Fractions and Decimals a. Addition and subtraction of fractions b. Multiplication and division on fractions c. Real life problems on fractions. Mathematics Primary 6 First Term Lesson Notes Week 6

Subject: 

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MATHEMATICS

Term:

FIRST TERM

Week:

WEEK 6

Class:

PRIMARY 6 / BASIC 6

Topic:

Fractions and Decimals

• Addition and Subtraction
• Multiplication and Division
• Real life problems .

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Previous lesson: 

The pupils have previous knowledge of

Multiplication of Numbers

that was taught as a topic in the previous lesson

 

Behavioural objectives:

At the end of the lesson, pupils will be able to

 

• Add or subtract any given set of Fractions
• Multiply or divide any given set of Fractions
• Change fractions to decimals and vice versa
• Interprete and solve real life problems on fractions and decimals.

 

Instructional Materials:

• Wall charts
• Pictures
• Related Online Video
• Flash Cards
• Abacus

 

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Methods of Teaching:

• Class Discussion
• Group Discussion
• Asking Questions
• Explanation
• Role Modelling
• Role Delegation

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Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• Lagos State Basic Education Curriculum

 

Content:

What is a fraction?

A fraction is a part of a whole. It is a way of representing a part of a whole or a number that is not a whole number. It consists of two numbers separated by a horizontal line, called a fraction bar. The number on top of the fraction bar is called the numerator, and the number on the bottom of the fraction bar is called the denominator.

For example, the fraction 3/4 represents 3 parts of a whole that has been divided into 4 equal parts. The numerator (3) represents the number of parts being considered, and the denominator (4) represents the total number of parts into which the whole has been divided.

Fractions can also represent quantities that are less than 1, such as 1/2, which represents 1 part of a whole that has been divided into 2 equal parts.

Fractions can be written in several different forms, including mixed numbers and decimals. A mixed number is a whole number and a fraction combined, such as 2 1/4, which represents 2 whole parts plus 1 part of a whole that has been divided into 4 equal parts. A decimal is a fraction represented in base-10 notation, with the numerator represented as a number to the right of the decimal point. For example, the fraction 3/4 can be written as a decimal as 0.75.

It’s important to remember that fractions represent quantities that are less than 1, whereas decimals represent quantities that can be greater than or less than 1.

Types of Fractions

There are some of the types of fractions:

1. Proper fractions: A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). For example, 1/2 and 3/4 are proper fractions.
2. Improper fractions: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 5/4 and 9/8 are improper fractions.
3. Mixed numbers: A mixed number is a whole number and a fraction combined, such as 2 1/4 or 3 3/8.
4. Simplest form: A fraction is in simplest form when the numerator and denominator have no common factors other than 1. For example, 4/8 is not in simplest form because both 4 and 8 can be divided by 2, but 1/4 is in simplest form because the only common factor is 1.
5. Reciprocal fractions: A reciprocal fraction is a fraction where the numerator and denominator are switched. For example, the reciprocal of 2/3 is 3/2.
6. Negative fractions: A negative fraction is a fraction with a negative sign in front of it. For example, -1/3 is a negative fraction.
7. Complex fractions: A complex fraction is a fraction that contains one or more fractions in the numerator, denominator, or both. For example, 1/(2/3) is a complex fraction.

 

Addition and Subtraction of Fractions

To add or subtract fractions, you must first make sure that the fractions have the same denominator (the bottom number). If the fractions have different denominators, you can use the least common denominator (LCD) to convert them to equivalent fractions with the same denominator.

For example, consider the following fractions:

1/3 + 1/4

The denominators of these fractions (3 and 4) are not the same, so you need to find the LCD to add them. The LCD of 3 and 4 is 12, so you can convert the fractions to equivalent fractions with a denominator of 12:

1/3 + 1/4 = 4/12 + 3/12 = 7/12

Now that the fractions have the same denominator, you can add them by adding the numerators (the top numbers) and keeping the denominator the same:

4/12 + 3/12 = 7/12

To subtract fractions, you follow the same process. First, convert the fractions to equivalent fractions with the same denominator, and then subtract the numerators while keeping the denominator the same:

1/3 – 1/4 = 4/12 – 3/12 = 1/12

It’s important to remember that you cannot add or subtract fractions with different denominators unless you first convert them to equivalent fractions with the same denominators.

 

Evaluation.

