chapter-2

Fractions

Tamanna is a student of Grade 5. She has two chocolates of different sizes. She says that 1/ 3 of one of her chocolates is bigger than 1/ 2 of the other chocolate. Is that correct? Explain why this is so.

Playing with a Grid

• Shade 1/ 8 of Grid A in red.
• Shade 1/6 of Grid B in blue
• Shade 1/12 of Grid C in yellow
• Do you see 1/3 in any of the grids? Mark it

Look at the picture and identify the fractions.

Are there two different ways to write the fraction represented by the shaded part? ___________________

Do you see that 1/ 3 = 2/6 ? Yes. These are called ‘equivalent fractions’. Let us see how equivalent fractions can be generated.

Fun with Fraction Kit

Gurpreet is playing with his fraction kit (a kit is given at the end of the textbook). Do you remember how to make a whole with pieces of the same size? How many 1 5 pieces will you need to make a whole?

He makes a whole using two different fraction pieces. The whole looks like the following.

One piece of 1/ 2 and two pieces of 1/ 4 make a whole. What is the relation between 1/ 2 and 1/ 4 ? Discuss in class.

1/ 2 = 2/ 4 ( 1/ 2 is equivalent to 2/ 4 ).
When a 1/ 2 piece is broken into 2 equal parts, each part is a 1/ 4 piece. 2 pieces of 1/ 4 are equal to 1/ 2 .

What else is equivalent to 1/ 2 ?

1/ 2 = 2/ 4 = ____ = ____ = ____

Let Us Do

1. In groups of 3 or 4, find different ways of making a whole with different fraction pieces from your kit. Write the equivalent fractions for the following that you may find in the process.

2. (a) 1/3 = = =


3. (b) 1/4 = = =


4. (c) 1/5 = = =


5. (d) 1/6 = = =

2. Find the following using your kit. You can also shade and check by shading the following. The first one is partially done for you.

B. How many 1/8 s make

C. How many 1 /12s make

(a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6 ?

• Make a whole using only 1/6 and 1/12 pieces.
• Make a whole using 1/12, 1/4 , and 1/2 pieces.
• Make a whole using any five pieces of the same size.
• Make a whole using any seven pieces.

Play in a group with this kit and find other interesting combinations to make a whole. Write or draw your findings.

Making Equivalent Fractions

Sameer has shaded one-third of the following figures. He draws horizontal lines to divide the shapes into more equal parts.

He observes an interesting pattern and says that 1/3 , 2/6 , 3/9 , and 4/12 show the same shaded region. 2/6 , 3/9 , and 4/12 are all equivalent to 1/3 . We use the word ‘equivalent’ to indicate the same part of a whole, with different names.

Divide the wholes given below into more equal parts and find fractions equivalent to 1/3 . Write them in the boxes below the images.

Do you see any pattern in all the equivalent fractions that you found?

How do you know when a fraction is equivalent to another? Discuss in class. The below pictures show 2 /5 of a whole. Find the different fractions that are equivalent to 2 /5 and write your fractions below each image.

Let Us Do

1. (a) 2/3 and 3/4


2. (b)3/5 and 6/10


3. (c)4/12and 2/6


4. (d) 6/9and 1/3

3. Fill in the boxes such that the fractions become equivalent.

Comparing Fractions—Same Denominator

Let Us Do

1. Compare the fractions given below using < and > signs .

Comparing Fractions—Same Numerator

I ate 4/6 paratha yesterday evening.

I ate 4/ 5 paratha yesterday evening

Between Sevi and Shami, can you tell who ate more? Use your fraction kit to find the answer.

Do the following pictures help you reason? Share your thoughts in the class.

Let Us Do

Fractions Greater Than 1

Raman’s father makes nice soft parathas. He cuts the parathas either into halves (2 equal parts) or fourths (4 equal parts) before serving them. He asks his children (Raman and Radhika) each day to find out the number of parathas he made.

Maa took 5 pieces of 1/2 paratha. How many parathas did she eat?

Raman’s sister Radhika took 6 pieces of 1 2 paratha. How many parathas did she eat?

Raman ate 6 pieces of 1/2 paratha, Dadaji ate 7 pieces of 1/2 paratha and Baba ate 5 pieces of 1 /2 paratha. How many parathas did each of them eat? Use the number line to find the answer.

How many parathas were made on this day? Find out.

Another day, Raman’s father cut all the parathas in 1/ 4 . Dadaji took 9 pieces of 1/4 paratha. How many parathas did he eat?

Raman ate 7 pieces of 1/4 , Radhika ate 6 pieces of 1/4 , Maa ate 8 pieces of 1/4 , Dadiji ate 10 pieces of 1/ 4 , and Baba ate 12 pieces of 1/4 paratha. Use a number line to find out how many parathas were eaten by each of them.

Raman’s family of 6 members ordered 2 pizzas and cut each pizza into 3 equal slices so that each family member had one slice. Dadiji and Dadaji gave their slices to Raman, Maa, and Baba gave theirs to Radhika. How much pizza do each of them have after this?

Raman could eat only 2 slices of pizza. So, he gave 1 to Radhika. How much pizza does Radhika have now?

Let Us Do

2. Circle the fractions that are greater than one (whole). How do you know? Discuss your reasoning in the class.

Comparing Fractions With Reference to 1

Let us compare some more fractions. Between Sevi and Shami can you tell who ate less?

I ate 7/ 8 paratha yesterday evening.

I ate 8/ 6 paratha yesterday evening.

Let Us Do

1. Compare the following fractions using 1 as a reference. Share your reasoning in the class.

Comparing Fractions with Reference to 1/2

Let Us Do

1. Circle the fractions below that are equal to 1/2.

2. Some fractions are written in the box below. Circle the fractions that are less than half. How do you know? Discuss your reasoning in the class.

I ate 5/ 8 paratha
yesterday evening

I ate 3/ 6 paratha
yesterday evening

Who do you think ate more paratha?

Let Us Do

Try This: