RBSE Solutions Class 5 Maths Chapter 7 Equivalent Fractions Important Questions

Multiple Choice Questions

Question 1. Value of numerator in fraction \( \frac {3}{4} \)
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c) 3
In simple words: In a fraction like \( \frac {3}{4} \), the top number (3) is called the numerator, and the bottom number (4) is called the denominator. The numerator tells us how many parts we have.

🎯 Exam Tip: Remember that the numerator is always the upper part of the fraction, showing the number of selected units.

Question 2. Value of denominator in fraction \( \frac {7}{8} \)
(a) 7
(b) 8
(c) 15
(d) 56
Answer: (b) 8
In simple words: For the fraction \( \frac {7}{8} \), the denominator is 8. The denominator tells us the total number of equal parts into which something is divided.

🎯 Exam Tip: The denominator represents the total number of equal parts of a whole, and it's always the bottom number in a fraction.

Question 3. Equivalent fraction of fraction \( \frac {4}{5} \)
(a) \( \frac {4}{20} \)
(b) \( \frac {8}{10} \)
(c) \( \frac {4}{15} \)
(d) \( \frac {8}{20} \)
Answer: (b) \( \frac {8}{10} \)
In simple words: An equivalent fraction means it has the same value as the original fraction. We get \( \frac {8}{10} \) by multiplying both the top and bottom of \( \frac {4}{5} \) by 2. This keeps the fraction's value the same, just represented differently.

🎯 Exam Tip: To find an equivalent fraction, multiply (or divide) both the numerator and the denominator by the same non-zero number.

Question 4. Simplest form of \( \frac {24}{30} \) is-
(a) \( \frac {4}{5} \)
(b) \( \frac {3}{5} \)
(c) \( \frac {5}{4} \)
(d) \( \frac {5}{3} \)
Answer: (a) \( \frac {4}{5} \)
In simple words: To find the simplest form, we divide both the numerator and the denominator by their greatest common factor. For 24 and 30, the largest number that divides both is 6. So, \( 24 \div 6 = 4 \) and \( 30 \div 6 = 5 \).

🎯 Exam Tip: Always divide by the greatest common factor (GCF) to reach the simplest form in one step, or keep dividing by common factors until no more are left.

Question 6. Equivalent fraction of \( \frac {3}{7} \)
(a) \( \frac {3}{14} \)
(b) \( \frac {9}{7} \)
(c) \( \frac {6}{14} \)
(d) \( \frac {10}{14} \)
Answer: (c) \( \frac {6}{14} \)
In simple words: To find an equivalent fraction, you can multiply both the top (numerator) and bottom (denominator) of \( \frac {3}{7} \) by the same number, which in this case is 2. This gives \( \frac {3 \times 2}{7 \times 2} = \frac {6}{14} \).

🎯 Exam Tip: Remember, equivalent fractions represent the same portion of a whole, even though they have different numbers.

Question 7. \( 1 \frac {1}{4} \) reads as -
(a) one quarter
(b) one and quarter
(c) one and half
(d) three by four
Answer: (b) one and quarter
In simple words: The mixed number \( 1 \frac {1}{4} \) means one whole part and one-fourth of another part. So, we say it as "one and quarter."

🎯 Exam Tip: When reading mixed numbers, always state the whole number first, followed by "and," and then the fraction.

Question 8. Value of numerator and denominator in fraction \( \frac {11}{13} \) -
(a) Numerator 13 denominator 0
(b) Numerator 13 denominator 11
(c) Numerator 11 denominator 13
(d) Numerator 1 denominator 3
Answer: (c) Numerator 11 denominator 13
In simple words: In any fraction, the number on top is the numerator, and the number at the bottom is the denominator. So for \( \frac {11}{13} \), 11 is the numerator and 13 is the denominator.

🎯 Exam Tip: Always clearly identify the top number as the numerator and the bottom number as the denominator in any given fraction.

