addition, subtraction, and multiplication of decimals
TRANSCRIPT
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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STUDY GUIDE
- 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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Mill
ion
ths
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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STUDY GUIDE
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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STUDY GUIDE
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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STUDY GUIDE
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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STUDY GUIDE
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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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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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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STUDY GUIDE
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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STUDY GUIDE
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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STUDY GUIDE
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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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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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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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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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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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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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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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!
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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