RBSE Solutions Class 6 Maths Chapter 5 Fractions More Ques

Fractions In Text Exercise

Question 1. Match the following images (coloured parts) with fractions:
(i)
(ii)
(iii)
(iv)
(a) \( \frac{1}{5} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{1}{8} \)
(d) \( 1 + \frac{1}{2} \)
Answer: To match the images with the correct fractions, observe how many equal parts each figure is divided into and how many of those parts are shaded.
(i) The image shows a circle divided into 5 equal parts, with 1 part shaded. This matches (a) \( \frac{1}{5} \).
(ii) The image shows a circle divided into 4 equal parts, with 1 part shaded. This matches (b) \( \frac{1}{4} \).
(iii) The image shows a circle divided into 8 equal parts, with 1 part shaded. This matches (c) \( \frac{1}{8} \).
(iv) The image shows a rectangle where one full part is shaded, and another similar rectangle has half of its part shaded. This represents one whole plus one half, matching (d) \( 1 + \frac{1}{2} \).
In simple words: Look at each picture and count how many total parts there are and how many are colored. This will give you the fraction for each picture, which you can then match to the list.

🎯 Exam Tip: Always carefully count the total number of equal parts and the number of shaded parts to correctly identify the fraction represented by an image.

Question 1. Write the shaded part of the following figures in the form of fractions.
(i) (Figure: A triangle divided into 4 parts, 1 shaded)
(ii) (Figure: A rectangle divided into 5 parts, 2 shaded)
(iii) (Figure: A circle divided into 8 parts, 3 shaded)
(iv) (Figure: A circle divided into 3 parts, 1 shaded)
Answer: To write the shaded part as a fraction, count the number of shaded sections and place it as the numerator, and count the total number of equal sections and place it as the denominator.
(i) The figure is divided into 4 equal parts, and 1 part is shaded. So, the fraction is \( \frac{1}{4} \).
(ii) The figure is divided into 5 equal parts, and 2 parts are shaded. So, the fraction is \( \frac{2}{5} \).
(iii) The figure is divided into 8 equal parts, and 3 parts are shaded. So, the fraction is \( \frac{3}{8} \).
(iv) The figure is divided into 3 equal parts, and 1 part is shaded. So, the fraction is \( \frac{1}{3} \).
In simple words: To find the fraction of the shaded part, count how many parts are shaded and divide it by the total number of equal parts in the figure. This gives the fraction.

🎯 Exam Tip: Ensure all parts are truly equal before counting them, as a fraction represents parts of a whole where each part has the same size.

Question 1. Which of the following diagram is right for \( \frac{1}{3} \) and which is not? State the reason as well.
(Diagram 1: A line segment divided into 3 equal parts, with 1 part shaded)
(Diagram 2: A figure with 3 parts, where the shaded part appears to be more than one-third)
Answer: The diagram showing a line divided into 3 equal parts with 1 part shaded is the correct representation for \( \frac{1}{3} \). This is because the fraction \( \frac{1}{3} \) means one out of three equal parts. For a visual representation of a fraction to be accurate, all the parts must be exactly the same size. The other diagram is not correct because, although it has three parts, the shaded portion is not exactly one-third of the whole figure, or the parts are not of equal size. A proper fraction visually splits a whole into pieces of the same size.
In simple words: The picture with a line split into three equal pieces and one piece colored is the correct one for \( \frac{1}{3} \). The other picture is wrong because its shaded part is not exactly one-third of the whole, or the parts are not equal.

🎯 Exam Tip: When representing fractions, always ensure that the whole is divided into parts of exactly equal size. Visual accuracy is key for understanding fractions.

Question 2. Show following fractions by proper diagrams, (i) \( \frac{2}{3} \) (ii) \( \frac{3}{4} \) (iii) \( \frac{1}{5} \)
Answer: We can visually represent these fractions using simple geometric shapes. For circles, we divide them into sectors, and for rectangles, we divide them into equal segments.
(i) \( \frac{2}{3} \) (This diagram shows a circle divided into 3 equal parts, with 2 parts shaded):
(ii) \( \frac{3}{4} \) (This diagram shows a circle divided into 4 equal parts, with 3 parts shaded):
(iii) \( \frac{1}{5} \) (This diagram shows a rectangle divided into 5 equal parts, with 1 part shaded):
In simple words: To show a fraction with a picture, divide a shape into the total number of equal parts shown by the bottom number (denominator). Then, color in the number of parts shown by the top number (numerator). This helps to see the fraction visually.

