NCERT Class 5 Mathematics Maths Mela Chapter 02 Fractions PDF Download

Chapter 2: Fractions

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

[Figure: Two chocolates of different sizes, with labels to identify \( \frac{1}{2} \) and \( \frac{1}{3} \) of each, See in your textbook]

When can we say that \( \frac{1}{2} \) of something is greater than \( \frac{1}{3} \) of something?

To compare two fractions of two wholes, the wholes from which the fractions are derived must be the same.

Playing with a Grid

• Shade \( \frac{1}{8} \) of Grid A in red.
• Shade \( \frac{1}{6} \) of Grid B in blue.
• Shade \( \frac{1}{12} \) of Grid C in yellow.
• Do you see \( \frac{1}{3} \) in any of the grids? Mark it.

[Figure: Three grids labeled A, B, and C for shading fractions, See in your textbook]

Teacher's Note

When comparing fractions of different wholes, remember that the size of the whole matters. \( \frac{1}{3} \) of a large chocolate can be bigger than \( \frac{1}{2} \) of a smaller chocolate, even though \( \frac{1}{2} \) is normally a larger fraction than \( \frac{1}{3} \). You can only compare fractions meaningfully when they come from the same whole.

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 \( \frac{1}{5} \) pieces will you need to make a whole?

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

[Figure: A circle divided into one \( \frac{1}{2} \) piece (orange) and two \( \frac{1}{4} \) pieces (purple), See in your textbook]

One piece of \( \frac{1}{2} \) and two pieces of \( \frac{1}{4} \) make a whole. What is the relation between \( \frac{1}{2} \) and \( \frac{1}{4} \)? Discuss in class.

\( \frac{1}{2} = \frac{2}{4} \) (\( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \)).

When a \( \frac{1}{2} \) piece is broken into 2 equal parts, each part is a \( \frac{1}{4} \) piece. 2 pieces of \( \frac{1}{4} \) are equal to \( \frac{1}{2} \).

What else is equivalent to \( \frac{1}{2} \)?

\( \frac{1}{2} = \frac{2}{4} = \) ____ = ____ = ____

Is \( \frac{1}{3} \) equal to \( \frac{2}{6} \)? Let us find out.

Look at the picture and identify the fractions.

[Figure: A rectangle divided into 6 equal parts with 2 parts shaded, representing \( \frac{2}{6} \), See in your textbook]

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

Do you see that \( \frac{1}{3} = \frac{2}{6} \)? Yes. These are called equivalent fractions.

Let us see how equivalent fractions can be generated.

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.
   (a) \( \frac{1}{3} \) = = =
   (b) \( \frac{1}{4} \) = = =
   (c) \( \frac{1}{5} \) = = =
   (d) \( \frac{1}{6} \) = = =

Do you see how to generate equivalent fractions for any given fraction? Discuss in class.

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.
   A. How many \( \frac{1}{6} \)s make \( \frac{1}{3} \)?
   [Figure: A rectangle with the shaded part labeled as \( \frac{1}{3} \), with instructions to identify \( \frac{1}{6} \) in the same whole and find how many \( \frac{1}{6} \)s fit into \( \frac{1}{3} \), See in your textbook]
   B. How many \( \frac{1}{8} \)s make
   (a) \( \frac{1}{4} \)? (b) \( \frac{1}{2} \)?
   [Figure: Two rectangles divided into 8 equal parts for working out the problem, See in your textbook]
   C. How many \( \frac{1}{12} \)s make
   (a) \( \frac{1}{2} \) (b) \( \frac{1}{3} \) (c) \( \frac{1}{4} \) (d) \( \frac{1}{6} \)?
   [Figure: Four grids of 12 squares each for working out the problem, See in your textbook]

Teacher's Note

To find how many smaller fraction pieces make a larger one, you can use your fraction kit or draw pictures. For example, if you want to know how many \( \frac{1}{6} \)s make \( \frac{1}{3} \), shade \( \frac{1}{3} \) first, then count how many \( \frac{1}{6} \) pieces fit exactly into that shaded space. This visual method helps you understand the relationships between fractions before learning the multiplication or division method.

Making Equivalent Fractions

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

[Figure: Four rectangles showing \( \frac{1}{3} \), \( \frac{2}{6} \), \( \frac{3}{9} \), and \( \frac{4}{12} \) with one-third shaded in each, See in your textbook]

He observes an interesting pattern and says that \( \frac{1}{3} \), \( \frac{2}{6} \), \( \frac{3}{9} \), and \( \frac{4}{12} \) show the same shaded region.

\( \frac{2}{6} \), \( \frac{3}{9} \), and \( \frac{4}{12} \) are all equivalent to \( \frac{1}{3} \). 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 \( \frac{1}{3} \). Write them in the boxes below the images.

[Figure: Three rectangles with one-third shaded, to be divided into more equal parts and labeled with equivalent fractions, See in your textbook]

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

\( \frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \) ______ = ______ = ______ = \( \frac{24}{} \) = \( \frac{}{36} \)

How do you know when a fraction is equivalent to another? Discuss in class.

The below pictures show \( \frac{2}{5} \) of a whole. Find the different fractions that are equivalent to \( \frac{2}{5} \) and write your fractions below each image.

[Figure: Four rectangles showing \( \frac{2}{5} \) and \( \frac{4}{10} \) shaded, with boxes for equivalent fractions to be filled in, See in your textbook]

\( \frac{2}{5} = \frac{4}{10} = \) _____ = _____ = \( \frac{}{50} \) = \( \frac{}{100} \)

Do as instructed using your fraction kit.

• Make a whole using only \( \frac{1}{6} \) and \( \frac{1}{12} \) pieces.
• Make a whole using \( \frac{1}{12} \), \( \frac{1}{4} \), and \( \frac{1}{2} \) 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.

Key Points

• When comparing fractions, the whole must be the same. \( \frac{1}{2} \) of a large object may not equal \( \frac{1}{2} \) of a smaller object in actual size.
• Equivalent fractions represent the same part of a whole but have different numerators and denominators. For example, \( \frac{1}{3} \), \( \frac{2}{6} \), \( \frac{3}{9} \), and \( \frac{4}{12} \) are all equivalent.
• You can create equivalent fractions by dividing shapes into more equal parts. When you divide each part of a fraction into smaller pieces, you get a new fraction with the same value.

This is a preview of the first 5 pages. To get the complete chapter, click below.