Addition, Subtraction, and Multiplication of Decimals

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Copyright © 2017 Quipper Limited 1 STUDY GUIDE GRADE 6 | UNIT 4 Addition, Subtraction, and Multiplication of Decimals Table of Contents Introduction ............................................................................................................................. 3 Test Your Prerequisite Skills ................................................................................................. 4 Objectives ................................................................................................................................ 5 Lesson 1: Addition of Decimal Numbers through Ten Thousandths - Warm Up! ...................................................................................................................... 6 - Learn about It! ............................................................................................................. 7 - Let’s Practice! ............................................................................................................... 9 - Check Your Understanding! ..................................................................................... 14 Lesson 2: Subtraction of Decimal Numbers through Ten Thousandths - Warm Up! .................................................................................................................... 15 - Learn about It! ........................................................................................................... 16 - Let’s Practice! ............................................................................................................. 18 - Check Your Understanding! ..................................................................................... 23 Lesson 3: Multiplying Decimals up to Two Decimal Places - Warm Up! .................................................................................................................... 24 - Learn about It! ........................................................................................................... 25 - Let’s Practice! ............................................................................................................. 27 - Check Your Understanding! ..................................................................................... 32 Lesson 4: Multiplying Decimals Mentally up to Two Decimal Places by 0.1, 0.01, 10, and 100 - Warm Up! .................................................................................................................... 33 - Learn about It! ........................................................................................................... 34

Transcript of Addition, Subtraction, and Multiplication of Decimals

Page 1: Addition, Subtraction, and Multiplication of Decimals

Copyright © 2017 Quipper Limited

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STUDY GUIDE

GRADE 6 | UNIT 4

Addition, Subtraction, and Multiplication of Decimals

Table of Contents

Introduction ............................................................................................................................. 3

Test Your Prerequisite Skills ................................................................................................. 4

Objectives ................................................................................................................................ 5

Lesson 1: Addition of Decimal Numbers through Ten Thousandths

- Warm Up! ...................................................................................................................... 6

- Learn about It! ............................................................................................................. 7

- Let’s Practice! ............................................................................................................... 9

- Check Your Understanding!..................................................................................... 14

Lesson 2: Subtraction of Decimal Numbers through Ten Thousandths

- Warm Up! .................................................................................................................... 15

- Learn about It! ........................................................................................................... 16

- Let’s Practice! ............................................................................................................. 18

- Check Your Understanding!..................................................................................... 23

Lesson 3: Multiplying Decimals up to Two Decimal Places

- Warm Up! .................................................................................................................... 24

- Learn about It! ........................................................................................................... 25

- Let’s Practice! ............................................................................................................. 27

- Check Your Understanding!..................................................................................... 32

Lesson 4: Multiplying Decimals Mentally up to Two Decimal Places by 0.1,

0.01, 10, and 100

- Warm Up! .................................................................................................................... 33

- Learn about It! ........................................................................................................... 34

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- Let’s Practice! ............................................................................................................. 35

- Check Your Understanding!..................................................................................... 39

Challenge Yourself! .............................................................................................................. 40

Performance Task ................................................................................................................ 40

Wrap-up ................................................................................................................................. 42

Key to Let’s Practice! ............................................................................................................. 43

References ............................................................................................................................ 44

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STUDY GUIDE

GRADE 6| MATHEMATICS

UNIT 4

Addition, Subtraction, and Multiplication

of Decimals

In the previous units, you have been familiarized with the concept of

fractions and how to perform the fundamental operations involving these

types of numbers. Fractions can be written in another way in the form of

decimal numbers.

A decimal number is very much present in our daily life.

Take for example the distance traveled on a mountain

hiking trip. It is not always the case that the distance

from your starting point up to the peak of a mountain is

expressed in whole numbers. It is beneficial to use one

or two decimal places to be accurate in documenting

your journey.

Currency is also expressed through decimal

numbers. When you buy groceries, most of the

items have price tags that show decimal numbers.

Decimal numbers are also useful in medicine. Using

a thermometer, we can determine our body

temperature in terms of these numbers, say

37.5 ℃.

