RBSE Solutions Class 5 Maths Chapter 7 Equivalent Fractions Exercise 7.1

Question 1. Convert the given fraction in to equivalent fraction by multiplying numerator and denominator by 2.
(i) \( \frac {1}{2} \)
(ii) \( \frac {2}{3} \)
(iii) \( \frac {1}{5} \)
(iv) \( \frac {2}{5} \)
(v) \( \frac {2}{7} \)
Answer:
(i) \( \frac {1}{2} = \frac {1 \times 2 }{ 2 \times 2 } = \frac {2}{4} \)
(ii) \( \frac {2}{3} = \frac {2 \times 2 }{3 \times 2 } = \frac {4}{6} \)
(iii) \( \frac {1}{5} = \frac {1 \times 2 }{ 5 \times 2} = \frac {2}{10} \)
(iv) \( \frac {2}{5} = \frac {2 \times 2 }{ 5 \times 2 } = \frac {4}{10} \)
(v) \( \frac {2}{7} = \frac {2 \times 2 }{ 7 \times 2 } = \frac {4}{14} \)
In each case, multiplying the numerator and denominator by the same number creates an equivalent fraction. This process shows how different fractions can represent the same part of a whole.
In simple words: To find an equivalent fraction, just multiply the top number and the bottom number by the same digit, in this case, by 2.

🎯 Exam Tip: Remember that an equivalent fraction represents the same value as the original fraction, even though the numbers look different. It's like cutting a cake into more slices but still eating the same amount.

Question 2. Convert the given fraction into equivalent fraction by multiplying numerator and denominator by 3.
(i) \( \frac {1}{4} \)
(ii) \( \frac {3}{5} \)
(iii) \( \frac {2}{5} \)
(iv) \( \frac {2}{7} \)
(v) \( \frac {1}{6} \)
Answer:
(i) \( \frac {1}{4} = \frac {1 \times 3 }{ 4 \times 3 } = \frac {3}{12} \)
(ii) \( \frac {3}{5} = \frac {3 \times 3 }{ 5 \times 3 } = \frac {9}{15} \)
(iii) \( \frac {2}{5} = \frac {2 \times 3 }{ 5 \times 3 } = \frac {6}{15} \)
(iv) \( \frac {2}{7} = \frac {2 \times 3 }{ 7 \times 3 } = \frac {6}{21} \)
(v) \( \frac {1}{6} = \frac {1 \times 3 }{ 6 \times 3 } = \frac {3}{18} \)
Multiplying both the top and bottom numbers of a fraction by the same non-zero number always results in an equivalent fraction. This is because you are essentially multiplying the fraction by 1, which doesn't change its value.
In simple words: To get an equivalent fraction, multiply the top and bottom numbers by 3. The new fraction will look different but shows the same amount.

🎯 Exam Tip: Always multiply both the numerator and the denominator by the *exact same number* to ensure the new fraction is truly equivalent and not just a new fraction.

Question 4. Represent the given equivalent fraction by filling colour in following diagrams.
Answer:
The diagrams should show the shaded portions matching the given equivalent fractions. For example, a diagram showing \( \frac{1}{5} \) would have 1 out of 5 parts shaded, and its equivalent \( \frac{3}{15} \) would have 3 out of 15 parts shaded, showing the same proportion. Similarly, \( \frac{1}{3} \) would have 1 out of 3 parts shaded, and \( \frac{2}{6} \) would have 2 out of 6 parts shaded, representing the same amount.
In simple words: Draw a shape, divide it into equal parts, and color the number of parts that match the top number of the fraction. For equivalent fractions, the amount colored should be the same.

🎯 Exam Tip: When drawing diagrams for equivalent fractions, make sure the overall size and shape of the original and equivalent fraction models are identical, to clearly show they represent the same amount.

Question 5. Fill in the blanks
(i) \( \frac {1 \times 3}{3 \times 3} = \frac {\boxed{\phantom{X}}}{9} \)
(ii) \( \frac {2}{5} = \frac { \boxed{\phantom{XX}} }{15} \)
(iii) \( \frac {\boxed{\phantom{XX}}}{5} = \frac {9}{15} \)
(iv) \( \frac {3}{ \boxed{\phantom{XX}} } = \frac {3}{18} \)
(v) \( \frac {14 \div 7}{21 \div 7} = \frac {2}{ \boxed{\phantom{X}} } \)
(vi) \( \frac {12 \div 4}{16 \div 4} = \frac {\boxed{\phantom{X}}}{4} \)
Answer:
(i) \( \frac {1 \times 3}{3 \times 3} = \frac {3}{9} \)
(ii) \( \frac {2}{5} = \frac {6}{15} \) (Since \( 5 \times 3 = 15 \), then \( 2 \times 3 = 6 \))
(iii) \( \frac {3}{5} = \frac {9}{15} \) (Since \( 5 \times 3 = 15 \), then \( \boxed{3} \times 3 = 9 \))
(iv) \( \frac {3}{18} = \frac {3}{18} \) (Since \( 3 \times 6 = 18 \), then \( \boxed{3} \times 6 = 18 \), but the numerator is already 3. The blank must be 6, as \( \frac{3}{6} \) is not equal to \( \frac{3}{18} \). The question implies the denominator must change. Therefore \( \frac{3}{6} \times \frac{3}{3} = \frac{9}{18} \). The blank should be 6, because \( \frac{3}{6} \times \frac{3}{3} = \frac{9}{18} \) or if we consider \( \frac{3}{18} \), then we are looking for a factor. For \( \frac{3}{\boxed{X}} = \frac{3}{18} \), the blank should be 18.) The source is \( \frac{3}{\boxed{\phantom{XX}}} = \frac{3}{18} \). This means the blank must be 18 to make the statement true. If the blank was a factor, it implies a simplification. Based on the other patterns, it seems to be about equivalent fractions by multiplication/division. If \( \frac{3}{X} = \frac{3}{18} \), then X must be 18.
(v) \( \frac {14 \div 7}{21 \div 7} = \frac {2}{3} \)
(vi) \( \frac {12 \div 4}{16 \div 4} = \frac {3}{4} \)
To find the missing number in an equivalent fraction, look at how the known numerator or denominator has changed. Then apply the same multiplication or division to the other part of the fraction. This keeps the fraction's value the same.
In simple words: Fill in the missing numbers by checking what you did to the top or bottom number. If you multiplied by 3, do the same to the other side. If you divided by 4, do that too.

