NCERT Solutions Class 5 Mathematics Mela Chapter 02 Fractions

Question 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) 1/3 = = = (b) 1/4 = = = (c) 1/5 = = = (d) 1/6 = = = Do you see how to generate equivalent fractions for any given fraction? Discuss in class.
Answer: (a) 1/3 = 2/6 = 3/9 = 4/12
(b) 1/4 = 2/8 = 3/12 = 4/16
(c) 1/5 = 2/10 = 3/15 = 4/20
(d) 1/6 = 2/12 = 3/18 = 4/24
To create equivalent fractions, take any fraction and multiply both the top and bottom numbers by the same value. For instance: \( \frac{1}{3} \times \frac{2}{2} = \frac{2}{6} \), \( \frac{1}{3} \times \frac{3}{3} = \frac{3}{9} \), and \( \frac{1}{3} \times \frac{4}{4} = \frac{4}{12} \). This method works because multiplying by the same number in both positions keeps the fraction's worth the same, even though it looks different.
In simple words: To make fractions that are the same value, multiply the top and bottom by the same number. The fraction stays the same size, just with bigger numbers.

Exam Tip: Always multiply both numerator and denominator by exactly the same number - this is the key rule for equivalent fractions.

Question 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 (1/6)s make (1/3)s?
Answer: Two (1/6)s combine to form (1/3).
In simple words: When you put two pieces of one-sixth together, you get one-third.

Exam Tip: Use a visual model or number line to see how smaller fractions fit into larger ones.

Question 2B. How many (1/8)s make (a) 1/4? (b) 1/2?
Answer: (a) Two (1/8)s make 1/4.
(b) Four (1/8)s make 1/2.
In simple words: Two eighth pieces add up to one quarter, and four eighth pieces add up to one half.

Exam Tip: Count carefully - the number of smaller pieces needed always multiplies by the denominator relationship between the fractions.

Question 2C. How many (1/12)s make (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6?
Answer: (a) Six (1/12)s make 1/2.
(b) Four (1/12)s make 1/3.
(c) Three (1/12)s make 1/4.
(d) Two (1/12)s make 1/6.
In simple words: Count how many small twelfth pieces you need to fill each larger fraction piece. The more parts you divide the whole into, the more of those pieces you'll require.

Exam Tip: Observe the pattern - if you know one equivalence, you can work out others by dividing the numerator and denominator.

Question 3. Do as instructed using your fraction kit. Make a whole using only 1/6 and 1/12 pieces.
Answer: Take 3 pieces of 1/6: \( 3 \times \frac{1}{6} = \frac{3}{6} = \frac{6}{12} \)
Take 6 pieces of 1/12: \( 6 \times \frac{1}{12} = \frac{6}{12} \)
Put them together: \( \frac{6}{12} + \frac{6}{12} = \frac{12}{12} = 1 \)
In simple words: Mix three sixth pieces and six twelfth pieces to make one complete whole.

Exam Tip: Convert all fractions to a common denominator first - this makes it easy to see if pieces add up to a whole.

Question 3B. Make a whole using 1/12, 1/4 and 1/2 pieces.
Answer: First, change all pieces to the same denominator = 12
\( \frac{1}{2} = \frac{6}{12} \)
\( \frac{1}{4} = \frac{3}{12} \)
\( \frac{1}{12} = \frac{1}{12} \)
Now, taking: 1 piece of \( \frac{1}{2} = \frac{6}{12} \)
1 piece of \( \frac{1}{4} = \frac{3}{12} \)
3 pieces of \( \frac{1}{12} = 3 \times \frac{1}{12} = \frac{3}{12} \)
Total = \( \frac{6}{12} + \frac{3}{12} + \frac{3}{12} = \frac{12}{12} = 1 \)
In simple words: Change each type of piece to twelfths, then add them up to see if you get a complete whole.

Exam Tip: Writing fractions with a common denominator helps you add them quickly and check your answer correctly.

Question 3C. Make a whole using any five pieces of the same size.
Answer: Take 5 pieces of \( \frac{1}{5} \): \( 5 \times \frac{1}{5} = \frac{5}{5} = 1 \)
In simple words: If you use five pieces where each piece is one-fifth of a whole, you get the complete whole.

Exam Tip: When all pieces are identical, the number of pieces needed equals the denominator of each piece.

Question 3D. Make a whole using any seven pieces.
Answer: Take 7 pieces of \( \frac{1}{7} \): \( 7 \times \frac{1}{7} = \frac{7}{7} = 1 \)
In simple words: Seven pieces, each one-seventh in size, combine perfectly to make one whole.