 

What are decimal numbers

A decimal fraction is a way of expressing a number that is between two whole numbers. It is written using a decimal point, which separates the whole number part of the number from the fractional part.

A decimal fraction has its denominator to be ten, one hundred, one thousand and so on based on the number of decimal places that are in that particular decimal number or fraction.

Examples of decimal fractions with their numbers of decimal places are

• 0.75 (two decimal places)
• 0.5 ( one decimal place)
• 12.45 (two decimal places)
• 100.1 (one decimal place)
• 32.13 (two decimal places)

For example, the number 0.75 is a decimal fraction. The “0” is the whole number part of the number, and the “75” is the fractional part. The decimal point separates these two parts.

 

Decimal fractions are used to represent numbers that are not whole numbers, such as 0.75 (which represents 3/4) or 0.5 (which represents 1/2). They are used in many different applications, including in mathematics, finance, and science.

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To write a decimal fraction, we place the whole number part to the left of the decimal point and the fractional part to the right. For example, the number 0.75 is written with the whole number “0” to the left of the decimal point and the fractional part “75” to the right.

Addition and Subtraction of Decimals.

To add or subtract decimals, you must first align the decimal points in a column. This ensures that the digits in the same place value are being added or subtracted.

For example, consider the following decimals:

2.34 + 0.56

To add these decimals, you can align the decimal points and add the digits in each place value:

2.34

+ 0.56

—————–

2.90

——————-

To subtract these decimals, you can align the decimal points and subtract the digits in each place value:

2.34

– 0.56

———————-

1.78

———————

It’s important to remember to carry or borrow as needed when adding or subtracting decimals. For example:

0.9 + 0.1 = 1.0

9.5 – 3.7 = 5.8

It’s also important to pay attention to the number of decimal places in the result. If the decimals being added or subtracted have different numbers of decimal places, you may need to add zeros to the end of one or more of the decimals to align the decimal points correctly.

For example:

0.9 + 0.10 = 1.00

9.5 – 3.70 = 5.80

By following these steps, you can easily add and subtract decimals.

Example 1: Addition of Fractions

1. Add 1/4 and 1/3. Solution:
   • Find a common denominator: 12 (the least common multiple of 4 and 3).
   • Rewrite both fractions with the common denominator: 3/12 + 4/12.
   • Add the numerators: 3 + 4 = 7.
   • Keep the common denominator: 7/12.

Example 2: Subtraction of Fractions 2. Subtract 2/5 from 3/5. Solution:

• Since the denominators are the same, you can subtract the numerators directly: 3/5 – 2/5 = 1/5.

Example 3: Multiplication of Fractions 3. Multiply 2/3 by 4/5. Solution:

• Multiply the numerators: 2 * 4 = 8.
• Multiply the denominators: 3 * 5 = 15.
• The result is 8/15.

Example 4: Division of Fractions 4. Divide 3/4 by 2/3. Solution:

• To divide fractions, multiply the first fraction by the reciprocal of the second: 3/4 * 3/2.
• Multiply the numerators: 3 * 3 = 9.
• Multiply the denominators: 4 * 2 = 8.
• The result is 9/8.

Example 5: Mixed Number to Improper Fraction 5. Convert the mixed number 2 1/4 to an improper fraction. Solution:

• Multiply the whole number by the denominator of the fraction and add the numerator: 2 * 4 + 1 = 9.
• Keep the denominator: 9/4.

Example 6: Addition of Mixed Numbers 6. Add 1 1/2 and 2 1/4. Solution:

• Convert both mixed numbers to improper fractions: 3/2 + 9/4.
• Find a common denominator: 4 (the least common multiple of 2 and 4).
• Rewrite both fractions with the common denominator: 6/4 + 9/4.
• Add the numerators: 6 + 9 = 15.
• Keep the common denominator: 15/4.

Example 7: Subtraction of Mixed Numbers 7. Subtract 3 2/5 from 4 3/4. Solution:

• Convert both mixed numbers to improper fractions: 19/5 – 23/4.
• Find a common denominator: 20 (the least common multiple of 5 and 4).
• Rewrite both fractions with the common denominator: 76/20 – 115/20.
• Subtract the numerators: 76 – 115 = -39.
• Keep the common denominator: -39/20.

Example 8: Multiplication of Mixed Numbers 8. Multiply 2 1/2 by 1 2/3. Solution:

• Convert both mixed numbers to improper fractions: 5/2 * 5/3.
• Multiply the numerators: 5 * 5 = 25.
• Multiply the denominators: 2 * 3 = 6.
• The result is 25/6.