1. Five by seven can be written as fractional form \( \frac {5}{7} \).
Answer: The phrase "five by seven" in fractional form is written as \( \frac {5}{7} \), where 5 is the numerator and 7 is the denominator. This represents 5 parts out of 7 equal parts.
In simple words: "Five by seven" just means the fraction \( \frac {5}{7} \).

🎯 Exam Tip: Remember that "by" in "X by Y" usually means X is the numerator and Y is the denominator in a fraction.

2. Fractions which are equal called equivalent fraction.
Answer: Fractions that have the same value, even if they look different, are called equivalent fractions. For example, \( \frac {1}{2} \) and \( \frac {2}{4} \) are equivalent because they represent the same amount.
In simple words: Fractions that show the same amount are called equivalent fractions.

🎯 Exam Tip: Always check if fractions simplify to the same value to determine if they are equivalent.

3. To obtain equivalent fraction of a fraction, the numerator and denominator of the fraction are multiplied by same number.
Answer: To get an equivalent fraction, you must multiply both the top number (numerator) and the bottom number (denominator) by the exact same non-zero number. This ensures the fraction's value stays unchanged.
In simple words: To get an equivalent fraction, multiply both the top and bottom numbers by the same number.

🎯 Exam Tip: The rule of multiplying both numerator and denominator by the same number is fundamental for creating equivalent fractions.

4. One of the equivalent fraction of \( \frac {1}{2} \) is \( \frac {2}{4} \).
Answer: One simple way to find an equivalent fraction for \( \frac {1}{2} \) is to multiply both its numerator and denominator by 2, which gives \( \frac {1 \times 2}{2 \times 2} = \frac {2}{4} \). Both fractions represent half of a whole.
In simple words: \( \frac {2}{4} \) is the same as \( \frac {1}{2} \).

🎯 Exam Tip: Always remember that there are many equivalent fractions for any given fraction, not just one.

5. Number written in the form of numerator and denominator called fraction.
Answer: A number that is written with a numerator (top number) and a denominator (bottom number) separated by a line is called a fraction. This form shows a part of a whole.
In simple words: A number with a top and bottom part, like \( \frac {1}{2} \), is called a fraction.

🎯 Exam Tip: Fractions are essential for representing parts of a whole or a collection.

Very Short Answer Type Questions

Question 1. Which are called equivalent fractions?
Answer: Fractions that represent the same value or portion of a whole, even if they have different numerators and denominators, are called equivalent fractions. For instance, \( \frac {1}{2} \) and \( \frac {3}{6} \) are equivalent because they both represent half.
In simple words: Equivalent fractions are different ways to write the same amount, like \( \frac {1}{2} \) and \( \frac {2}{4} \).

🎯 Exam Tip: To confirm if fractions are equivalent, you can cross-multiply or simplify them to their lowest terms.

Question 2. What can be done to obtain equivalent fraction of a fraction.
Answer: To get an equivalent fraction, you can multiply both the numerator (top number) and the denominator (bottom number) of the original fraction by the same non-zero number. You can also divide both by the same common factor. This process ensures the value of the fraction remains constant.
In simple words: To get an equivalent fraction, multiply or divide both the top and bottom numbers by the same number.

🎯 Exam Tip: Remember to apply the same operation (multiplication or division) to both the numerator and the denominator to maintain the fraction's value.

Question 3. Write three equivalent fractions \( \frac {3}{5} \)
Answer: Three equivalent fractions for \( \frac {3}{5} \) can be found by multiplying both the numerator and denominator by 2, 3, and 4 respectively.
\( \frac {3 \times 2}{5 \times 2} = \frac {6}{10} \)
\( \frac {3 \times 3}{5 \times 3} = \frac {9}{15} \)
\( \frac {3 \times 4}{5 \times 4} = \frac {12}{20} \) So, \( \frac {6}{10}, \frac{9}{15}, \frac {12}{20} \) are three equivalent fractions for \( \frac {3}{5} \).
In simple words: Three equivalent fractions for \( \frac {3}{5} \) are \( \frac {6}{10} \), \( \frac {9}{15} \), and \( \frac {12}{20} \). We get these by multiplying the top and bottom of \( \frac {3}{5} \) by 2, 3, and 4.

