Section/Lesson: Fractions Equal And Unequal Parts EQUAL UNEQUAL One Half, One Third and One Quarter

Objectives By the end of this section/lesson, students should be able to: Read and write fractions Compare fractions

Equal v/s Unequal Parts B If the loaf is divided into 4 equal parts, which would be the result: A or B?

Definition of Fraction B If we take one part of the loaf and represent it in terms of the whole, B cannot be used since all parts are not of the same size.

Definition of Fraction However, every part is of the same size in loaf A. Hence, we can clearly say that the whole loaf is divided into four equal parts and one piece represents 1 part of a total of 4 parts.

Activity 1: Equal Parts Pairs of students are provided with square/circle shaped paper cuttings. Teacher introduces the given shape as a whole. Students are asked to form two equal parts with one whole by folding. Teacher introduces equal and unequal parts. (emphasizing on the importance of equality)

Activity 1: Equal Parts Teacher brainstorms with students about the properties of the parts for the equal and unequal folding. Teacher queries about the name given to the equal parts and introduces the concept of writing and naming a fraction. 1 2 half

Writing of fraction a is the number of parts - Numerator 1 2 a B is similar to b is the total number of parts in the whole - Denominator

Consolidation Work Is the fraction represented by the shaded part equal to 1 2 ? A. Yes B. No Justify your answer.

More Fractions Divide the given figure into 3 equal parts.

More Fractions Now try to divide the given figure into 3 equal parts.

Brainstorm: More Fractions Try to divide the given figure into 3 equal parts. Is it possible to have 3 equal parts? A. Yes B. No Why?

More fractions What would be the fraction of the region in white?

More fractions When a whole is divided into 3 equal parts, each part is called a ‘third’. Here the section is one third of the whole and the white section is two third.

Fractions and the names 2 equal parts 1 2 , 2 2 half third 1 3 , 2 3 , 3 3 3 equal parts 4 equal parts quarter 1 4 , 2 4 , 3 4 , 4 4

Fractions and the names 5 equal parts 1 5 , 2 5 , 3 5 , 4 5 , 5 5 fifth 6 equal parts 1 6 , 2 6 , 3 6 , 4 6 , 5 6 , 6 6 sixth 1 7 , 2 7 , 3 7 , 4 7 , 5 7 , 6 7 , 7 7 seventh 7 equal parts

Fractions and the names 8 equal parts eighth 1 8 , 2 8 , 3 8 , 4 8 , 5 8 , 6 8 , 7 8 , 8 8 9 equal parts 1 9 , 2 9 , 3 9 , 4 9 , 5 9 , 6 9 , 7 9 , 8 9 , 9 9 ninth 1 10 , 2 10 , 3 10 , 4 10 , 5 10 , 6 10 , 7 10 , 8 10 , 9 10 , 10 10 tenth 10 equal parts

More fractions and the names 𝑎 11 , eleventh 𝑎 17 , seventeenth 11 equal parts 17 equal parts 12 equal parts 𝑎 12 , twelfth 18 equal parts 𝑎 18 , eighteenth 𝑎 13 , thirteenth 𝑎 19 , nineteenth 13 equal parts 19 equal parts 𝑎 14 , fourteenth 𝑎 20 , twentieth 14 equal parts 20 equal parts 𝑎 15 , fifteenth 15 equal parts 𝑎 16 , sixteenth 16 equal parts

Consolidation Work 1. What fractions are represented below?

Consolidation Work 2. What is the denominator of 3 4 ? A. 3 B. 4 C. 7

Consolidation Work 3. Which fraction has 4 in the numerator? A. 1 4 B. 4 5 C. 1 3

Consolidation Work 4. Does this figure show 5 6 ? A. Yes B. No

Consolidation Work 5. What fraction of the whole is shaded?

Consolidation Work 6. What fraction of the whole is white?

Consolidation Work 7. What fraction could this picture show? A. 1 2 B. 4 8 C. Both A and B D. Neither A nor B

Fraction of a group Earlier, we have seen fraction of a whole shape. We can also have fraction of a group of objects with a similarity. From above, we can say the fraction of green apple is 1 2 1 2 number of green apple Total number of apples

Fraction of a group What fraction of the shapes are circles? Step 1: Count the circles. That is the numerator. Step 2: Count all the shapes. That is the denominator. 𝟐 𝟕 Answer:

Consolidation work 1. What fraction of the ten rupees are heads up?

Consolidation work 2. Are 3 5 of the lions in the triangle? Yes No

Consolidation work 3. What fraction of the frogs are inside the rectangle below? A. 1 3 B. 2 4 C. 5 6 D. 2 6

Consolidation work 4. What fraction is not circled?