🎯 Exam Tip: Always divide the whole shape into *equal* parts. If the parts are not equal, the diagram does not correctly represent the fraction.

Question 1. Express the following mixed fractions into improper fractions.
(i) \( 3 \frac{2}{3} \)
(ii) \( 7 \frac{1}{9} \)
Answer: To convert a mixed fraction into an improper fraction, multiply the whole number by the denominator, then add the numerator. Place this result over the original denominator. A mixed fraction combines a whole number and a proper fraction, which is just another way to write an improper fraction.
Formula: \( \frac{\text{(Whole number} \times \text{Denominator) + Numerator}}{\text{Denominator}} \)
(i) \( 3 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \)
(ii) \( 7 \frac{1}{9} = \frac{(7 \times 9) + 1}{9} = \frac{63 + 1}{9} = \frac{64}{9} \)
In simple words: When you have a whole number with a fraction (mixed fraction), change it into a fraction where the top number is bigger than the bottom number (improper fraction). Just multiply the whole number by the bottom number, add the top number, and put this new total over the old bottom number.

🎯 Exam Tip: Always remember the formula: (Whole number × Denominator + Numerator) / Denominator. Practicing this conversion ensures speed and accuracy.

Question 1. Make three equivalent fractions of the following.
(i) \( \frac{3}{4} \)
(ii) \( \frac{1}{3} \)
(iii) \( \frac{2}{7} \)
Answer: To find equivalent fractions, you multiply both the numerator (top number) and the denominator (bottom number) by the same non-zero number. This creates a new fraction that has the same value but is written differently.
(i) For \( \frac{3}{4} \):
First equivalent fraction: \( \frac{3}{4} \times \frac{2}{2} = \frac{6}{8} \)
Second equivalent fraction: \( \frac{3}{4} \times \frac{3}{3} = \frac{9}{12} \)
Third equivalent fraction: \( \frac{3}{4} \times \frac{4}{4} = \frac{12}{16} \)
Thus, three equivalent fractions of \( \frac{3}{4} \) are \( \frac{6}{8}, \frac{9}{12}, \) and \( \frac{12}{16} \).
(ii) For \( \frac{1}{3} \):
First equivalent fraction: \( \frac{1}{3} \times \frac{2}{2} = \frac{2}{6} \)
Second equivalent fraction: \( \frac{1}{3} \times \frac{3}{3} = \frac{3}{9} \)
Third equivalent fraction: \( \frac{1}{3} \times \frac{4}{4} = \frac{4}{12} \)
Thus, three equivalent fractions of \( \frac{1}{3} \) are \( \frac{2}{6}, \frac{3}{9}, \) and \( \frac{4}{12} \).
(iii) For \( \frac{2}{7} \):
First equivalent fraction: \( \frac{2}{7} \times \frac{2}{2} = \frac{4}{14} \)
Second equivalent fraction: \( \frac{2}{7} \times \frac{3}{3} = \frac{6}{21} \)
Third equivalent fraction: \( \frac{2}{7} \times \frac{4}{4} = \frac{8}{28} \)
Thus, three equivalent fractions of \( \frac{2}{7} \) are \( \frac{4}{14}, \frac{6}{21}, \) and \( \frac{8}{28} \).
In simple words: Equivalent fractions are different ways to write the same amount. You can make them by multiplying the top and bottom of a fraction by the same number. For example, half a pizza is the same as two quarters of a pizza.

🎯 Exam Tip: Remember that you must multiply both the numerator and the denominator by the *exact same* non-zero number to keep the fraction equivalent.