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Table of Contents

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Apparently, decimals are everywhere. It is important to learn how to perform

basic operations on these numbers too. In the following lesson, you will learn

how to add, subtract, and multiply decimals. Shown below is the decimal

place value chart which is useful in getting a good grasp of the lessons in this

unit.

Decimal Place Value Chart

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Before you get started, answer the following items to help you assess your

prior knowledge and practice some skills that you will need in studying the

lessons in this unit.

A. Rewrite the fractions into its decimal form.

1. 3

10 2.

25

100 3.

35

100 4.

6

10 5.

375

1000

• Rewriting fractions into decimal form

• Multiplying whole numbers by multiples of 10

• Arranging decimals in ascending or descending order

• Comparing decimals using > or <

Test Your Prerequisite Skills

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B. Multiply the following numbers.

1. 672 × 20

2. 724 × 40

3. 9 702 × 30

C. Arrange the set of decimals into its ascending order.

1. 2.5 , 1.2, 7.3, 8.3, 2.4

2. 0.02, 0.1, 0.03, 0.001, 0.4

3. 5.6, 5.62, 5.05, 5.5, 5.1

D. Compare the decimals using > or <.

1. 9.02 ____ 9.002

2. 0.03____ 0.04

3. 7.8 ____ 8.7

At the end of this unit, you should be able to

• add and subtract decimals and mixed decimals through ten

thousandths without or with regrouping;

• solve one or more steps routine and non-routine problems involving

addition and/or subtraction of decimals and mixed decimals using

appropriate problem solving strategies and tools;

• multiply decimals and mixed decimals with factors up to 2 decimal

places;

• mentally multiply decimals up to 2 decimals places by 0.1, 0.01,10, and

100;

Objectives

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• solve routine and nonroutine problems involving multiplication of

decimals and mixed decimals including money using appropriate

problem solving strategies; and

• solve multistep problems involving multiplication and addition or

subtraction of decimals, mixed decimals and whole numbers including

money using appropriate problem solving strategies and tool.

Hopping along the Number Line

Materials Needed: paper with written number line, markers of

different colors

Instructions:

1. This activity may be done individually or in pairs.

2. On the number line, mark your starting point at zero. Make three

small steps to the right.

What part of the number line did you land on?

Lesson 1: Addition of Decimal Numbers through Ten

Thousandths

Warm Up!

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3. Try another starting point at 1 and use a different color for this mark.

Make 12 small steps to the right. What part of the number line did

you land on?

4. Upon your observation, is there a mathematical operation that can

represent the relationship between your starting point, the number

of steps made, and the part of the number you landed after

performing the steps?

5. Can you guess the appropriate number sentence that can express

the answer in number 2? How about in number 3?

The activity you performed in Warm Up! demonstrates the concept of adding

decimal numbers. In item 2, making three small steps from 0 lands you in the

0.3 mark. Note that every small step represents 0.1 unit. Thus three 0.1 units

is equal to 0.3 units. When the decimal 0.3 is added to the starting point 0,

you get 0.3.

In item 3, twelve small steps from the starting point 1 lands you in the 2.2

mark. The decimal 1.2 represents these twelve small steps since there are 12

0.1 units. When 1.2 is added to the starting point 1, you obtain 2.2.

How do we add decimal numbers?

Learn about It!

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Let us find out using this word problem below.

Mary bought a notebook for ₱109.75 and a set of pencils

for ₱64.50. What was the total cost of her school

supplies?

The prices ₱109.75 and ₱64.50 are decimal numbers. To find the total cost,

add the amounts of the school supplies.

Step 1: Align the decimal points.

Step 2: Start adding from the right, which in this case is the hundredths

place.

Step 3: Continue adding up to the left. Regroup if necessary.

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Step 4: Align the decimal point in your total with the decimal points in the

addends.

The total cost of Mary’s coloring materials was ₱174.25.

Example 1: 56.32 + 18.7 + 40.076 = _________

Solution:

Step 1: Align the decimal points.

Step 2: Notice that zeros are placed to fill in the missing places.

Let’s Practice!

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Step 3: Proceed to addition similar to whole numbers. Regroup if

necessary.