Exam Tip: The pattern holds for any number - n identical pieces of size 1/n always make exactly one whole.

Question 1. Fill in the blanks with equivalent fractions. There may be more than one answer. (a) 1/7 = _____ (b) 2/3 = _____ (c) 3/4 = _____ (d) 3/5 = _____
Answer: To find equivalent fractions, multiply the numerator and denominator with the same number:
(a) \( \frac{1}{7} = \frac{2}{14} = \frac{3}{21} \)
(b) \( \frac{2}{3} = \frac{4}{6} = \frac{8}{12} \)
(c) \( \frac{3}{4} = \frac{6}{8} = \frac{9}{12} \)
(d) \( \frac{3}{5} = \frac{6}{10} = \frac{9}{15} \)
In simple words: Multiply the top and bottom by the same number to get different-looking fractions that mean the same thing.

Exam Tip: You can multiply by any whole number - there are endless equivalent fractions for each starting fraction.

Question 2. Put a tick (✔) against the fractions that are equivalent. (a) 2/3 and 3/4 (b) 3/5 and 6/10 (c) 4/12 and 2/6 (d) 6/9 and 1/3
Answer: (a) 2/3 and 3/4 - Not equivalent
(b) 3/5 and 6/10 (✔) - Equivalent, because \( \frac{3}{5} \times \frac{2}{2} = \frac{6}{10} \)
(c) 4/12 and 2/6 (✔) - Equivalent, because both simplify to \( \frac{1}{3} \)
(d) 6/9 and 1/3 - Not equivalent (6/9 simplifies to 2/3, not 1/3)
In simple words: Two fractions are equivalent when they stand for the same part of a whole, even if they look different.

Exam Tip: Cross-multiply or reduce both fractions to lowest terms to check if they are truly equivalent.

Question 3. Fill in the boxes such that the fractions become equivalent. (a) 2/5 = ▢/10 (b) 3/4 = ▢/16 (c) 4/7 = 8/▢ (d) 5/9 = 25/▢
Answer: (a) \( \frac{2}{5} = \frac{4}{10} \) - Multiply numerator and denominator by 2
(b) \( \frac{3}{4} = \frac{12}{16} \) - Multiply numerator and denominator by 4
(c) \( \frac{4}{7} = \frac{8}{14} \) - Multiply numerator and denominator by 2
(d) \( \frac{5}{9} = \frac{25}{45} \) - Multiply numerator and denominator by 5
In simple words: Figure out what number you multiplied the top by, then multiply the bottom by the same number.

Exam Tip: Find the pattern first - see if the numerator was multiplied by 2, 3, 4, or 5, then apply that same multiplier to the denominator.

Question 1. Compare the fractions given below using < and > signs. (a) 1/4 ___ 3/4 (b) 3/5 ___ 4/5 (c) 5/7 ___ 2/7 (d) 7/8 ___ 3/8 (e) 5/10 ___ 6/10 (f) 2/6 ___ 1/6
Answer: (a) \( \frac{1}{4} < \frac{3}{4} \)
(b) \( \frac{3}{5} < \frac{4}{5} \)
(c) \( \frac{5}{7} > \frac{2}{7} \)
(d) \( \frac{7}{8} > \frac{3}{8} \)
(e) \( \frac{5}{10} < \frac{6}{10} \)
(f) \( \frac{2}{6} > \frac{1}{6} \)
In simple words: When fractions have the same bottom number, just look at the top numbers - the bigger top number means the bigger fraction.

Exam Tip: Comparing fractions with the same denominator is simple - just compare the numerators directly.

Question 1. Compare the following fractions using < and > signs. (a) 3/8 ______ 3/7 (b) 4/9 ______ 4/10 (c) 2/7 ______ 2/5 (d) 5/7 ______ 5/6 (e) 6/9 ______ 6/10 (f) 7/9 ______ 7/11
Answer: (a) \( \frac{3}{8} < \frac{3}{7} \)
(b) \( \frac{4}{9} > \frac{4}{10} \)
(c) \( \frac{2}{7} < \frac{2}{5} \)
(d) \( \frac{5}{7} < \frac{5}{6} \)
(e) \( \frac{6}{9} > \frac{6}{10} \)
(f) \( \frac{7}{9} > \frac{7}{11} \)
In simple words: When the top numbers match, look at the bottom numbers - a smaller bottom number means a bigger piece, so the fraction is larger.

Exam Tip: When numerators are the same, the fraction with the smaller denominator is always larger - think of cutting a pizza into fewer pieces gives you bigger slices.

