1.

Understanding Fractions as a Part of a Whole

A fraction is a way to show part of a whole. It is made up of two numbers: the numerator (the top
number) and the denominator (the bottom number). The numerator tells us how many parts we have,
and the denominator tells us how many parts the whole is divided into. For example, in the fraction 3/4,
the 3 is the numerator, showing that we have three parts, and the 4 is the denominator, showing that
the whole is divided into four parts.

Teaching Method (T.M.): Use visual aids like fraction bars or pie charts to show a whole divided into
equal parts. For instance, if you have a pie chart divided into 4 equal parts, color in 3 parts to show 3/4.
This will help students visualize how fractions represent parts of a whole.

Activity/Homework: Ask the students to draw a fraction bar divided into 6 equal parts. After rolling a
dice, they should shade the number of parts corresponding to the number rolled. For example, if they
roll a 4, they should shade 4 parts and write 4/6. They should also mark the numerator and
denominator with arrows.

2. Equivalent Fractions

Equivalent fractions are fractions that may look different but represent the same value or part of a
whole. For example, 2/4 is equivalent to 1/2 because both fractions represent the same amount, even
though the numbers are different.

T.M.: To explain this, you can simplify fractions by dividing both the numerator and denominator by the
same number. For example, 6/8 is equivalent to 3/4 because if we divide both the numerator (6) and
the denominator (8) by 2, we get 3/4. This shows that both fractions represent the same value.

Example: Start by showing a visual example of a fraction bar divided into 4 equal parts, then shade 2
parts to show 2/4. Then show how reducing the fraction (dividing both numbers by 2) gives 1/2. This will
help students understand that fractions can look different but still mean the same thing.

3. Simplifying Fractions

Simplifying fractions means reducing them to their simplest form, where the numerator and
denominator cannot be divided by the same number except 1. To simplify a fraction, we divide both the
numerator and the denominator by their greatest common divisor (GCD).

T.M.: For example, 8/12 can be simplified by dividing both the numerator (8) and the denominator (12)
by 4, which is their greatest common divisor. 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 simplifies to 2/3.

Activity: Give students a list of fractions and ask them to simplify them. For example: 6/9, 10/15, 4/8.
Have them use their knowledge of division and the GCD to reduce the fractions to their simplest form.

4. Adding and Subtracting Fractions

When adding or subtracting fractions, the fractions must have the same denominator (the bottom
number). If the fractions have the same denominator, you just add or subtract the numerators (the top
numbers).

T.M.: For example, 2/5 + 1/5. Since the denominators are the same (both are 5), you just add the
numerators: 2 + 1 = 3, so 2/5 + 1/5 = 3/5. For subtraction, the same rule applies. For example, 5/8 - 2/8
= 3/8.

When the denominators are different, you need to make them the same before adding or subtracting.
This means finding a common denominator. You can do this by multiplying the denominators or finding
the lowest common multiple of the two numbers.

Example: 1/4 + 1/2. First, change 1/2 to 2/4 (because 2/4 is equivalent to 1/2). Now, add the
numerators: 1/4 + 2/4 = 3/4.

5. Multiplying Fractions

When you multiply fractions, you multiply the numerators (top numbers) together and the
denominators (bottom numbers) together.

T.M.: For example, 2/3 × 4/5. Multiply the numerators: 2 × 4 = 8. Then, multiply the denominators: 3 × 5
= 15. So, 2/3 × 4/5 = 8/15.

Activity: Have the students practice multiplying different fractions. For example, 1/2 × 3/4. This will help
them become comfortable with multiplying fractions and understanding how to handle both the
numerators and denominators.

6. Dividing Fractions

To divide by a fraction, you multiply by the reciprocal (the second fraction flipped). The reciprocal of a
fraction is obtained by swapping the numerator and denominator.

T.M.: For example, 3/4 ÷ 2/5. First, flip the second fraction (reciprocal): 5/2. Then, multiply: 3/4 × 5/2.
Multiply the numerators: 3 × 5 = 15, and multiply the denominators: 4 × 2 = 8. So, 3/4 ÷ 2/5 = 15/8.

Activity: Have students practice dividing fractions by finding the reciprocal and multiplying. For example,
1/3 ÷ 2/5.

7. Comparing Fractions

To compare fractions, you can either find a common denominator or convert the fractions to decimals
and compare the decimal values.

T.M.: For example, 3/4 and 5/6. Convert both fractions to a common denominator (12). So, 3/4 = 9/12
and 5/6 = 10/12. Now you can easily see that 5/6 is greater than 3/4.
Activity: Have the students compare different fractions, first by finding a common denominator and
then by comparing the numerators.

8. Fraction of a Whole

A fraction can be used to express a part of a number. For example, to find 1/2 of 100, you divide 100
into 2 equal parts and take one part, which is 50.

T.M.: For example, 3/4 of 80: Divide 80 into 4 equal parts (each part is 20). Then, take 3 parts (3 × 20 =
60). So, 3/4 of 80 = 60.

Activity: Ask students to calculate fractions of numbers using different examples. For example, what is
1/3 of 90? (Answer: 30).

9. Converting Between Fractions, Decimals, and Percentages

Fractions can be converted into decimals and percentages. To convert a fraction to a decimal, divide the
numerator by the denominator. To convert a decimal to a percentage, multiply the decimal by 100.

T.M.: For example, 3/4. Divide 3 ÷ 4 = 0.75. Then, multiply 0.75 × 100 = 75%.

Activity: Give students several fractions to convert into decimals and percentages. For example, 2/5,
1/2, 7/10.

10. Improper Fractions and Mixed Numbers

An improper fraction is when the numerator is greater than or equal to the denominator. This can be
converted into a mixed number.

T.M.: For example, 7/4. Divide 7 ÷ 4. The result is 1 with a remainder of 3. So, 7/4 is equal to 1 ¾.

Activity: Have students convert improper fractions like 9/4, 10/3, and 11/6 into mixed numbers.

By breaking down each concept clearly and providing hands-on practice, students will be able to
understand fractions and apply them confidently in various situations.