🎯 Exam Tip: Always show your working steps clearly when finding equivalent fractions to avoid errors and earn full marks.

Short Answer and Essay Type Questions

Question 1. Write three equivalent fractions each of the following fraction
(1) \( \frac {2}{3} \)
(2) \( \frac {1}{7} \)
Answer:
(1) For \( \frac {2}{3} \):
\( \frac {2}{3} = \frac {2 \times 2}{3 \times 2} = \frac {4}{6} \)
\( \frac {2}{3} = \frac {2 \times 3}{3 \times 3} = \frac {6}{9} \)
\( \frac {2}{3} = \frac {2 \times 4}{3 \times 4} = \frac {8}{12} \)
So, three equivalent fractions for \( \frac {2}{3} \) are \( \frac {4}{6}, \frac {6}{9}, \frac {8}{12} \).
(2) For \( \frac {1}{7} \):
\( \frac {1}{7} = \frac {1 \times 2}{7 \times 2} = \frac {2}{14} \)
\( \frac {1}{7} = \frac {1 \times 3}{7 \times 3} = \frac {3}{21} \)
\( \frac {1}{7} = \frac {1 \times 4}{7 \times 4} = \frac {4}{28} \)
So, three equivalent fractions for \( \frac {1}{7} \) are \( \frac {2}{14}, \frac {3}{21}, \frac {4}{28} \).
In simple words: We find equivalent fractions by multiplying the top and bottom of the original fraction by the same number. For \( \frac {2}{3} \), we get \( \frac {4}{6}, \frac {6}{9}, \frac {8}{12} \). For \( \frac {1}{7} \), we get \( \frac {2}{14}, \frac {3}{21}, \frac {4}{28} \).

🎯 Exam Tip: Ensure you multiply both the numerator and the denominator by the same factor consistently for each equivalent fraction you generate.

Question 2. Write four equivalent fractions of \( \frac {9}{10} \).
Answer: To find four equivalent fractions for \( \frac {9}{10} \), we multiply both the numerator and the denominator by 2, 3, 4, and 5 respectively.
(i) \( \frac {9}{10} \times \frac {2}{2} = \frac {18}{20} \)
(ii) \( \frac {9}{10} \times \frac { 3 }{ 3 } = \frac {27}{30} \)
(iii) \( \frac {9}{10} \times \frac {4}{4} = \frac {36}{40} \)
(iv) \( \frac {9}{10} \times \frac {5}{5} = \frac {45}{ 50 } \)
Therefore, four equivalent fractions of \( \frac {9}{10} \) are \( \frac { 18 }{20}, \frac {27}{30}, \frac {36}{40} \) and \( \frac {45}{50} \). These fractions all represent the same value as \( \frac {9}{10} \).
In simple words: We can get four equivalent fractions for \( \frac {9}{10} \) by multiplying its top and bottom by 2, 3, 4, and 5. This gives us \( \frac {18}{20} \), \( \frac {27}{30} \), \( \frac {36}{40} \), and \( \frac {45}{50} \).

🎯 Exam Tip: You can choose any common whole numbers to multiply by, but using sequential numbers like 2, 3, 4, 5 is often the easiest way to generate a series of equivalent fractions.

Question 4. Shade the region of each figure representing fraction given below :
Answer: The figures below represent the equivalent fractions \( \frac {1}{3} \) and \( \frac {2}{6} \). Both show the same proportion of the whole circle shaded.
In simple words: The picture shows two circles that are divided into parts. The first circle shows 1 part out of 3 shaded, representing \( \frac {1}{3} \). The second circle shows 2 parts out of 6 shaded, representing \( \frac {2}{6} \). Both shaded areas are the same size.

🎯 Exam Tip: Always make sure the shaded portion accurately reflects the given fraction, and for equivalent fractions, visually confirm that the shaded areas are indeed equal.

