RBSE Solutions Class 6 Maths Chapter 5 Fractions Important Questions

Rajasthan Board RBSE Class 6 Maths Chapter 5 Fractions Additional Questions

Multiple Choice Questions

Question 1. Parts of fractions:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2
In simple words: A fraction is made of two main parts: the top number (numerator) and the bottom number (denominator). These two parts show how many pieces you have out of the total.

🎯 Exam Tip: Remember, the numerator is the number of parts taken, and the denominator is the total number of equal parts in the whole.

Question 2. Improper fraction in the following:
(a) \( \frac {4}{7} \)
(b) \( \frac {2}{3} \)
(c) \( \frac {6}{5} \)
(d) \( \frac {7}{8} \)
Answer: (c) \( \frac {6}{5} \)
In simple words: An improper fraction is when the top number (numerator) is bigger than or equal to the bottom number (denominator). This means the fraction is equal to or more than one whole.

🎯 Exam Tip: To identify an improper fraction quickly, just check if the numerator is greater than or equal to the denominator.

Question 3. Proper fraction in the following:
(a) \( \frac {1}{4} \)
(b) \( \frac {8}{3} \)
(c) \( \frac {5}{2} \)
(d) \( \frac {4}{3} \)
Answer: (a) \( \frac {1}{4} \)
In simple words: A proper fraction is when the top number (numerator) is smaller than the bottom number (denominator). This type of fraction always represents a value less than one whole.

🎯 Exam Tip: Always remember that a proper fraction looks like a "normal" fraction, representing a part of a whole, not more than a whole.

Question 5. Bigger fraction in \( \frac {5}{7} \) and \( \frac {6}{7} \):
(a) \( \frac {5}{7} \)
(b) \( \frac {6}{7} \)
(c) \( \frac {1}{7} \)
(d) \( \frac {7}{6} \)
Answer: (b) \( \frac {6}{7} \)
In simple words: When two fractions have the same bottom number (denominator), the fraction with the bigger top number (numerator) is the larger fraction. This is because they are divided into the same number of parts, but one has more of those parts.

🎯 Exam Tip: For fractions with common denominators, comparing numerators directly gives you the larger or smaller fraction. The greater the numerator, the greater the fraction.

Question 6. Smaller fraction in \( \frac {7}{9} \) and \( \frac {8}{9} \):
(a) \( \frac {7}{9} \)
(b) \( \frac {8}{9} \)
(c) \( \frac {1}{9} \)
(d) \( \frac {9}{8} \)
Answer: (a) \( \frac {7}{9} \)
In simple words: If two fractions share the same bottom number, the one with the smaller top number is the smaller fraction. It's like having fewer slices from the same-sized cake.

🎯 Exam Tip: When denominators are the same, simply compare the numerators. The fraction with the smaller numerator is the smaller fraction.

Question 7. Bigger fraction in \( \frac {1}{4} \) and \( \frac {1}{7} \):
(a) \( \frac {1}{3} \)
(b) \( \frac {1}{2} \)
(c) \( \frac {1}{7} \)
(d) \( \frac {1}{4} \)

🎯 Exam Tip: When numerators are the same, the fraction with the smaller denominator is actually the bigger fraction because the whole is divided into fewer, larger pieces.

Question 8. Simplified form of \( \frac {25}{35} \) is
(a) \( \frac {25}{35} \)
(b) \( \frac {2}{3} \)
(c) \( \frac {5}{7} \)
(d) \( \frac {4}{5} \)

🎯 Exam Tip: To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF) until no further division is possible.

(i) In a fraction, the total number of divisions of a unit is called the denominator.
Answer: The total number of equal parts into which a whole is divided in a fraction is known as the denominator. This bottom number helps us understand the size of each part.
In simple words: The denominator shows how many equal pieces a whole thing is cut into.

🎯 Exam Tip: Always remember the denominator tells you the 'total' or 'whole' number of parts.

(ii) In a fraction, some parts taken from divisions of a unit are called the numerator.
Answer: In a fraction, the parts that are selected or taken from the total divisions of a unit are called the numerator. This is the top number of the fraction.
In simple words: The numerator is the number on top that tells you how many pieces you have.

🎯 Exam Tip: Think of the numerator as "how many you have" out of the "total parts" (denominator).

(iii) In a mixed fraction, one part is a whole number and the other part is a fraction.
Answer: A mixed fraction consists of two parts: one part is a whole number, and the other part is a proper fraction. For example, \(2\frac{1}{2}\) means two whole units and half of another unit.
In simple words: A mixed fraction has a whole number and a fraction together.

🎯 Exam Tip: Mixed fractions combine whole units and parts of a unit, offering a clear representation of amounts greater than one.

(iv) Equivalent fraction of \( \frac {4}{9} \) will be \( \frac {8}{18} \).
Answer: An equivalent fraction of \( \frac {4}{9} \) can be found by multiplying both the numerator and the denominator by the same non-zero number. If we multiply both by 2, we get \( \frac {4 \times 2}{9 \times 2} = \frac {8}{18} \). Equivalent fractions represent the same portion of a whole, just with different numbers.
In simple words: To get an equivalent fraction, multiply the top and bottom numbers by the same number. \( \frac {8}{18} \) is the same as \( \frac {4}{9} \).