Question 1. Use parathas and number lines to show the following fractions in your notebook. (a) 2/3 and 5/3
Answer: For \( \frac{2}{3} \): Shade 2 parts out of 3 equal sections of one paratha. On the number line, place a point between 0 and 1, closer to 1, at the position where 2 parts of 3 have been counted.
For \( \frac{5}{3} \): This needs more than one whole paratha. Shade all 3 parts of the first paratha, then shade 2 more parts of a second paratha. On the number line, place a point past 1, at the position \( 1\frac{2}{3} \), showing that we have 1 complete paratha plus \( \frac{2}{3} \) of another.
In simple words: Use shaded rectangles and a number line to show where each fraction sits - some are smaller than a whole, and some are bigger.

Exam Tip: Always draw rectangles divided into equal parts and mark them clearly - this visual helps you see proper fractions (less than 1) and improper fractions (greater than 1) side by side.

Question 1B. Use parathas and number lines to show the following fractions in your notebook. (b) 3/4 and 5/4
Answer: For \( \frac{3}{4} \): Divide one paratha into 4 equal parts and shade 3 of them. On the number line, mark a point at \( \frac{3}{4} \), which sits between 0 and 1.
For \( \frac{5}{4} \): Take one complete paratha (all 4 parts shaded) plus another paratha with 1 out of 4 parts shaded. On the number line, mark a point at \( 1\frac{1}{4} \), which goes just past 1.
In simple words: Draw and shade paratha diagrams - the first fraction doesn't fill a whole paratha, but the second one goes past a whole paratha into a second one.

Exam Tip: Label your number line marks clearly from 0 to 2, and show that improper fractions always land to the right of 1 on the line.

Question 1C. Use parathas and number lines to show the following fractions in your notebook. (c) 4/8 and 9/8
Answer: For \( \frac{4}{8} \): Draw one paratha split into 8 equal pieces and shade 4 of them. This shows one-half of the paratha. On the number line, place the marker at \( \frac{4}{8} \), which is exactly at the halfway point between 0 and 1.
For \( \frac{9}{8} \): Color in all 8 parts of one paratha, then shade 1 part from a second paratha. On the number line, mark the point at \( 1\frac{1}{8} \), which is just a little past 1.
In simple words: The first fraction is exactly half a paratha, and the second fraction is a whole paratha plus one extra small piece.

Exam Tip: Notice that 4/8 is equivalent to 1/2 - this helps you place it exactly in the middle of the 0 to 1 segment on the line.

Question 2. Circle the fractions that are greater than one (whole). How do you know? Discuss your reasoning in the class.
Answer: Fractions greater than one are called improper fractions. These occur when the numerator (top number) is bigger than the denominator (bottom number). Looking at the given set, identify and circle the fractions where the top is larger than the bottom. For instance, \( \frac{5}{3} \), \( \frac{5}{4} \), and \( \frac{9}{8} \) all have numerators that exceed their denominators, making them larger than 1. You can verify this by dividing - if the top number is bigger, you will always get a result greater than 1.
In simple words: If the top number is bigger than the bottom number, the fraction is bigger than a whole. These fractions need more than one paratha to show.

Exam Tip: A quick rule - improper fractions always have numerator ≥ denominator, and they always represent more than one whole or exactly one whole unit.

Question 1. Compare the following fractions using 1 as a reference. Share your reasoning in the class. (a) 8/7 ______ 9/15 (b) 13/20 ______ 17/15 (c) 7/6 ______ 8/8 (d) 6/6 ______ 19/12 (e) 12/9 ______ 4/5 (f) 15/5 ______ 16/4
Answer: (a) \( \frac{8}{7} > \frac{9}{15} \) - The first fraction is greater than 1 (8 > 7), while the second is less than half (less than \( \frac{1}{2} \)), so the first is bigger.
(b) \( \frac{13}{20} < \frac{17}{15} \) - The first is less than 1 (13 < 20), while the second is greater than 1 (17 > 15), so the second is bigger.
(c) \( \frac{7}{6} > \frac{8}{8} \) - The first exceeds 1 (7 > 6), while the second equals 1, so the first is larger.
(d) \( \frac{6}{6} < \frac{19}{12} \) - The first equals 1, while the second is larger than 1 (19 > 12), so the second is bigger.
(e) \( \frac{12}{9} > \frac{4}{5} \) - The first is greater than 1 (12 > 9), while the second is less than 1 (4 < 5), so the first is larger.
(f) \( \frac{15}{5} < \frac{16}{4} \) - The first equals 3 (15 ÷ 5 = 3), while the second equals 4 (16 ÷ 4 = 4), so the second is bigger.
In simple words: Check if each fraction is bigger, smaller, or equal to 1 - this helps you compare them fast without doing lots of calculations.