🎯 Exam Tip: For fill-in-the-blank fraction questions, always find the relationship between the complete parts of the equivalent fractions (either the numerators or the denominators), and then apply that same relationship to find the missing part.

Question 6. Give some more examples where we get \( \frac {1}{4} \) after dividing equally and write down below.
Answer:
The question asks for fractions that simplify to \( \frac{1}{4} \) when divided equally, or, more simply, equivalent fractions of \( \frac{1}{4} \). We can find these by multiplying the numerator and denominator by the same number:
\( \frac {1}{4} = \frac {1 \times 2 }{4 \times 2 } = \frac {2}{8} \)
\( \frac {1}{4} = \frac {1 \times 3 }{4 \times 3 } = \frac {3}{12} \)
\( \frac {1}{4} = \frac {1 \times 4 }{4 \times 4 } = \frac {4}{16} \)
\( \frac {1}{4} = \frac {1 \times 5}{4 \times 5 } = \frac {5}{20} \)
\( \frac {1}{4} = \frac {1 \times 6 }{ 4 \times 6 } = \frac {6}{24} \)
All these fractions, such as \( \frac{2}{8} \), \( \frac{3}{12} \), \( \frac{4}{16} \), \( \frac{5}{20} \), and \( \frac{6}{24} \), are equivalent to \( \frac{1}{4} \). They represent the same amount or proportion, just expressed with different numbers. This is a common way to demonstrate the concept of equivalent fractions.
In simple words: We can get many fractions that are the same as \( \frac{1}{4} \). Just multiply the top and bottom of \( \frac{1}{4} \) by the same number, like 2, 3, 4, or 5, to get new fractions like \( \frac{2}{8} \) or \( \frac{3}{12} \).

🎯 Exam Tip: When asked for examples of equivalent fractions, always remember that you can multiply or divide both the numerator and denominator by the same number. It's helpful to show at least three different examples.

Question 7. Write four equivalent fractions of \( \frac {1}{5} \)
Answer:
To find equivalent fractions, we multiply both the numerator and the denominator by the same whole number (other than 1). Here are four equivalent fractions for \( \frac {1}{5} \):
1. \( \frac {1}{5} = \frac {1 \times 2 }{ 5 \times 2 } = \frac {2}{10} \)
2. \( \frac {1}{5} = \frac {1 \times 3 }{ 5 \times 3 } = \frac {3}{15} \)
3. \( \frac {1}{5} = \frac {1 \times 4 }{ 5 \times 4 } = \frac {4}{20} \)
4. \( \frac {1}{5} = \frac {1 \times 5 }{ 5 \times 5} = \frac {5}{25} \)
Each of these fractions represents the same portion as \( \frac{1}{5} \), meaning if you had a pizza cut into 5 slices and ate 1, it's the same amount as eating 2 slices from a pizza cut into 10.
In simple words: To get fractions that are the same as \( \frac{1}{5} \), just multiply the top number (1) and the bottom number (5) by the same number. Do this four times using different numbers like 2, 3, 4, and 5.

🎯 Exam Tip: To create equivalent fractions, you can choose any whole number to multiply both the numerator and denominator, but pick small, easy numbers for quick calculations.

Question 8. Ranu bought 6 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:
Total length of ribbon = 6 meters.
Number of friends = 4.
To find out how much ribbon each friend gets, we divide the total length by the number of friends:
Length for each friend = \( \frac{6 \text{ meters}}{4 \text{ friends}} \)
\( = \frac{6}{4} \text{ meters} \)
We can simplify this fraction by dividing both the numerator and denominator by 2:
\( = \frac{6 \div 2}{4 \div 2} = \frac{3}{2} \text{ meters} \)
As a mixed number, \( \frac{3}{2} \) meters is \( 1 \frac{1}{2} \) meters.
So, each friend will get \( 1 \frac{1}{2} \) meters of ribbon. This is a practical example of dividing a quantity equally and expressing the result as a fraction.
In simple words: Ranu has 6 meters of ribbon and 4 friends. Each friend will get \( 1 \frac{1}{2} \) meters of ribbon when it is divided equally.

🎯 Exam Tip: When solving word problems involving division, write down the given information clearly, set up the division, and remember to simplify the fraction or convert it to a mixed number if appropriate for the answer.