Therefore, 56.32 + 18.7 + 40.076 = 115.096.

Try It Yourself!

Complete the number sentence:

156.89 + 312.8903 = ________

Example 2: What is the sum of 126.04 and 78?

Solution:

Step 1: Align the decimal points. Note that the decimal point of a whole

number is found at the end of the last digit.

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Step 2: Place zeros to fill in the missing places.

Step 3: Proceed to addition similar to whole numbers. Regroup if

necessary.

Try It Yourself!

What is the sum of 56 and 1 082.95?

Example 3: Add: 5.8902 + (12.91 + 3.551)

Solution:

Step 1: Add first the decimal numbers inside the grouping symbols.

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Step 2: Add 16.461 to 5.8902. Make sure that the decimal numbers are

aligned, and missing places are filled with zeros.

Thus, 5.8902 + (12.91 + 3.551) is equal to 22.3512.

Try It Yourself!

Complete the statement:

(1 250.392 + 225.32) + 712.5895 = _______

Real-World Problems

Example 4: Perez family lives in Manila. They want to take a vacation in

Baguio City. They agreed that Mr. Perez would drive the first

82.7 kilometers (km), his wife Camille would

drive the next 75.95 km, and he would drive

again for the rest of 89.35 km. How far is

Baguio City from Manila?

Solution: To find how far Baguio City is from Manila, add the number of

kilometers driven by Mr.Perez and his wife.

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Step 1: Align the decimal points.

Step 2: Place zeros to fill in the missing places.

Step 3: Proceed to addition similar to whole numbers. Regroup if

necessary.

Therefore, Baguio City is 248 km away from Manila.

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Try It Yourself!

Your mother will use 3.4 meters (m) of a yellow ribbon

as tablecloth lining, 0.62 m of red ribbon for a flower

design on an apron, and 6.21 m of blue ribbon for

various party decorations. How many meters of

ribbon will your mother have to buy to complete all of

her projects?

A. Add the following decimal numbers

1. 45.091 + 20.07 + 1.5173

2. 3.005 + .0971 + 3.5

3. 51.023 + .004 + 78.83

4. 1.0089 + 11.223 + 98.0001

5. 0.417 + .0003 + 8.8

B. Answer the following questions:

1. What is the sum of 14.07 and 367?

2. What is the result when 675 is added to 26.1?

3. If 134.09 is added to the sum of 56.934 and 1.0023, then what will be

the answer?

Check Your Understanding!

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C. Analyze and solve the word problems below.

1. A rectangular fence measures 651.09 m by 31.0071 m. Determine

the perimeter of the fence.

(Hint: Perimeter = Sum of the measures of all the sides of a figure)

2. Shirley needs 8.5 kilos of chicken, 6 kilos of pork, and 4.75 kilos of

beef for her child’s birthday party. How many kilos of meat does she

need?

Shading the Decimals Away

Materials Needed: paper, pen, coloring materials, ruler

Instructions:

1. This activity can be done individually or in pairs.

2. Using a base 10 blocks model, illustrate the fraction 4

10.

3. Convert the fraction 4

10 into its decimal form by dividing the numerator

by the denominator.

Lesson 2: Subtraction of Decimal Numbers through Ten

Thousandths

Warm Up!

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4. Illustrate the answer in number 3 using the base 10 blocks.

If each block in fraction form is 1

10, what will each block be in decimal

form?

5. Is the first illustration similar to the second illustration?

6. Based on the illustration in number 3, how many blocks in all (in

decimal form) are shaded? How many in all are not shaded?

7. Is there a mathematical operation that represents the number of

unshaded blocks in terms of the total number of blocks and the

number of shaded blocks?

The activity in Warm Up! illustrates the concept of subtraction of decimal

numbers. When the number of shaded blocks, represented as 0.4, is

subtracted from the total number of blocks, denoted by 1.0, we get the

number of unshaded blocks which is 0.6.

How do we subtract decimals?

Learn about It!

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STUDY GUIDE

Let us use the problem below.

The current foreign exchange rate shows 1 EUR is equal to

₱63.52 while 1 USD is equal to ₱52.05. By how much does

the Euro conversion to peso exceed the US dollar

conversion to peso?