Question 5. Seema bought 5 meter long ribbon from market, if she equally divides it between 4 friends, then what is the length of ribbon each friend will get ?
Answer: Seema has a 5-meter ribbon that she wants to divide equally among 4 friends.
Length of ribbon each friend will get \( = 5 \div 4 \) meters
\( = \frac {5}{4} \) meters
This can also be written as a mixed number: \( 1 \frac {1}{4} \) meters.
So, each friend will receive one and a quarter meters of ribbon. Dividing helps share items fairly.
In simple words: Seema divides 5 meters of ribbon among 4 friends. Each friend gets \( 1 \frac {1}{4} \) meters of ribbon.

🎯 Exam Tip: When dividing a whole quantity among several people, express the answer as a fraction or a mixed number to show any remaining parts.

Question 6. 5 kg. Jaggery divided equally among two families then how much jaggery each family will get ?
Answer: If 5 kg of jaggery is divided equally between two families, we need to perform division to find out how much each family gets.
Amount each family will get \( = 5 \div 2 \) kg
\( = \frac {5}{2} \) kg
As a mixed number, this is \( 2 \frac {1}{2} \) kg.
So, each family will get two and a half kilograms of jaggery. This simple division helps share items fairly.
In simple words: When 5 kg of jaggery is shared between two families, each family will receive \( 2 \frac {1}{2} \) kg.

🎯 Exam Tip: In word problems, always identify the total quantity and the number of groups to ensure correct division and obtain the share for each group.

Question. 6 litre milk distributed between 12 children, then much litre milk each children will drink?
Answer: To find out how much milk each child drinks when 6 liters are shared among 12 children, we divide the total milk by the number of children.
Milk each child will drink \( = 6 \div 12 \) liters
\( = \frac {6}{12} \) liters
Simplifying the fraction, we get \( \frac {1}{2} \) liter.
So, each child will drink half a liter of milk. This shows how division helps distribute quantities evenly.
In simple words: If 6 liters of milk are shared by 12 children, each child drinks \( \frac {1}{2} \) liter.

🎯 Exam Tip: Always simplify fractions to their lowest terms to provide the clearest and most understandable answer in real-world scenarios.

Question 8. Nazeeb needs \( 2 \frac {1}{2} \) meter (two and half) cloth to make a payjama. How much cloth he needs to make three such payjamas.
Answer: Nazeeb needs \( 2 \frac {1}{2} \) meters of cloth for one payjama. To find out how much cloth he needs for three payjamas, we multiply the cloth needed for one by three.
Cloth needed for 1 payjama \( = 2 \frac {1}{2} \) meters
This can be written as an improper fraction: \( \frac {5}{2} \) meters.
Cloth needed for 3 payjamas \( = 3 \times \frac {5}{2} \) meters
\( = \frac {15}{2} \) meters
Converting this back to a mixed number, \( \frac {15}{2} = 7 \frac {1}{2} \) meters.
Therefore, Nazeeb needs \( 7 \frac {1}{2} \) (seven and a half) meters of cloth to make three payjamas. This calculation helps determine total material required.
In simple words: Nazeeb needs \( 2 \frac {1}{2} \) meters of cloth for one payjama. For three payjamas, he will need \( 7 \frac {1}{2} \) meters of cloth.

🎯 Exam Tip: When multiplying mixed numbers, convert them to improper fractions first to simplify the calculation, then convert back to a mixed number if required.

Question 9. 17kg. wheat divided equally among 4 families then how much kg wheat each family will get ?
Answer: If 17 kg of wheat is divided equally among 4 families, we must divide the total amount of wheat by the number of families.
Amount each family will get \( = 17 \div 4 \) kg
\( = \frac {17}{4} \) kg
When converted to a mixed number, \( \frac {17}{4} = 4 \frac {1}{4} \) kg.
So, each family will get \( 4 \frac {1}{4} \) (four and one by four) kg of wheat. This demonstrates a real-world application of fractions in sharing.
In simple words: 17 kg of wheat is shared by 4 families. Each family gets \( 4 \frac {1}{4} \) kg of wheat.