Question 2. Check which are the equivalent fractions of the following?
(i) \( \frac{5}{10} \) and \( \frac{1}{2} \)
(ii) \( \frac{3}{7} \) and \( \frac{11}{13} \)
Answer: To check if two fractions are equivalent, you can either simplify both fractions to their lowest terms or use cross-multiplication. If the simplified forms are the same, or the cross-products are equal, then the fractions are equivalent.
(i) For \( \frac{5}{10} \) and \( \frac{1}{2} \):
Simplify \( \frac{5}{10} \): Divide both numerator and denominator by their greatest common divisor, which is 5.
\( \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \)
Since \( \frac{1}{2} \) is equal to \( \frac{1}{2} \), these fractions are equivalent.
(ii) For \( \frac{3}{7} \) and \( \frac{11}{13} \):
Use cross-multiplication: Multiply the numerator of the first fraction by the denominator of the second, and vice-versa.
\( 3 \times 13 = 39 \)
\( 7 \times 11 = 77 \)
Since \( 39 \ne 77 \), the cross-products are not equal, so these fractions are not equivalent. You can also see that \( \frac{3}{7} \) (approximately 0.42) is much smaller than \( \frac{11}{13} \) (approximately 0.84), confirming they are different.
In simple words: To see if two fractions are the same, you can simplify them until they can't be simplified anymore. If they end up being the same simple fraction, then they are equivalent. Another way is to multiply the top of one by the bottom of the other, and if those two results are equal, the fractions are equivalent.

🎯 Exam Tip: Cross-multiplication is a quick and reliable method to check for equivalence, especially with larger numbers or when simplification is not immediately obvious.

Question 1. Dolly get a \( \frac{1}{5} \) of the cake and Teenu gets \( \frac{1}{7} \) of the cake. Then who got the more cake?
Answer:
Dolly's share of cake \( = \frac{1}{5} \)
Teenu's share of cake \( = \frac{1}{7} \)
When comparing unit fractions (fractions with a numerator of 1), the fraction with the smaller denominator is greater. This is because when you divide something into fewer parts, each part is larger.
Since \( 5 < 7 \), it means that the fraction \( \frac{1}{5} \) is greater than \( \frac{1}{7} \).
Therefore, Dolly got more cake than Teenu. Each person gets one piece, so the person whose cake was cut into fewer pieces gets a larger portion.
In simple words: If two friends get a slice of cake, and the whole cake was cut into 5 pieces for one and 7 pieces for the other, the one who got a piece from the 5-piece cake got a bigger slice. So, Dolly got more cake.

🎯 Exam Tip: For unit fractions (where the numerator is 1), the smaller the denominator, the larger the fraction. This is a common concept in fraction comparison.

Question 2. Which fraction is greater?
(i) \( \frac{1}{3} \) and \( \frac{1}{5} \)
(ii) \( \frac{2}{5} \) and \( \frac{2}{7} \)
Answer: To find which fraction is greater, you can either convert them to a common denominator, convert them to decimals, or use cross-multiplication.
(i) For \( \frac{1}{3} \) and \( \frac{1}{5} \):
These are unit fractions (numerator is 1). When comparing unit fractions, the fraction with the smaller denominator is greater.
Since \( 3 < 5 \), therefore \( \frac{1}{3} > \frac{1}{5} \).
Alternatively, using cross-multiplication:
Multiply \( 1 \times 5 = 5 \)
Multiply \( 3 \times 1 = 3 \)
Since \( 5 > 3 \), then \( \frac{1}{3} > \frac{1}{5} \).
(ii) For \( \frac{2}{5} \) and \( \frac{2}{7} \):
These fractions have the same numerator (2). When comparing fractions with the same numerator, the fraction with the smaller denominator is greater.
Since \( 5 < 7 \), therefore \( \frac{2}{5} > \frac{2}{7} \).
Alternatively, using cross-multiplication:
Multiply \( 2 \times 7 = 14 \)
Multiply \( 5 \times 2 = 10 \)
Since \( 14 > 10 \), then \( \frac{2}{5} > \frac{2}{7} \). Fractions with common numerators indicate that fewer parts mean bigger portions when the quantity of parts taken is the same.
In simple words: To see which fraction is bigger, you can imagine sharing something. If the top numbers are the same, the fraction with the smaller bottom number is bigger because the item is divided into fewer, larger pieces. If the top numbers are different, you can multiply diagonally and compare those numbers.

