Fractions Equivalent fractions Addition and subtraction of like and unlike fractions. Reducing to lowest term

SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS

SUBJECT: MATHEMATICS

CLASS: BASIC FOUR / / PRIMARY 4

WEEK 2

TOPIC : Fractions
Equivalent fractions
Addition and
subtraction of like and
unlike fractions.
Reducing to lowest
term

IMPORTANCE

It helps pupils know how
to divide whatever they
are given among
themselves into equal
sizes.

Behavioural Objectives 

Pupils should be able to

• obtain equivalent fractions of
  a given fraction.
• calculate addition and
  subtraction of like and unlike
  terms fractions.
• apply fractions in sharing
  commodities in home,
  market, school etc
• solve quantitative reasoning
  on equivalent fractions.

Learning Activities

• Pupils as individuals design number line showing equivalent fractions.
• Pupils in small groups design a pattern block card to find equivalent fractions.

Embedded Core Skills

• Critical thinking and
  problem solving
• Communication and
  collaboration
• Leadership and
  personal development
• Creativity and
  imagination

Learning Resources

AUDIO VISUAL
RESOURCES

• Paper cuttings of
  different shapes
  Squares
  Cardboards

Content

What are fractions

Fractions are a way to represent a part of a whole or a portion of a quantity. A fraction consists of two parts: the numerator and the denominator, separated by a horizontal line. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts that make up the whole.

For example, the fraction 3/4 represents three parts out of a total of four equal parts. Another way to think of this is that if we divide something into four equal parts, three of those parts make up 3/4 of the whole.

Fractions can be represented in different forms. For example, 3/4 is equivalent to 6/8 or 9/12, because all of these fractions represent the same proportion of a whole.

Fractions are used in many different areas, including mathematics, science, and everyday life. They are used to represent quantities that are not whole numbers, such as parts of a dollar or parts of a measurement, as well as in many mathematical operations such as addition, subtraction, multiplication, and division.

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Equivalent Fractions

Equivalent fractions are fractions that represent the same portion or amount, even though they may look different. To understand equivalent fractions, it’s important to know that fractions are like pictures or representations of something, and just like a picture, you can draw it in different ways, but it’s still the same thing.

Let’s start with a simple example: the fraction 1/2. This fraction represents one part out of a total of two equal parts. Now, let’s imagine that we divide the same thing into four equal parts. If we shade in two of those parts, we would have 2/4, which also represents the same portion as 1/2. So, 1/2 and 2/4 are equivalent fractions.

We can also show equivalent fractions by multiplying or dividing both the numerator and denominator of a fraction by the same number. For example, if we have the fraction 2/3 and we multiply both the numerator and denominator by 2, we get 4/6. Even though the numbers are different, these two fractions represent the same amount or portion, so they are equivalent.

Here’s another example: let’s say we have the fraction 3/5. If we want to find an equivalent fraction that has a denominator of 10, we can multiply both the numerator and denominator by 2. This gives us 6/10, which represents the same portion or amount as 3/5.

So, equivalent fractions are fractions that represent the same portion or amount, even though they may look different. We can find equivalent fractions by dividing or multiplying the numerator and denominator of a fraction by the same number, or by dividing the same whole into different numbers of equal parts.

Addition and subtraction of Equivalent Fractions

When we add or subtract fractions, it’s important to make sure that the fractions have the same denominator, because we can only add or subtract parts that are the same size. Equivalent fractions are fractions that have the same value, or represent the same amount, but may have different denominators.

To add or subtract equivalent fractions, we first need to find a common denominator. We can do this by finding a multiple of both denominators, or by using the least common multiple. Once we have a common denominator, we can add or subtract the numerators.

Here’s an example: let’s say we want to add 1/4 and 1/6. First, we need to find a common denominator. One way to do this is to find the least common multiple of 4 and 6, which is 12. We can then convert both fractions to have a denominator of 12. To do this, we can multiply the numerator and denominator of 1/4 by 3, and the numerator and denominator of 1/6 by 2. This gives us:

1/4 = 3/12 1/6 = 2/12

Now, we can add these two equivalent fractions by adding their numerators:

3/12 + 2/12 = 5/12

So, 1/4 + 1/6 = 5/12.