To find the difference between the peso rates, subtract the decimals.

Step 1: Align the decimal points. Add zeros to the right of the last digit

if necessary.

Step 2: Start subtracting from the right, which in this case is the

hundredths place.

Step 3: Continue the process from right going to the left. Regroup if

necessary.

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Step 4: The decimal point of the answer should be aligned with the

decimal points in the minuend and the subtrahend.

The difference between the peso rates is ₱11.47.

Example 1: 49.5 – 17.896 = _____

Solution:

Step 1: Align the decimal points.

Step 2: Notice that zeroes are placed to fill in the missing places.

Let’s Practice!

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STUDY GUIDE

Step 3: Proceed to subtraction similar to whole numbers. Regroup if

necessary.

Therefore, 49.500 – 17.896 = 31.604.

Try It Yourself!

Complete the number sentence:

497.07 – 243.88 = _____

Example 2: Solve for the value of the missing number 𝑛:

754.216 + 𝑛 = 852.046

Solution: Notice that the given is an addition number sentence.

However, solving for the value of 𝑛 will require subtraction.

Step 1: Align the decimal points.

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Step 2: Since the missing value 𝑛 is an addend, change the number

sentence into a subtraction number sentence. The difference in

the original number sentence will now become the minuend,

while one of the addends will become the subtrahend.

Step 3: Proceed to subtraction. Regroup if necessary.

Thus, the value of 𝑛 is 97.830 or 97.83.

Try It Yourself!

Solve for the value of 𝑛: 1 300 + 𝑛 = 1 459.956

Example 3: Subtract the sum of 51.0251 and 0.0005 from 102.8931.

Solution: Write the statement into number sentence. Consider the

phrase “sum of.” This phrase indicates that you need to add

51.0251 and 0.0005 first.

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STUDY GUIDE

51.0251 + 0.0005 = 51.0256

After getting the sum, subtract 51.0256 from 102.8931. Thus,

102.8931 – 51.0256 = difference

Step 1: Align the decimal points.

Step 2: Proceed to subtraction. Regroup if necessary.

Therefore, when the sum of 51.0251 and 0.0005 is subtracted

from 102.893, the difference is 51.8675.

Try It Yourself!

Subtract the sum of 49.031 and 30.8156 from 100.0467.

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Real-World Problems

Example 4: Myla bought a book for ₱432.75. She

gave the cashier a ₱1000 bill. How

much was her change?

Solution: The problem asks for the change which implies subtraction.

Solve the problem by following the steps mentioned in the

previous examples.

Step 1: Align the decimal points.

Step 2: Proceed to subtraction. Regroup if necessary.

Myla’s change was ₱567.25.

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Try It Yourself!

To help the typhoon victims, a grade 6 class decided to hold a rummage

sale. During the sale, they were able to collect ₱4

567.80. However, they had to pay for rent and

utilities, which amounted to ₱678.25. How much

were the net proceeds of the rummage sale?

A. Find the difference.

1. 71.041 – 35.901

2. 161.0003 – 98.014

3. 784.1065 – 351.0371

4. 5 893 – 4 720.7802

5. 30 601.0004 – 29 023.7192

B. Find the value of 𝑛.

1. 561.0002 + 𝑛 = 819.0356

2. 𝑛 + (45.9012 + 192.0561) = 5 028.7183

3. 601.9736 + 𝑛 = 74 302.0051

C. Analyze and solve the following problems.

1. What is the difference between the sum of 501.877 + 3 007.2019 and

7 021.5537?

2. Andi bought a pen worth ₱75.25. If she gave ₱500.00 to the cashier

upon payment, how much is her change?

Check Your Understanding!

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Growing Decimals

Materials Needed: coloring materials, pen, transparent hundredths

grids

Instructions:

1. This activity will be done in pairs.

2. Shown below is the illustration of the decimal 0.3 (shaded vertically)

using the hundredths grid.

Note: There are 10 tenths in a hundredths grid.

3. Using another hundredths grid, illustrate the decimal number 0.7

(shade horizontally).

Lesson 3: Multiplying Decimals up to 2 Decimal Places

Warm Up!