🎯 Exam Tip: Remember the rules for comparing fractions: for unit fractions, smaller denominator means larger fraction; for same numerators, smaller denominator means larger fraction. Cross-multiplication works for all cases.

Question 1. Write the following in ascending and descending order.
(i) \( \frac{3}{7}, \frac{1}{7}, \frac{4}{7}, \frac{8}{7}, \frac{6}{7} \)
(ii) \( \frac{4}{13}, \frac{12}{13}, \frac{8}{13} \)
Answer: When fractions have the same denominator, comparing and ordering them is simple: just compare their numerators (the top numbers). The fraction with the smallest numerator is the smallest, and the one with the largest numerator is the largest.
(i) Given fractions: \( \frac{3}{7}, \frac{1}{7}, \frac{4}{7}, \frac{8}{7}, \frac{6}{7} \)
All denominators are 7. Order the numerators from smallest to largest: 1, 3, 4, 6, 8.
Ascending order (smallest to largest): \( \frac{1}{7} < \frac{3}{7} < \frac{4}{7} < \frac{6}{7} < \frac{8}{7} \)
Descending order (largest to smallest): \( \frac{8}{7} > \frac{6}{7} > \frac{4}{7} > \frac{3}{7} > \frac{1}{7} \)
(ii) Given fractions: \( \frac{4}{13}, \frac{12}{13}, \frac{8}{13} \)
All denominators are 13. Order the numerators from smallest to largest: 4, 8, 12.
Ascending order (smallest to largest): \( \frac{4}{13} < \frac{8}{13} < \frac{12}{13} \)
Descending order (largest to smallest): \( \frac{12}{13} > \frac{8}{13} > \frac{4}{13} \)
In simple words: When all the fractions have the same bottom number, you just need to put the top numbers in order from smallest to biggest for ascending order, or biggest to smallest for descending order. It's like comparing whole numbers directly.

🎯 Exam Tip: This comparison method (ordering numerators) only works when all fractions share a common denominator. If denominators are different, first find a common denominator before ordering.

Question 1. Can you define proper fraction?
Answer: Yes, a proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number). This means the value of a proper fraction is always less than 1 whole. For example, \( \frac{4}{9} \) and \( \frac{5}{7} \) are proper fractions because in both cases, the top number is smaller than the bottom number.
In simple words: A proper fraction is like saying you have part of something, but not the whole thing. The top number is always smaller than the bottom number.

🎯 Exam Tip: Always remember that in a proper fraction, the numerator is always less than the denominator, making the fraction's value less than one whole.

Question 2. Rashmi has put some pieces of khakhre, O looking at these write them in the fractions and tell us which is proper and improper fraction.
Answer: A proper fraction has its numerator smaller than its denominator, meaning its value is less than 1. An improper fraction has its numerator equal to or greater than its denominator, meaning its value is 1 or more. Let's look at the pieces of khakhre and classify them:

In simple words: Look at each picture of khakhre. If the shaded part is less than a whole khakhra, it's a proper fraction. If the shaded part is a whole khakhra or more, it's an improper fraction.

🎯 Exam Tip: Remember that fractions like \( \frac{4}{4} \) (one whole) are often classified as improper fractions because their numerator is equal to or greater than their denominator.

Question 1. Are all the coloured parts of unit in following diagrams equal?
(Diagram 1: A circle divided into 6 equal parts, 2 of which are shaded, representing \( \frac{2}{6} \))
(Diagram 2: A circle divided into 9 equal parts, 3 of which are shaded, representing \( \frac{3}{9} \))
(Diagram 3: A circle divided into 12 equal parts, 4 of which are shaded, representing \( \frac{4}{12} \))
Answer: Yes, all the coloured parts of the unit in the given diagrams are equal. This is because all the fractions shown ( \( \frac{2}{6}, \frac{3}{9}, \frac{4}{12} \) ) simplify to the same fraction, \( \frac{1}{3} \). Even though the circles are divided into different numbers of parts, the total shaded area in each diagram represents the exact same portion of the whole. This clearly demonstrates the concept of equivalent fractions.
In simple words: Yes, the colored parts are all the same size. Each picture shows one-third of the whole colored, even though the total number of slices is different.

