This document discusses dividing decimals. It explains that division is the inverse of multiplication and that decimals are fractions written in a special form. It defines terminating and non-terminating decimals and provides examples of each. It describes how to convert terminating decimals to fractions by removing the decimal point and non-terminating decimals using a repeating pattern. The document provides steps for dividing whole numbers by decimals, decimals by whole numbers, and decimals by decimals. It includes examples and problems for readers to practice these skills.

1. Dividing
Decimals

2. Keys to Learn:
Division - The division is the process of
repetitive subtraction. It is the inverse of the
multiplication operation.
Decimal - A decimal is a fraction written in a special form.
A decimal is a number that consists of a whole and a
fractional part. Decimal numbers lie between integers and
represent numerical value for quantities that are whole
plus some part of a whole.

4. What are terminating decimals?
Terminating decimal is a fraction decimal having a finite number of
digits after decimal point. In this case division ends after a finite
number of stages or numbers that end after a few repetitions, after
the decimal point. For example : 1/5, 1/4, 1/8 etc. are terminating
decimals because,

5. What are non-terminating decimals?
Non-terminating decimal is a fraction decimal having infinite
number of digits after decimal point. In this case division
never ends but recur the same digit or group of digits again
and again. So they are also called recurring decimals. For
example: 1/3, 2/3, 2/11 etc. are non-terminating decimals
because,

6. Here, a number or group of numbers are repeated
and do not end after a finite number of stages, such
number are denoted by a dot (.) or a bar(–) above
it.

7. Types of Non-terminating
Decimals:
There are two types of non-terminating (recurring)
decimals:
a. Simple recurring decimals: In this case the recurring
starts just after the decimal point. For example, 0.333…
b. Mixed recurring decimals: In this case the recurring
does not start just after the decimal point. For example,
0.5181818

8. Types of Non-terminating
Decimals:
There are two types of non-terminating (recurring)
decimals:
a. Simple recurring decimals: In this case the recurring
starts just after the decimal point. For example, 0.333…
b. Mixed recurring decimals: In this case the recurring
does not start just after the decimal point. For example,
0.5181818

9. For terminating decimal we can convert a decimal into
fraction simply by removing decimal and dividing by 10 if
there is 1 decimal place, by 100 if there is 2 decimal places
and by 1000 if there is 3 decimal places and so on.
CONVERSION OF DECIMAL INTO
FRACTION

10. For non-terminating decimal we can convert a decimal into
fraction by the following method as given in the example
below:
CONVERSION OF DECIMAL INTO
FRACTION

11. For non-terminating decimal we can convert a decimal into
fraction by the following method as given in the example
below:
CONVERSION OF DECIMAL INTO
FRACTION

12. For non-terminating decimal we can convert a decimal into
fraction by the following method as given in the example
below:
CONVERSION OF DECIMAL INTO
FRACTION

13. CONVERSION OF DECIMAL INTO
FRACTION
For non-terminating decimal we can convert a decimal into
fraction by the following method as given in the example
below:

14. ACTIVITY
Find the quotient and
differentiate the quotients
if it is terminating decimal
or repeating decimal.
1. 2 ÷ 9 4. 13 ÷ 16
2. 1 ÷ 6 5. 9 ÷ 45
3. 8 ÷ 9

15. A. Dividing Whole Number
by Decimal
B. Dividing Decimal by
Whole Number
C. Dividing Decimal by
another Decimal

17. DRILL:
MULTIPLY MENTALLY:
56 ÷ 0.1 125 ÷ 0.1
56 ÷ 0.001 125 ÷ 0.001
342 ÷ 0.001 48 ÷ 0.01
592 ÷ 0.001 72 ÷ 0.1

18. Dividing Whole
Number by
Decimal

19. Dividing Whole Number by
Decimal
Step 1: Multiply the divisor by a power of 10 to make it a whole
number or just move the decimal point to the right.
Step 2: Multiply the dividend by the same power of 10. Use 0 as
placeholder if needed. Move the decimal point of the dividend by
as many times
Step 3: Insert a decimal point in the quotient matching the decimal
in the dividend
Step 4 : Complete the division process
Form 1:
Dividend ÷ Divisor = Quotient
Example:
10 ÷ 5 = 2
Form 2:
Example:

20. Dividing Whole Number by
Decimal
Example Problems:
1.58÷2.5
2.248÷0.4
3.25÷1.5
4.36÷1.8
5.110÷0.01
175
5
.
2
105
5
.
3
648
2
.
7
460
5
.
2