Exam Tip: Using 1 as a benchmark is a powerful strategy - it immediately tells you which side of the comparison each fraction falls on.

Question 1. Circle the fractions below that are equal to 1/2.
Answer: Fractions equal to \( \frac{1}{2} \) are those where the numerator is exactly half of the denominator. From the given set, the fractions that equal \( \frac{1}{2} \) are: \( \frac{5}{10} \), \( \frac{6}{12} \), and \( \frac{8}{16} \). You can verify each by simplifying - for example, \( \frac{6}{12} \) reduces to \( \frac{1}{2} \) when you divide both top and bottom by 6.
In simple words: A fraction equals one-half when you can cut the top and bottom by the same number and end up with 1 on top and 2 on the bottom.

Exam Tip: Check by cross-multiplying: if numerator × 2 = denominator, then the fraction equals 1/2.

Question 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.
Answer: A fraction is less than half when the numerator is less than half of the denominator. You can determine this in several ways:
- Using a number line: Place the fraction on a line from 0 to 1, and check if it lands to the left of \( \frac{1}{2} \).
- Using equivalent fractions: Convert both fractions to a common denominator and compare numerators directly.
- Looking at numerator and denominator: If the numerator is less than half the denominator, the fraction is definitely less than \( \frac{1}{2} \). For example, \( \frac{3}{9} < \frac{1}{2} \) because 3 is less than half of 9 (which would be 4.5).
In simple words: A fraction is less than half when its top number is smaller than half its bottom number.

Exam Tip: A quick mental check - compare the numerator to half the denominator: if numerator < denominator ÷ 2, then the fraction is less than 1/2.

Question 1. Compare the following fractions. Where possible, compare the fractions with 1/2. (a) 2/9 and 4/7 (b) 11/14 and 7/20 (c) 5/7 and 3/9 (d) 6/7 and 4/10 (e) 9/17 and 3/15 (f) 7/12 and 3/11 (g) 1/3 and 5/9 (h) 3/9 and 4/7
Answer: (a) \( \frac{2}{9} < \frac{4}{7} \) - Both are less than \( \frac{1}{2} \), but \( \frac{4}{7} \) is closer to \( \frac{1}{2} \), making it larger.
(b) \( \frac{11}{14} > \frac{7}{20} \) - The first is more than \( \frac{1}{2} \) (11 > 7, and 11 is more than half of 14), while the second is less than \( \frac{1}{2} \) (7 < 10).
(c) \( \frac{5}{7} > \frac{3}{9} \) - The first exceeds \( \frac{1}{2} \) (5 > 3.5), while the second is less than \( \frac{1}{2} \) (3 < 4.5).
(d) \( \frac{6}{7} > \frac{4}{10} \) - The first is much greater than \( \frac{1}{2} \), while the second is less than \( \frac{1}{2} \).
(e) \( \frac{12}{9} > \frac{4}{5} \) - The first is greater than 1 (improper fraction), while the second is less than 1.
(f) \( \frac{7}{12} < \frac{3}{11} \) - Wait, let me recalculate: \( \frac{7}{12} > \frac{3}{11} \) because 7/12 is slightly more than 1/2, while 3/11 is less than 1/3.
(g) \( \frac{1}{3} < \frac{5}{9} \) - Convert to ninths: \( \frac{1}{3} = \frac{3}{9} \), so \( \frac{3}{9} < \frac{5}{9} \).
(h) \( \frac{3}{9} < \frac{4}{7} \) - The first simplifies to \( \frac{1}{3} \), which is less than \( \frac{4}{7} \).
In simple words: When both fractions are near 1/2, it's hard to tell - convert them to the same denominator or use a number line for accuracy.

Exam Tip: Using 1/2 as a reference point speeds up comparisons - first figure out if each fraction is above, below, or equal to 1/2, then compare within each group.

What does Class 5 Maths Mela Chapter 2 Fractions teach?

Class 5 Maths Mela Chapter 2 Fractions brings students into the world of showing parts of something whole by using numbers. Beginning with simple fractions such as 1/2, 1/3, and 1/4, it then moves toward putting fractions side by side, figuring out which one is bigger or smaller, and working with fractions of various wholes. The chapter emphasizes equivalent fractions, making clear that fractions that look different can actually stand for the same amount. Visual tools like fraction kits, grids, and coloured diagrams help make the concepts clear and easy to learn. The chapter teaches students about improper fractions and mixed numbers - fractions that go beyond one whole. The section brings real-world settings like pizzas and parathas into activities and problems, turning fraction learning into something hands-on, useful, and connected to daily life. This method builds both solid knowledge and the ability to use these skills in real situations.