🎯 Exam Tip: Remember that different fractions can represent the same amount if they are equivalent. Always simplify fractions to their lowest terms to easily compare their values.

Question 1. Can you compare fractions like numbers 18, 81, 28?
Answer: Yes, we can definitely compare fractions, similar to how we compare whole numbers like 18, 81, or 28. The method for comparing fractions depends on their denominators. If their denominators are the same, we simply compare their numerators. If the denominators are different, we first need to make them the same by finding a common denominator before comparing their numerators. This step is crucial for accurate comparison, as it ensures we are comparing like quantities.
In simple words: Yes, you can compare fractions. If the bottom numbers are the same, just look at the top numbers. If the bottom numbers are different, you first need to change them so they are the same before you can compare.

🎯 Exam Tip: The key to comparing fractions is always to have a common basis, either by making denominators the same or by converting to decimals. This allows for a direct comparison of their values.

Question 2. Look at the above diagram and state which fraction is smaller \( \frac{1}{3} \) or \( \frac{1}{5} \).
(Diagram showing a visual comparison between \( \frac{1}{3} \) and \( \frac{1}{5} \), where \( \frac{1}{5} \) appears smaller.)
Answer: From the diagram provided, it is clear that \( \frac{1}{5} \) is smaller than \( \frac{1}{3} \). This is because \( \frac{1}{3} \) represents one part out of three equal parts of a whole, while \( \frac{1}{5} \) represents one part out of five equal parts of the same whole. When a whole object (like a pizza) is divided into more parts, each individual part becomes smaller. Therefore, sharing a cake with 5 people means each person gets a smaller piece than if the cake was shared among 3 people.
In simple words: If you cut a pizza into 3 slices, each slice is bigger than if you cut it into 5 slices. So, \( \frac{1}{5} \) is a smaller piece than \( \frac{1}{3} \).

🎯 Exam Tip: Visualizing fractions, especially unit fractions, by thinking of sharing a whole item (like a pizza or a bar of chocolate) can help in understanding their relative sizes effectively.

Question 3. Which is greater in unit fractions \( \frac{1}{4} \) and \( \frac{1}{7} \)?
Answer: Between the unit fractions \( \frac{1}{4} \) and \( \frac{1}{7} \), the fraction \( \frac{1}{4} \) is greater. This is because both are unit fractions (their numerator is 1), and among unit fractions, the one with the smaller denominator represents a larger share of the whole. Imagine dividing a whole into 4 parts; each part is bigger than if the same whole was divided into 7 parts. This principle applies universally to any comparison of unit fractions.
In simple words: When the top number of fractions is the same (like 1), the fraction with the smaller bottom number is the bigger one. So, \( \frac{1}{4} \) is bigger than \( \frac{1}{7} \).

🎯 Exam Tip: A good rule of thumb for unit fractions: a smaller denominator always equals a larger piece of the pie because the whole is split into fewer, thus bigger, portions.

Question 1. Take a paper and colour it half. Fold it differently and write the respective fraction. But be aware that all parts should be equal while folding.
Answer: We can demonstrate the concept of equivalent fractions by folding a paper.
First, take a square piece of paper and colour one half of it. This visually represents the fraction \( \frac{1}{2} \).
Next, fold the same paper again so that it is now divided into four equal parts. The originally coloured half will now cover two of these four smaller parts. This represents the fraction \( \frac{2}{4} \).
From this demonstration, we clearly see that \( \frac{2}{4} \) is equivalent to \( \frac{1}{2} \). If we continue this process, for instance, by folding the paper into 6 parts (where 3 parts would be shaded, \( \frac{3}{6} \)), we would consistently find more equivalent fractions of \( \frac{1}{2} \). The total shaded area remains the same, only the number of parts changes.
In simple words: When you fold a paper and color half of it, that's \( \frac{1}{2} \). If you fold it again into more equal pieces, the colored part will now show a different fraction, like \( \frac{2}{4} \), but it's still the same amount of paper colored.

🎯 Exam Tip: Paper folding is a great hands-on way to understand equivalent fractions and visually confirm that different fractions can represent the same quantity of a whole.