 papayas. What was the average weight of each papaya?

What have you learned?

 2. How many 8/15 are there in 1 5/9?

3. A 9-meter-long stick was cut into pieces. If each piece was ¾ m, how many pieces were there?

What have you learned?

Make a poster showing real-life situations of solving word problems about fractions.

What have you learned?

Creating Problems (With Reasonable Answers) Involving Division Without or With any other operations of Fractions �and Mixed Fractions

At the end of the lesson, the learners are expected to:

*create problems (with reasonable answers) involving division without or with any of the other operations of fractions and mixed numbers. (M6NS-Ic-97.2)

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FRACTION RHYME

Fractions require actions

The denominators

To blame…

For Addition and subtraction

They got to be the same!

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But to multiply is easy just do it

They say…

Division you must KEEP, CHANGE and FLIP

See…

Fractions are just a game!

*Can we use the steps in solving routine problems to solve non-routine problems?�*Identify the different steps.

Have you tried making problems out of the mathematical sentences presented to you by your Math teacher?

If yes, were you able to do it easily?

Today, we are going to discuss creating problems involving division of fractions.

Read and learn:

Mario was asked by his teacher to create a problem out of the situations:

1. Motorcycle, 51 ½ liter, liters of gasoline for a 120 km trip.

2. Airplane flies 2880 km in 4 ½ hours, average speed of the airplane.

Mario had created the following problems:

1. A motorcycle diver consumes one liter of gasoline for every 51 ½ km that he travels. If he will cover a total distance of 120 km for a particular trip, how many liters of gasoline are needed for a 120-km trip?

Mario had created the following problems:

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2. An airplane flies a distance of 2880 km in 4 ½ hours. Find the average speed of the airplane.

In creating a word problem, think of the following:

*the concept in Math

*type of problem to be created

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*read examples of word-problems and study their solutions

*data given to solve the problem must be there

*the answer must be the answer to what is asked and must be reasonable.

Think-pair-share: Study the problem.

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Mikka did 2/13 of a load of laundry on Thursday and 5/13 of a load of laundry on Friday. If she will still do laundry on Saturday and Sunday, what part of the remaining laundry will each day have?

Directions: Create word-problems about the mathematical sentence below.

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1. 5 3/4 ÷ 4

2. 3 5 7 ÷ 2 3 

1. Write a problem similar to “Don Antonio has 7 7/8 hectares of land. His wife has 2/3 of what he has. If they will divide their lands among their 7 children, what part will each child have?” 

2. Write a story problem that shows: 3 5/7 ÷ 4/5 = �

If you will relate to a song your experience in creating word problems, what would it be and why?

What are the points to remember in creating word-problem involving division of fractions?

What have you learned?

Create a problem out of the following:

1. 96 cups of buko salad; number of servings that can be made; 2/3 cups per serving

What have you learned?

2. Mariano family’s-spent 1/10 of the income on electricity, monthly income is Php.19, 260;amount spent on electric bill

Answer page 37 of your Math Workbook (Enhance your skills)

What have you learned?

SUMMATIVE TEST IN MATHEMATICS 6

At the end of the lesson, the learners are expected to:

*analyze test questions carefully

*answer test questions correctly

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