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4. Combine the two grids by putting one on the top of the other.

5. How many shaded cells are of the combination of the two? Express

your answer in decimal form.

The activity you did in Warm Up! models the multiplication of decimals.

Overlapping the grid that shows 0.3 by the grid that displays 0.7 gives you 21

colored cells out of a hundred. Thus, this 21 cells illustrates 0.21.

How do we multiply decimals even without the use of grids?

Let us find out through the problem below.

The Philippine monkey-eating eagle is considered as one of the

largest birds of prey in the world. It can fly 1.67 km per minute.

If the Philippine eagle flies for 15 minutes, how far is it able to

travel? (Note: Distance = Speed × Time)

Let us analyze the total distance the Philippine eagle can fly in 15 minutes

using the illustration below.

Learn about It!

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For every 1 minute that the Philippine eagle flies, it can travel 1.67 km.

Therefore, to find the total distance covered in 15 minutes, we must multiply

1.67 by 15.

Step 1: Arrange the factors vertically. Multiply the same way as you

would multiply whole numbers.

Step 2: The sum of the number of decimal places in the factors is the

number of decimal places in the product.

Therefore, the total distance the Philippine eagle can fly in 15

minutes is 25.05 km.

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STUDY GUIDE

Example 1: Find the product of 13.74 and 2.5.

Solution:

Step 1: Arrange the factors vertically. Multiply the same way as you

would multiply whole numbers.

Step 2: The sum of the number of decimal places in the factors is the

number of decimal places in the product.

Note: The rightmost zero after the decimal point can be

removed without changing the value of the number; that is,

34.350 = 34.35.

Let’s Practice!

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Try It Yourself!

What is the product of 81.4 and 2?

Example 2: Multiply 45 000 by 0.24.

Solution:

Step 1: Arrange the factors vertically. Multiply the same way as you

would multiply whole numbers.

Step 2: The sum of the number of decimal places in the factors is the

number of decimal places in the product.

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Thus, the product is 10 800.00 or 10 800.

Try It Yourself!

Multiply 5 600 by 3.65.

Example 3: Simplify: (310.53 + 481.004) × 0.35

Solution:

Step 1: Add first the decimal numbers inside the grouping symbol.

Step 2: Multiply the sum in step 1 by 0.35. Apply the procedure in the

previous examples.

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Therefore, simplifying (310.53 + 481.004) × 0.35 results in

277.0369.

Try It Yourself!

Multiply 0.48 by the difference of 890.12 and 527.83.

Real-World Problems

Example 4: Maria went out to the supermarket to do her

weekly errand. She was asked to buy 2.5 kg

of beef. If a kilogram of beef costs ₱184.50,

how much should Maria pay to the cashier?

Solution: To solve for the price of 2.5 kg of beef, multiply ₱184.50 by 2.5.

Step 1: Arrange the factors vertically. Multiply the same way as you

would multiply whole numbers.

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Step 2: The sum of the number of decimal places in the factors is the

number of decimal places in the product.

Therefore, Maria needs to pay an amount of ₱461.25 to the

cashier upon buying 2.5 kg of beef.

Try It Yourself!

The chef of a restaurant needs 6.5 kg of chicken. If the chicken costs

₱215.38 per kilogram, how much will it cost the chef?

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STUDY GUIDE

A. Multiply the following decimal numbers.

1. 35.43 × 121.9

2. 74.28 × 95.16

3. 14 095 × 13.15

4. 1 000 × 0.021

5. 145.9 × 1.55

B. Simplify the expressions below.

1. (358.8 − 192.7 ) × 0.83

2. 5.8 × (13.04 + 2.68)

3. (448.44 − 105.3) × (0.29 + 0.55)

C. Analyze and solve the following problems completely.

1. Juan found out that a kilogram of oranges costs ₱85.45. If he wishes

to buy 6.5 kg, how much must he pay the seller?

2. A rectangular lot measures 6 892.43 m long and 8.4 m wide. What is

the land area of the rectangular lot? (Hint: Area = length × width)

Check Your Understanding!

