Decimal Fractions : Addition, Subtraction and Conversion of Decimals

SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS

SUBJECT: MATHEMATICS

CLASS: BASIC FOUR / / PRIMARY 4

WEEK 3

Topic : Decimal Fractions : Addition and Subtraction of Decimals 

Importance

• To calculate degree
  accuracy on weight,
  money and distance
  events.
• To record winning tin
  at a track meet

Learning Objectives

Pupils should be able to:

• identify decimal fractions up
  to tenths, hundredth and
  thousandths
• change from fractions to
  decimals
• calculate addition and
  subtraction of decimals
• solve quantitative reasoning
  involving decimal problems

Learning Activities

Pupils in a small groups use cardboard to

design 0.25 which is one quarter of a circle.

Embedded Core Skills

• Critical thinking and problem solving
• Communication and Collaboration
• Leadership skills and Personal Development
• Creativity and Imagination

Learning Materials

Card board

Marker

Scissors

Record of time in sport events.

Content

What are Decimal Fractions?

Decimal fractions, also known as decimal numbers or decimal notation, are a way of expressing fractions using a base-ten place value system. In decimal fractions, the denominator is always a power of ten, such as 10, 100, 1000, etc., and the numerator is a whole number.

The decimal point is used to separate the whole number part from the fractional part. The digits to the right of the decimal point represent the fractional part of the number. For example, the decimal number 2.34 can be written as the fraction 234/100, which simplifies to 117/50.

Decimal fractions are commonly used in everyday life, such as in money and measurements, as they provide a simple and easy-to-understand way of expressing fractions. They are also used extensively in mathematics, science, and engineering.

Evaluation

1. Which of the following is a decimal fraction? a. 1/4 b. 3/5 c. 0.5 d. 2/3
2. What is the decimal representation of 5/8? a. 0.375 b. 0.4 c. 0.6 d. 0.625
3. Which of the following is equivalent to 0.125? a. 1/8 b. 1/4 c. 1/3 d. 1/2
4. What is the decimal representation of 3/20? a. 0.15 b. 0.3 c. 0.35 d. 0.4
5. Which of the following is a terminating decimal? a. 1/3 b. 1/6 c. 1/8 d. 1/10
6. What is the decimal representation of 7/25? a. 0.28 b. 0.275 c. 0.29 d. 0.3
7. What is the value of the digit 5 in the decimal number 3.578? a. 0.005 b. 0.05 c. 0.5 d. 5
8. What is the decimal representation of 2/9? a. 0.222… b. 0.24 c. 0.25 d. 0.27
9. Which of the following is a repeating decimal? a. 0.375 b. 0.416 c. 0.529 d. 0.6
10. What is the decimal representation of 4 and 1/3? a. 4.33 b. 4.3 c. 4.25 d. 4.5

Addition and Subtraction of Decimals

Addition of Decimals: Adding decimals is similar to adding whole numbers, except we have to make sure that the decimal points are lined up. Here’s an example:

1.25

• 0.75

2.00

We start by adding the ones place, which gives us 5. We carry over the 1 to the tenths place, and add 2 and 7 to get 9. Finally, we add the decimal point to get the answer of 2.00.

Subtraction of Decimals: Subtracting decimals is also similar to subtracting whole numbers, except we have to make sure that the decimal points are lined up. Here’s an example:

3.50

• 1.25

2.25

We start by subtracting the ones place, which gives us 2. We then subtract the tenths place, which gives us 2 and 5, but since we can’t subtract 5 from 0, we borrow 1 from the tens place to make the tenths place 10. We then subtract 5 from 10 to get 5, and subtract the decimal point to get the answer of 2.25.

It’s important to note that when we’re lining up the decimals, we add zeroes to the end of the shorter number so that they have the same number of decimal places. For example:

4.6

• 2.01

6.61

Here, we add a zero to the end of 4.6 to make it 4.60, so that we can line up the decimal points with 2.01. Then, we add the two numbers just like we did in the first example

Evaluation

1. What is the sum of 2.5 and 1.25? a. 2.75 b. 3.25 c. 3.5 d. 3.75
2. What is the difference between 6.25 and 3.5? a. 2.75 b. 2.5 c. 2.25 d. 1.75
3. What is the sum of 0.25 and 0.75? a. 1.5 b. 0.75 c. 1 d. 1.25
4. What is the difference between 4.8 and 2.15? a. 2.35 b. 2.65 c. 2.75 d. 2.95
5. What is the sum of 4.35 and 2.5? a. 6.25 b. 6.85 c. 7.15 d. 7.85
6. What is the difference between 5.75 and 2.25? a. 3.25 b. 3.5 c. 3.75 d. 4
7. What is the sum of 1.3 and 2.46? a. 3.76 b. 3.63 c. 3.56 d. 3.43
8. What is the difference between 7.6 and 5.25? a. 2.25 b. 2.35 c. 2.45 d. 2.55
9. What is the sum of 3.7 and 1.25? a. 4.75 b. 5 c. 5.15 d. 5.35
10. What is the difference between 10.5 and 8.25? a. 2.25 b. 2.35 c. 2.45 d. 2.55

Identification of decimal fractions up
to tenths, hundredth and
thousandths

A decimal fraction is a fraction that has a denominator of 10, 100, 1000, or another power of 10. It is written using a decimal point and digits to the right of the decimal point, which represent parts of a whole.