Let’s look at another example, this time with subtraction: suppose we want to subtract 1/3 from 2/3. Again, we need to find a common denominator. Since the denominators are already multiples of each other, we can use 3 as our common denominator. We can write the fractions as:

2/3 = 2/3 1/3 = 1/3

Now, we can subtract these equivalent fractions by subtracting their numerators:

2/3 – 1/3 = 1/3

So, 2/3 – 1/3 = 1/3.

That’s the basic idea of how to add and subtract equivalent fractions! By finding a common denominator and then adding or subtracting the numerators, we can add or subtract fractions that may have different denominators.

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Evaluation

1. What is the first step in adding or subtracting fractions with different denominators? a) Multiply the numerators and denominators b) Find a common denominator c) Divide the numerators and denominators d) None of the above
2. Which of the following fractions is equivalent to 3/8? a) 6/16 b) 5/8 c) 9/16 d) 1/3
3. What is the result of adding 2/5 and 3/10? a) 1/2 b) 5/10 c) 1/5 d) 5/15
4. What is the result of subtracting 1/4 from 2/3? a) 5/12 b) 1/3 c) 3/4 d) 2/7
5. Which of the following fractions is equivalent to 4/9? a) 8/18 b) 5/9 c) 2/3 d) 6/12
6. What is the result of adding 2/7 and 3/5? a) 29/35 b) 1/35 c) 17/35 d) 5/35
7. Which of the following fractions is equivalent to 2/3? a) 4/5 b) 8/12 c) 5/6 d) 1/2
8. What is the result of subtracting 1/2 from 3/4? a) 1/2 b) 1/4 c) 1/8 d) 1/16
9. What is the result of adding 2/9 and 5/18? a) 7/27 b) 1/6 c) 2/7 d) 11/18
10. Which of the following fractions is equivalent to 3/4? a) 12/16 b) 6/8 c) 9/12 d) All of the above

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Multiplication and Division of Equivalent Fractions

When we multiply or divide fractions, it’s important to understand that we are multiplying or dividing the whole, and that we are not changing the value of the fraction. In other words, if we multiply both the numerator and denominator of a fraction by the same number, the value of the fraction remains the same.

To multiply fractions, we simply multiply the numerators together and the denominators together. For example, if we want to multiply 2/3 by 4/5, we can write:

2/3 x 4/5 = (2 x 4) / (3 x 5) = 8/15

So, 2/3 x 4/5 = 8/15.

To divide fractions, we flip the second fraction (the one we are dividing by) and then multiply. For example, if we want to divide 2/3 by 4/5, we can write:

2/3 ÷ 4/5 = 2/3 x 5/4 = (2 x 5) / (3 x 4) = 10/12

So, 2/3 ÷ 4/5 = 10/12.

Now, let’s talk about equivalent fractions. If we multiply or divide both the numerator and denominator of a fraction by the same number, we get an equivalent fraction that represents the same amount or portion.

For example, if we have the fraction 1/2 and we multiply both the numerator and denominator by 2, we get 2/4. Even though the numbers are different, these two fractions represent the same amount or portion, so they are equivalent.

To see how this works in multiplication and division, let’s take the example of 2/3 and 4/5 again. If we multiply both fractions by 2, we get:

2/3 x 2/2 = 4/6 4/5 x 2/2 = 8/10

Now, we can multiply these equivalent fractions to get:

4/6 x 8/10 = (4 x 8) / (6 x 10) = 32/60

So, 2/3 x 4/5 = 32/60.

Similarly, if we divide both fractions by 2, we get:

2/3 ÷ 2/2 = 2/6 4/5 ÷ 2/2 = 4/10

Now, we can divide these equivalent fractions to get:

2/6 ÷ 4/10 = 2/6 x 10/4 = (2 x 10) / (6 x 4) = 20/24

So, 2/3 ÷ 4/5 = 20/24.