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STUDY GUIDE

Speed in Multiplication

Materials Needed: paper and pen

Instructions:

1. This activity is to be done individually. You have to accomplish this

work in not more than 10 minutes.

2. What is the product of

a. 91 and 20?

b. 213 and 40?

c. 77 and 200?

d. 429 and 500?

e. 822 and 70?

3. How were you able to multiply the given whole numbers with speed

and accuracy?

4. What technique did you apply?

5. Can we say that the technique you have used will be applicable as

well to decimal numbers?

Lesson 4: Multiplying Decimals Mentally up to Two

Decimal Places by 0.1, 0.01, 10, and 100

Warm Up!

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STUDY GUIDE

According to an article in The Arithmetic Teacher (Vol. 32 No. 6) written by

Robert E. Reys, the idea of mental computation is to solve a problem "all in

the head" without the use of other methods or tools such as calculators or

pencils and paper. The skill of mental computation is useful as we need to

compute numbers we see in our daily lives such as shopping, cooking, using

a foreign currency, among others. Most of these numbers are in the form of

decimals.

Using your skills in multiplying decimals, find the product of the following

numbers:

a. 0.1 and 9.42 __________

b. 0.01 and 9.42 __________

c. 10 and 9.42 __________

d. 100 and 9.42 __________

Listed below are the answers to the above items.

a. 0.942

b. 0.0942

c. 94.2

d. 942

Did you obtain the same answers? Have you noticed any pattern?

Learn about It!

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To multiply decimal numbers by 10 and 100, just move the decimal point to

the right to as many zeros as there are in 10 or 100.

Factors Product

2.3 × 100 230

2.3 × 10 23

2.3 × 1 2.3

To multiply decimal numbers by 0.1 and 0.01, just move the decimal point to

the left to as many decimal places as there are in 0.1 and 0.01.

Factors Product

2.3 × 0.1 0.23

2.3 × 0.01 0.023

Example 1: Find the value of 𝑛 in 45.67 × 100 = 𝑛

Solution: To multiply by 100, simply move the decimal point 2 places to

the right.

Let’s Practice!

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Therefore, 45.67 × 100 = 4 567.

Try It Yourself!

Multiply 781.301 × 100

Example 2: What is the product of 87.3 and 0.1?

Solution: To multiply by 0.1, simply move the decimal point 1 place to the

left.

Thus, 87.3 × 0.1 = 8.73.

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Try It Yourself!

Find the product of 2 782.57 and 0.01.

Example 3: Simplify: (74.21 + 82.04) × 0.01

Solution:

Step 1: Add 74.21 and 82.04 to clear the grouping symbols.

Step 2: Multiply the 156.25 by 0.01. To multiply by 0.01, simply move

the decimal point 2 places to the left.

Thus, when (74.21 + 82.04) × 0.01 is simplified, the result is

1.5625.

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STUDY GUIDE

Try It Yourself!

Simplify: (678.43 – 219.02) × 0.01

Real-World Problems

Example 4: A bank cashier has one hundred 25-centavo

coins in her drawer. How much are the coins

worth in pesos?

Solution:

Step 1: Write the number sentence.

₱0.25 × 100 = _______

Step 2: Count the number of zeros.

Step 3: Move the decimal point 2 places to the right.

The cashier has ₱25.00 worth of 25¢ coins in her drawer.

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STUDY GUIDE

Try It Yourself!

Samantha was able to save one hundred 10-centavo coins in

her piggy bank. How much are the coins worth in pesos?

A. Complete the table by multiplying the given numbers by 0.1, 0.01, 10,

and 100.

Given Multiply

by 0.1

Multiply by

0.01

Multiply by

10

Multiply by

100

450.043

7 510.387

520.718

B. Solve the following word problems.

1. Multiply the sum of 28.9 and 5.5 by 0.01.

2. A box is 5 181.2 cm long, 10 cm wide, and 100 cm tall. What is its

total volume? (Hint: Volume = Length × Width × Height)

3. How much is ten 25-centavo coins?

Check Your Understanding!

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STUDY GUIDE

1. How is the process of adding decimal numbers related to multiplying

decimal numbers?

2. Can you think of another way to multiply decimal numbers by 0.1? How

about by 0.01? How about by 10 and 100?