For example, the fraction 1/10 can be written as the decimal 0.1, the fraction 1/100 can be written as the decimal 0.01, and the fraction 1/1000 can be written as the decimal 0.001. Here are some examples of how to identify decimal fractions:

Example 1: Identify the decimal fraction in the number 3.4.

The digit 4 is in the tenths place, so the decimal fraction is 0.4.

Example 2: Identify the decimal fraction in the number 2.16.

The digit 1 is in the hundredths place and the digit 6 is in the tenths place, so the decimal fraction is 0.16.

Example 3: Identify the decimal fraction in the number 0.075.

The digit 5 is in the thousandths place, the digit 7 is in the hundredths place, and the digit 0 is in the tenths place, so the decimal fraction is 0.075.

To identify a decimal fraction, you just need to look at the digits to the right of the decimal point and determine which place value they correspond to. If the digit is in the tenths place, the decimal fraction is a tenth; if the digit is in the hundredths place, the decimal fraction is a hundredth; and if the digit is in the thousandths place, the decimal fraction is a thousandth.

Evaluation

1. What is the decimal fraction in the number 2.5? a. 0.25 b. 0.5 c. 0.05 d. 0.025
2. What is the decimal fraction in the number 1.06? a. 0.6 b. 0.06 c. 0.16 d. 0.106
3. What is the decimal fraction in the number 0.8? a. 0.08 b. 0.8 c. 0.008 d. 0.0008
4. What is the decimal fraction in the number 3.42? a. 0.3 b. 0.04 c. 0.42 d. 0.342
5. What is the decimal fraction in the number 0.015? a. 0.005 b. 0.05 c. 0.15 d. 0.015
6. What is the decimal fraction in the number 7.01? a. 0.7 b. 0.1 c. 0.01 d. 0.001
7. What is the decimal fraction in the number 5.63? a. 0.6 b. 0.03 c. 0.63 d. 0.563
8. What is the decimal fraction in the number 2.005? a. 0.005 b. 0.05 c. 0.5 d. 0.0055
9. What is the decimal fraction in the number 0.235? a. 0.023 b. 0.23 c. 0.0035 d. 0.235
10. What is the decimal fraction in the number 1.008? a. 0.1 b. 0.008 c. 0.0008 d. 0.08

Change from Fractions to decimals

To change a fraction to a decimal, we need to divide the numerator by the denominator. Here’s an example:

Example 1: Change the fraction 3/4 to a decimal.

To change 3/4 to a decimal, we divide 3 by 4:

0.75

So 3/4 as a decimal is 0.75.

Example 2: Change the fraction 1/8 to a decimal.

To change 1/8 to a decimal using long division, we can set up the division problem like this:

0.125 (quotient)
8 | 1.000 (dividend)

-0.8

0.20

-0.16

0.04

So 1/8 as a decimal is 0.125.

It’s important to remember that when we divide the numerator by the denominator, the result will be a terminating decimal (a decimal with a finite number of digits) or a repeating decimal (a decimal with a repeating pattern of digits). For example:

• 1/2 = 0.5 (terminating decimal)
• 1/3 = 0.333… (repeating decimal)
• 2/7 = 0.2857142857… (repeating decimal)

To write repeating decimals, we can use a line over the digits that repeat. For example, 2/7 can be written as 0.285714̅.

Evaluation

1. What is 3/5 as a decimal? a. 0.3 b. 0.5 c. 0.6 d. 0.8
2. What is 2/10 as a decimal? a. 0.02 b. 0.2 c. 0.20 d. 0.002
3. What is 1/4 as a decimal? a. 0.1 b. 0.25 c. 0.4 d. 0.75
4. What is 1/3 as a decimal? a. 0.33 b. 0.3 c. 0.333 d. 0.3333
5. What is 4/5 as a decimal? a. 0.4 b. 0.5 c. 0.8 d. 0.125
6. What is 3/8 as a decimal? a. 0.375 b. 0.38 c. 0.383 d. 0.385
7. What is 5/6 as a decimal? a. 0.6 b. 0.833 c. 0.85 d. 0.666
8. What is 1/12 as a decimal? a. 0.12 b. 0.08 c. 0.083 d. 0.0083
9. What is 2/3 as a decimal? a. 0.66 b. 0.67 c. 0.75 d. 0.83
10. What is 7/10 as a decimal? a. 0.7 b. 0.07 c. 0.10 d. 0.71

Change from decimals to fractions

To change a decimal to a fraction, we need to use the place value of each digit to write the decimal as a fraction. Here’s an example:

Example 1: Change the decimal 0.5 to a fraction.