That’s the basic idea of how to multiply and divide equivalent fractions! By multiplying or dividing both the numerator and denominator of a fraction by the same number, we get an equivalent fraction that represents the same amount or portion. We can then use these equivalent fractions to multiply or divide.

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Evaluation

1. What is the result of multiplying 2/3 and 3/4? a) 6/12 b) 1/2 c) 3/8 d) 5/7
2. Which of the following fractions is equivalent to 2/5? a) 4/10 b) 8/20 c) 1/2 d) All of the above
3. What is the result of dividing 2/3 by 4/5? a) 10/12 b) 5/6 c) 8/15 d) 3/8
4. Which of the following fractions is equivalent to 3/4? a) 6/8 b) 9/12 c) 12/16 d) All of the above
5. What is the result of multiplying 1/3 by 3/4? a) 1/4 b) 1/3 c) 3/12 d) 9/12
6. Which of the following fractions is equivalent to 1/2? a) 2/4 b) 5/10 c) 3/6 d) All of the above
7. What is the result of dividing 1/2 by 2/3? a) 3/4 b) 2/3 c) 1/3 d) 3/2
8. What is the result of multiplying 4/5 by 5/6? a) 4/6 b) 20/30 c) 1/2 d) 9/10
9. Which of the following fractions is equivalent to 4/7? a) 8/14 b) 12/21 c) 16/28 d) All of the above
10. What is the result of dividing 3/5 by 1/4? a) 12/5 b) 12/20 c) 15/4 d) 15/20

Lesson Presentation

Introduction: Begin the lesson by reviewing what fractions are and how to identify the numerator and denominator. Use visual aids such as fraction circles or bars to help students understand how fractions represent a part of a whole. Then introduce the four operations of addition, subtraction, multiplication, and division and explain that the rules for these operations apply to fractions as well.

Body:

1. Addition and Subtraction of Fractions

• Explain that when adding or subtracting fractions, the denominators must be the same.
• Demonstrate how to find a common denominator by using the least common multiple or by multiplying the denominators.
• Model how to add or subtract the numerators and then simplify the result if necessary.
• Give examples and have students practice on the board or with manipulatives.

2. Multiplication of Fractions

• Explain that when multiplying fractions, we multiply the numerators and denominators separately.
• Show examples of multiplying fractions with and without simplifying the result.
• Have students practice on the board or with manipulatives.

3. Division of Fractions

• Explain that when dividing fractions, we flip the second fraction and then multiply.
• Demonstrate how to simplify the result if possible.
• Show examples of dividing fractions and have students practice on the board or with manipulatives.

Conclusion: Summarize the main points of the lesson and review the rules for addition, subtraction, multiplication, and division of fractions. Encourage students to ask questions and clarify any confusion. Provide worksheets for further practice and assessment materials to evaluate student understanding.

Assessment: To assess student understanding, use a variety of assessment methods such as written assignments, quizzes, or performance tasks. Monitor student progress throughout the lesson and provide feedback to guide their learning. Use the assessment results to adjust the lesson plan and provide targeted instruction as needed.

Extension: For advanced students, provide more challenging problems or extend the lesson to include mixed numbers or improper fractions. For struggling students, provide additional practice and support to help them master the basics before moving on to more complex problems. Encourage students to use real-life examples to apply their knowledge of fractions in practical situations.

Weekly Assessment /Test 

1. To add or subtract fractions, the ___________________ must be the same.
2. To find a common denominator, you can use the least common ___________________ or by multiplying the denominators.
3. To multiply fractions, you multiply the _________________ together and the denominators together.
4. To divide fractions, you flip the second fraction and then ___________________.
5. 1/4 + 1/4 = ___________________.
6. 3/8 – 1/8 = ___________________.
7. 2/3 x 3/4 = ___________________.
8. 3/4 ÷ 1/2 = ___________________.
9. 2/5 + 3/5 = ___________________
10. 1/2 ÷ 1/4 = ___________________.

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