3. Which of the two statements is true? Justify your answer.

A. 256.23 + 0.42 × 0.01 = 2.5665

B. 256.23 + 0.42 × 0.01 = 256.2342

Part of growing is being socially aware and responsible. Home is one of the

base grounds for social awareness. One of the things a young student like

you should learn is to be mindful of financial management, which you can

apply later on in your daily living.

In grounding, your task is to interview your parents/guardian about the

expenses in your home. Focus on the monthly budget allotted and the bills

for electricity and water consumption in three months’ time. Use the chart

for your data entry.

Performance Task

Challenge Yourself!

Page 41: Addition, Subtraction, and Multiplication of Decimals

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STUDY GUIDE

Monthly budget Amount of electric bill Amount of

water consumption bill

Share your chart with the class. Answer the following questions as your guide

in sharing.

1. How much in total is the amount of electric bill in three months?

2. How much is the total amount water consumption bill in three months?

3. How much is the remaining budget if both electric bill and water

consumption bill are deducted from a monthly budget?

4. Are there differences in the amount of electric bill every month? How

about in the amount of water consumption? Support your answer.

Performance Task Rubric

Criteria

Below

Expectation

(0–49%)

Needs

Improvement

(50–74%)

Successful

Performance

(75–99%)

Exemplary

Performance

(99+%)

Simplification

of decimal

numbers

Some

solutions are

correct, and

no final

answer is

simplified.

Some

solutions are

correct, but

some of the

final answers

are not

simplified.

All solutions

are correct,

but some of

the final

answers are

not

simplified.

All solutions

are correct,

and all of the

final answers

are

simplified.

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STUDY GUIDE

Creativity,

neatness,

and

organization

of work

The chart is

less creative

and

unorganized.

The chart is

creative with

proper

designs, and

illustrations

are related to

the topic.

Organization

and neatness

is less

observable.

The chart is

creative with

proper

designs, and

illustrations

are related to

the topic.

Organization

and neatness

is more

observable.

The chart is

creative with

proper

designs, and

illustrations

are related to

the topic.

Organization

and neatness

is evidently

observable.

Wrap-up

Multiplied

Decimal points are

aligned.

Decimal points are

counted to determine

the decimal places of

the product.

can be

Added Subtracted

DECIMALS

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STUDY GUIDE

Key Terms/Formulas

Concept Description

Addition of

Decimals

When adding decimals, the decimal points of the

addends and that of the sum must be aligned. Zeros

can also be added to the far right of the addend that

has fewer decimal places than the other addends.

Subtraction of

Decimals

Subtraction of decimals is also performed similarly to

the subtraction of whole numbers. The decimal points

should be aligned, and zeros are to be included to the

right of the last digit, if necessary.

Multiplication of

Decimals

When multiplying decimals, multiply the factors as you

would when multiplying whole numbers. Then, count

the total number of decimal places in the factors and

use this in the product.

Multiplication of

Decimals by 0.1,

0.01, 10, and 100

When multiplying by 0.1 or 0.01, move the decimal

point one or two to places to the left, respectively. If

multiplying by 10 or 100, move the decimal places one

or two to places to the right, respectively.

Lesson 1

1. 469.7803

2. 1 138.95

3. 2 188.3015

4. 10.23 meters

Lesson 2

1. 253.19

2. 159.956

3. 20.2001

4. ₱3 889.55

Key to Let’s Practice!

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STUDY GUIDE

Lesson 3

1. 162.8

2. 20 440

3. 173.8992

4. ₱1 399.97

Lesson 4

1. 78 130.1

2. 27.8257

3. 4.5941

4. ₱10.00

De Leon Jr., Angel, et al. Today’s Math 6. 3rd ed. Philippines: SIBS Publishing

House Inc., 2000.

Prentice, Hall. “Chapter 3 Decimals.” Accessed February 19, 2018.

http://esminfo.prenhall.com/samplechps/tobey/pdf/ch03.pdf

Decimal Pocket. “Decimals.” Accessed February 19, 2018.

https://www.northshore.edu/cas/pdf/decimals_comp_packet.pdf

References