The digit 5 is in the tenths place, so we can write 0.5 as: 5/10

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 5:  5/10 = 1/2

So 0.5 as a fraction is 1/2.

We can also change decimals to fractions with larger denominators by multiplying both the numerator and denominator by the same power of 10. For example:

Example 2: Change the decimal 0.25 to a fraction with a denominator of 100.

The digit 2 is in the tenths place and the digit 5 is in the hundredths place, so we can write 0.25 as:  25/100

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 25:  25/100 = 1/4

So 0.25 as a fraction with a denominator of 100 is 1/4.

It’s important to remember that when we write a decimal as a fraction, we should simplify the fraction by dividing both the numerator and denominator by their greatest common factor. For example:

• 0.2 = 1/5 (already simplified)
• 0.375 = 3/8 (simplified by dividing by 125, the greatest common factor of 3 and 8)

Evaluation

1. What is 0.5 as a fraction in simplest form? a. 1/2 b. 1/4 c. 2/5 d. 2/10
2. What is 0.25 as a fraction in simplest form? a. 1/4 b. 1/2 c. 2/5 d. 2/10
3. What is 0.75 as a fraction in simplest form? a. 3/8 b. 1/2 c. 3/4 d. 7/10
4. What is 0.125 as a fraction in simplest form? a. 1/125 b. 1/25 c. 1/8 d. 1/3
5. What is 0.6 as a fraction in simplest form? a. 3/5 b. 2/3 c. 6/10 d. 6/100
6. What is 0.333 as a fraction in simplest form? a. 1/3 b. 1/6 c. 1/9 d. 3/10
7. What is 0.8 as a fraction in simplest form? a. 4/5 b. 8/10 c. 2/5 d. 8/100
8. What is 0.4 as a fraction in simplest form? a. 2/5 b. 1/5 c. 4/10 d. 4/100
9. What is 0.1250 as a fraction in simplest form? a. 1/8 b. 1/80 c. 125/1000 d. 1250/10000
10. What is 0.2 as a fraction in simplest form? a. 1/2 b. 2/5 c. 1/20 d. 20/100

Lesson Presentation

I. Introduction

• Greet the students and explain that today, we will be learning how to change decimals to fractions
• Review the concept of decimals and fractions, and their relationship to each other

II. Direct Instruction

• Explain that to change a decimal to a fraction, we need to use the place value of each digit
• Provide examples on the board and show the students how to write the decimal as a fraction, simplifying the fraction by dividing both the numerator and denominator by their greatest common factor
• Provide additional examples and ask the students to identify the place value of each digit and write the decimal as a fraction
• Show the students how to change a decimal to a fraction with a larger denominator by multiplying both the numerator and denominator by the same power of 10
• Provide additional examples and ask the students to write the decimal as a fraction with a specified denominator

III. Guided Practice

• Provide a worksheet with practice problems and ask the students to work through the problems with your guidance
• Monitor the students’ progress and provide assistance as needed

IV. Independent Practice

• Provide a worksheet with practice problems and ask the students to work independently to complete the problems
• Collect the worksheets and provide feedback to the students

V. Conclusion

• Review the key concepts covered in the lesson
• Provide examples for the students to work through on their own and ask them to share their answers with the class
• Answer any remaining questions and provide additional resources for students to practice changing decimals to fractions

VI. Assessment

• Observe the students during the guided and independent practice activities to assess their understanding of the concept
• Collect and review the students’ worksheets to assess their ability to change decimals to fractions

VII. Weekly Assessment /Test

• Decimal fractions are fractions with denominators of ___________, ___________, ___________, etc.
• The digits to the right of the decimal point in a decimal represent fractions of a whole unit, such as ___________, ___________, or ___________.
• When adding or subtracting decimals, we need to make sure that the ___________ ___________ line up.
• In the expression 3.45 + 2.1, the sum is ___________.
• In the expression 7.63 – 4.92, the difference is ___________.
• To convert a decimal to a fraction, we use the ___________ ___________ of each digit to write the decimal as a fraction.
• To simplify a fraction, we divide both the numerator and denominator by their greatest ___________ ___________.
• To convert a fraction to a decimal, we divide the numerator by the ___________.
• A terminating decimal has a ___________ number of digits.
• A repeating decimal has a ___________ ___________ of digits