A line can be equally divided. Fraction on a line A line can be equally divided. A B 2 equal parts A B OR 3 equal parts A B

Fraction on a line Since AB is the whole and it is divided by 2, the first segment of the line is equal to 1 2 . Suppose, we attribute ‘0’ to A position and ‘1’ to the B position. The middle marking would be 1 2 . 1 2 1

Now, let’s do the same for AB when it is divided into 3 equal parts. Consolidation work Now, let’s do the same for AB when it is divided into 3 equal parts. 3 equal parts A B 1 1 3 2 3

Consolidation Work 1. What denominator would you use if the number line was divided into 4 equal parts?

Consolidation Work 2. Should you use a ‘6’ in the denominator for this number line? Yes No

Consolidation Work 3. Move the fractions to label the dashes on the number line.

Consolidation Work 4. Divide the number line into 7 equal parts and label it.

Consolidation work 5. What fraction is missing from the number line?

Consolidation work 6. Where should 4 8 be placed? Option 1: A Option 2 : B Option 3: C Answer: __________

Consolidation work 6. Where should 8 8 be placed? Option 1: A Option 2 : B Option 3: C Option 4: D Answer: __________

Fraction on a line When the line starts with 0, the fractions in-between becomes ¼, ½, ¾, etc. However, when the line already have some figures, the intervals are broken into fractions and these fractions are considered together with the whole numbers.

Fraction on a line Example: 10 1 4 10 2 4 10 3 4 Since the interval between 10 and 11 is broken into four equal parts, we have the denominator 4. That is, 1 4 , 2 4 , 3 4 .

Consolidation work 1. What values would A and B take? A B 5 1 4 5 3 4 6 1 4 6 2 4 B

Consolidation work 2. Write the missing values at A and B? A B

2 5 is less than 4 5 or mathematically, 2 5 < 4 5 Compare fractions Let’s compare 4 5 and 2 5 . Which one is greater? Both fractions have the same denominator and we compare the numerators like 2 natural numbers. First, we try to arrange both fractions on a number line. 2 5 4 5 Since 2 5 comes before 4 5 , 2 5 is less than 4 5 or mathematically, 2 5 < 4 5

Consolidation work Compare each set of fractions. Place the correct symbol between the 2 fractions.

Compare fractions How do we compare two fractions when the numerator is the same but we have different denominators? Compare 1 5 and 1 2

Compare fractions 1 5 : dividing 1 whole into 5 parts Therefore, the bigger the denominator, the smaller the fraction (provided the numerator is the same). 1 5 < 1 2

Consolidation work Compare each set of fraction. Place the correct symbol between the 2 fractions.

Compare Fractions Unlike denominators/numerators How to compare two fractions, with both the numerator and denominator not same? 1 5 6 7

Compare Fractions Unlike denominators/numerators 1 5 6 7 ∴ 1 5 < 6 7

Compare Fractions Unlike denominators/numerators How to compare two fractions, with both the numerator and denominator not same? We can also use number lines 2 7 4 9

Compare Fractions Unlike denominators/numerators 2 7 2 7 4 9 4 9 ∴ 𝟐 𝟕 < 𝟒 𝟗

Consolidation work Compare each set of fraction. Place the correct symbol between the 2 fractions. (You can use squared papers)

Equivalent fractions The fraction bars below are equivalent because they are of the same size. 1 2 = 2 4 = 3 6 = 4 8 = 5 10 = 6 12 =

Equivalent fractions The fractions are of the same size but the denominators are different for each set of equivalent fractions.

Consolidation work Write the three different fractions equivalent to 1 3 . 1 3 = = =

Equivalent fractions What do you note about the denominators of these equivalent fractions? 1 2 2 4 3 6 4 8 5 10 6 12 = = = = = 1 3 2 6 3 9 4 12 = = = Well, the denominators of the equivalent fractions are multiples of the smallest denominator That is, 4 = 2 x 2 6 = 2 x 3 8 = 2 x 4 10= 2 x 5 6 = 3 x 2 9 = 3 x 3 12= 3 x 4

Equivalent fractions So, and 1×2 2×2 2 4 1×2 3×2 2 6 = = 1×3 2×3 3 6 1×3 3×3 3 9 = = 4 8 1×4 2×4 = 1×4 3×4 4 12 = 1×5 2×5 5 10 = Like it can be seen, the numerator and the denominator are both multiplied by the same factor. 1×5 2×5 6 12 =

Consolidation work Fill in the missing number. a. 1 2 = 6 e. 1 4 = 3 b. 3 4 = 9 f. 1 4 = 4 c. 1 3 = 4 d. 2 3 = 4

End of the Section/Lesson: Fraction