🎯 Exam Tip: Always include the correct units (e.g., kg, liters, meters) in your final answer for word problems.

Question 10. 14 litre kerosene filled equally in 4 stoves, then how much kerosene will be filled in each stove?
Answer: To find out how much kerosene goes into each stove when 14 liters are divided among 4 stoves, we perform a division.
Kerosene filled in each stove \( = 14 \div 4 \) liters
\( = \frac {14}{4} \) liters
This fraction can be simplified to \( \frac {7}{2} \) liters.
Converting this to a mixed number, \( \frac {7}{2} = 3 \frac {1}{2} \) liters.
Therefore, \( 3 \frac {1}{2} \) (three and a half) liters of kerosene will be filled in each stove. This shows a practical use of dividing quantities.
In simple words: 14 liters of kerosene are shared among 4 stoves. Each stove will get \( 3 \frac {1}{2} \) liters of kerosene.

🎯 Exam Tip: Remember to simplify fractions to their lowest terms and convert them to mixed numbers if the context of the problem implies whole units and remaining parts.

Question 11. Hemlata studied for 2 hours. She has read \( \frac {3}{4} \) (Three by four) hour. Now, how much time is it to read Hemlata
Answer: Hemlata studied for a total of 2 hours. She has already read for \( \frac {3}{4} \) of an hour. To find out how much more time she needs to read, we subtract the time she has already read from her total study time.
Total study time \( = 2 \) hours
Time already read \( = \frac {3}{4} \) hour
Remaining time to read \( = 2 - \frac {3}{4} \) hours
To subtract, convert 2 hours to a fraction with a denominator of 4: \( 2 = \frac {8}{4} \) hours.
Remaining time to read \( = \frac {8}{4} - \frac {3}{4} = \frac {8-3}{4} = \frac {5}{4} \) hours.
This can also be expressed as a mixed number: \( 1 \frac {1}{4} \) hours.
Therefore, Hemlata still needs to read for \( 1 \frac {1}{4} \) (one and one-quarter) hours. This calculation helps manage study time effectively.
In simple words: Hemlata studied for 2 hours and read for \( \frac {3}{4} \) hour. She still needs to read for \( 1 \frac {1}{4} \) hours.

🎯 Exam Tip: When subtracting fractions from whole numbers, always convert the whole number into a fraction with the same denominator as the fraction being subtracted.

Question 12. Meena took \( \frac {1}{2} \) litre milk, her sister took \( 1 \frac {1}{2} \) liters of milk and brought it ? How much milk came in the house ? If milk is Rs 20 per litre then how much rupees did Meena spend and how much her sister did spend ?
Answer: First, let's find the total milk brought home.
Meena took \( \frac {1}{2} \) liter milk.
Her sister took \( 1 \frac {1}{2} \) liters milk, which is \( \frac {3}{2} \) liters.
Total milk in the house \( = \frac {1}{2} + 1 \frac {1}{2} = \frac {1}{2} + \frac {3}{2} = \frac {1+3}{2} = \frac {4}{2} = 2 \) liters.
So, 2 liters of milk came into the house.
Next, we calculate the cost. The price is Rs 20 per liter.
Meena's cost \( = \frac {1}{2} \text{ liter} \times \text{Rs } 20/\text{liter} = \text{Rs } 10 \).
Sister's cost \( = 1 \frac {1}{2} \text{ liters} \times \text{Rs } 20/\text{liter} = \frac {3}{2} \times \text{Rs } 20 = \text{Rs } 30 \).
Therefore, Meena spent Rs 10, and her sister spent Rs 30. This problem combines addition and multiplication of fractions.
In simple words: Meena brought \( \frac {1}{2} \) liter and her sister brought \( 1 \frac {1}{2} \) liters, making a total of 2 liters. Meena spent Rs 10, and her sister spent Rs 30 since milk costs Rs 20 per liter.

🎯 Exam Tip: For problems involving multiple steps, break them down into smaller, manageable parts. Clearly calculate total quantities first, then individual costs.