Example 9: Division of Mixed Numbers 9. Divide 3 3/4 by 1 1/2. Solution:

• Convert both mixed numbers to improper fractions: 15/4 ÷ 3/2.
• To divide fractions, multiply the first fraction by the reciprocal of the second: 15/4 * 2/3.
• Multiply the numerators: 15 * 2 = 30.
• Multiply the denominators: 4 * 3 = 12.
• The result is 30/12, which can be simplified to 5/2.

Example 10: Decimal to Fraction 10. Convert 0.75 to a fraction. Solution: – Identify the place value: 0.75 is read as seventy-five hundredths. – Write it as a fraction: 75/100. – Simplify the fraction: Divide both the numerator and denominator by their greatest common divisor, which is 25. The result is 3/4.

 

Evaluation :

1. What is the sum of 2.34 and 0.56? a) 2.90 b) 2.91 c) 2.92 d) 2.93
2. What is the difference between 4.12 and 2.01? a) 2.11 b) 2.10 c) 2.09 d) 2.08
3. What is the sum of 5.678 and 6.432? a) 12.110 b) 12.111 c) 12.112 d) 12.113
4. What is the difference between 8.9 and 7.1? a) 1.8 b) 1.7 c) 1.6 d) 1.5
5. What is the sum of 0.1 and 0.2? a) 0.3 b) 0.4 c) 0.5 d) 0.6
6. What is the difference between 0.9 and 0.8? a) 0.1 b) 0.2 c) 0.3 d) 0.4
7. What is the sum of 1.23 and 4.56? a) 5.79 b) 5.78 c) 5.77 d) 5.76
8. What is the difference between 6.7 and 9.8? a) -3.1 b) -3.2 c) -3.3 d) -3.4
9. What is the sum of 8.9 and 1.2? a) 10.1 b) 10.2 c) 10.3 d) 10.4
10. What is the difference between 5.6 and 2.5? a) 3.1 b) 3.2 c) 3.3 d) 3.4
11. 3/5 + 2/5 = ____. a) 5/10 b) 5/5 c) 3/5 d) 2/10
12. 5/6 – 1/6 = ____. a) 4/6 b) 1/6 c) 5/12 d) 6/5
13. 2/3 × 4/5 = ____. a) 8/15 b) 6/20 c) 10/12 d) 1/3
14. 3/4 ÷ 2/3 = ____. a) 9/8 b) 6/7 c) 1/2 d) 4/6
15. Convert 1 3/4 to an improper fraction: ____. a) 1/4 b) 7/4 c) 4/3 d) 4/7
16. 1 1/2 + 2 1/2 = ____. a) 4/4 b) 3/4 c) 4/2 d) 3/2
17. 2 3/4 – 1 1/4 = ____. a) 1/2 b) 2/2 c) 1/4 d) 1 1/2
18. 2 1/3 × 3/4 = ____. a) 2/9 b) 3/2 c) 2 2/3 d) 2 3/4
19. 4 1/2 ÷ 1 1/2 = ____. a) 3 b) 4/3 c) 1 d) 2 2/3
20. Convert 0.25 to a fraction: ____. a) 25/100 b) 1/4 c) 5/20 d) 0/100
21. 0.6 – 0.3 = ____. a) 0.3 b) 3 c) 0.03 d) 0.03
22. 0.5 × 0.4 = ____. a) 0.2 b) 20 c) 2 d) 0.02
23. 0.9 ÷ 0.3 = ____. a) 0.6 b) 3 c) 0.6 d) 6
24. Solve 2/3 + 0.25 = ____. a) 5/4 b) 1 1/4 c) 1 1/3 d) 2 1/4
25. Solve 3/4 – 0.5 = ____. a) 1/4 b) 3/2 c) 3/4 d) 1 1/4

 

Presentation

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The topic is presented step by step

 

Step 1:

The class teacher revises the previous topics

 

Step 2.

He introduces the new topic

 

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

 

 

 

Conclusion

In conclusion, addition and subtraction of decimals involves aligning the decimal points in a column and performing the operations on the digits in each place value. It’s important to carry or borrow as needed and to pay attention to the number of decimal places in the result. By following these steps, you can easily add and subtract decimals to solve problems in various contexts.

The class teacher wraps up or concludes the lesson by giving out short notes to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where the needs arise.

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