21. Dividing
Decimal by
Whole Number

22. Dividing Decimal by Whole
Number
Step 1: Divide as you would divide in whole number
Step 2: Place the decimal point in the quotient directly above the
decimal point in the dividend
Form 1:
Dividend ÷ Divisor = Quotient
Example:
10 ÷ 5 = 2
Form 2:
Example:

23. Dividing Decimal by Whole
Number

24. Dividing Decimal by Whole
Number

25. Dividing
Decimal by
another
Decimal

26. Dividing Decimal by Whole
Number
Step 1: Multiply the divisor by a power of 10 to make it a whole
number or just move the decimal point to the right.
Step 2: Multiply the dividend by the same power of 0. Use 0 as
placeholder if needed.
Step 3: Divide as you would divide in whole number
Step 4: Place the decimal point in the quotient directly above the
decimal point in the dividend.
Form 1:
Dividend ÷ Divisor = Quotient
Example:
10 ÷ 5 = 2
Form 2:
Example:

27. Dividing Decimal by Another
Decimal

28. Dividing Decimal by Another
Decimal

29. Solve routine and non-
routine problems
involving division of
decimals, mixed
decimals and whole
numbers

30. Comprehension questions:
• What is asked?
• What are given?
• b. What operation should you use
to solve the problem? Why?
• c. Let the pupils write the number
sentence on the board.

31. MOTIVATION
Samuel’s daily allowance is
P20. He is saving P5 a day
and puts it in his piggy bank.
How would you describe
Samuel?
Would you do the same? Why?

32. Kenneth is saving P2.50 each
day. How many days
will it take him to save P50.00?
PRESENTATION

33. What does the
problem ask you to
find?
How will you find the
answer to the
problem?

34. PERFORMING
THE
ACTIVITY

35. PROBLEM SOLVING
UNDERSTAND: Find the number
of days it will take Kenneth to
save P50.00
PLAN: To solve the problem,
divide P50.00 by P2.50
SOLVE: Show your solution
Move the decimal point in the
divisor to make it a whole
number.
(Multiply it by 100)
a. x 100 = 250

36. Divide:
Check by multiplying the
quotient and the divisor.
ANSWER: It will take
Kenneth 20 days to save
P50.00

37. PROCESSING THE
ACTIVITY:
How did you SOLVE
THE PROBLEM?

38. REINFORCING THE CONCEPT
Read, analyze and solve
a. Lily earned P618.76 in 2.75
hours. How much did she earn
per hour?
B. Mirabela paid P783.75 for
4.75 kg of grapes. What was
the price per kilo?

39. C. Olive needs to repack
141 kg of rice in plastic
bags containing 2.4 kg of
rice sack. How many
plastic bags of rice will
she be able to make?

40. Summarizing the lesson:
How do we solve routine
and non-routine problems
involving division of
decimals, mixed decimals
and whole numbers
including money?

41. 2. Jimmy, John and six other
members of the delegation of
teachers and students will share
equally the cost of cabin rented. If
the cost is P10,225.50. How much
will each person pay?
3. The Girl scouts raised an amount
of P288.75 for a Cleanup project
after giving P5.25 each. How many
girl scouts contributed?

42. APPLICATION
Read and Solve:
Aubrey has 22.8 meters of
cloth. She wants to cut it
into pieces of 1.2 meters
long, how many pieces of
clothes will she get?

43. ASSESSMENT
Read and understand the
problems. Then solve.
1. An art teacher gives Joshua
several containers with a total
of 28.5 liters of paint for a
mural. He asks him to pour 1.5
liters into each smaller
containers. How many small
contaiNERS WILL JOSHUA
NEED?

44. 2. Jimmy, John and six other
members of the delegation of
teachers and students will
share equally the cost of cabin
rented. If the cost is
P10,225.50. How much will
each person pay?
3. The Girl scouts raised an
amount of P288.75 for a Cleanup
project after giving P5.25 each.
How many girl scouts contributed?

45. 4. For 6 days, Rolando had a
total of 10.5 hours of
overtime in his office. What
was his daily overtime?
5. The driver in a racing car
drove 190 km in 3.4 hours.
What was his average speed
expressed in kilometers per
hour?

46. Assignment:
Read and Solve
1. Roxanne has P38.50 left in her purse.
She has to buy ribbons for the gift. Each
meter of a ribbon costs P5.50. How many
meters of ribbon can she buy?
2. Mang Tony has 7.5 hectares of land. He
wants to divide it into 1.5 hectares each
for his sons. How many sons does Mang
Tony has?