🎯 Exam Tip: To find equivalent fractions, you can multiply or divide both the numerator and denominator by the same number.

(v) Fractions with like denominators are called like fractions.
Answer: Fractions that have the same denominator (the bottom number) are called like fractions. This means they are parts of a whole that has been divided into the same number of pieces, making them easy to compare or add.
In simple words: Fractions are "like" each other if their bottom numbers are the same.

🎯 Exam Tip: Like fractions are simple to compare because you only need to look at their numerators.

Very Short Answer Type Questions

Question 1. Arrange \( \frac {1}{7},\frac {1}{4},\frac {1}{9},\frac {1}{5} \) in ascending order.
Answer: To arrange fractions with the same numerator in ascending order, we look at their denominators. The fraction with the largest denominator will be the smallest value, and the fraction with the smallest denominator will be the largest value.
\( \frac {1}{9} < \frac {1}{7} < \frac {1}{5} < \frac {1}{4} \)
In simple words: When the top numbers are all 1, the fraction with the biggest bottom number is the smallest. So, we put them in order from the smallest bottom number to the biggest.

🎯 Exam Tip: For fractions with the same numerator, a larger denominator means a smaller fraction, as the whole is divided into more pieces.

Question 2. What will be the sum of \( \frac {8}{7} + \frac {9}{2} \)?
Answer: To add fractions with different denominators, we first find a common denominator. For 7 and 2, the least common multiple is 14.
\( \frac {8}{7} + \frac {9}{2} \)
To make the denominators 14, we multiply \( \frac {8}{7} \) by \( \frac {2}{2} \) and \( \frac {9}{2} \) by \( \frac {7}{7} \).
\( = \frac {8 \times 2}{7 \times 2} + \frac {9 \times 7}{2 \times 7} \)
\( = \frac {16}{14} + \frac {63}{14} \)
Now we can add the numerators.
\( = \frac {16 + 63}{14} \)
\( = \frac {79}{14} \)
This is an improper fraction, meaning its value is greater than 1.
In simple words: To add these fractions, we first find a common bottom number, which is 14. Then we change both fractions to have 14 at the bottom. After that, we add the top numbers together.

🎯 Exam Tip: Always find the least common multiple (LCM) of the denominators before adding or subtracting fractions to simplify calculations.

Question 3. Convert mixed fraction \( 7\frac {1}{2 } \) in improper fraction.
Answer: To convert a mixed fraction into an improper fraction, we multiply the whole number by the denominator and then add the numerator to that product. The denominator remains the same.
For \( 7\frac{1}{2} \):
Multiply the whole number (7) by the denominator (2): \( 7 \times 2 = 14 \).
Add the numerator (1) to the result: \( 14 + 1 = 15 \).
Keep the original denominator (2).
So, \( 7\frac{1}{2} = \frac {15}{2} \).
This improper fraction means you have 15 halves, which is equivalent to 7 whole units and one half.
In simple words: To change a mixed fraction to a top-heavy fraction, multiply the big whole number by the bottom number, then add the top number. Keep the same bottom number.

🎯 Exam Tip: Remember the order: multiply the whole number by the denominator, then add the numerator, keeping the original denominator.

Short/Long Answers Type Questions

Question 1. Find five equivalent fractions of \( \frac {2}{5} \).
Answer: To find equivalent fractions, we multiply both the numerator and the denominator by the same non-zero whole number.
1. Multiply by 2: \( \frac {2}{5} \times \frac {2}{2} = \frac {4}{10} \)
2. Multiply by 3: \( \frac {2}{5} \times \frac {3}{3} = \frac {6}{15} \)
3. Multiply by 4: \( \frac {2}{5} \times \frac {4}{4} = \frac {8}{20} \)
4. Multiply by 5: \( \frac {2}{5} \times \frac {5}{5} = \frac {10}{25} \)
5. Multiply by 6: \( \frac {2}{5} \times \frac {6}{6} = \frac {12}{30} \)
Thus, five equivalent fractions of \( \frac {2}{5} \) are \( \frac {4}{10}, \frac {6}{15}, \frac {8}{20}, \frac {10}{25}, \) and \( \frac {12}{30} \). These fractions all represent the same portion, just expressed with different numbers.
In simple words: To get fractions that are worth the same as \( \frac {2}{5} \), you can multiply both the top and bottom numbers by the same counting number (like 2, 3, 4, 5, 6).

🎯 Exam Tip: Make sure to multiply both the numerator and the denominator by the *exact same* number to maintain the fraction's value.

Question 2. Reena ate \( \frac {3}{5} \) part of a fruit and Kamal ate \( \frac {2}{5} \) part of that fruit. How much fruit they ate together?
Answer: To find out how much fruit Reena and Kamal ate together, we need to add the parts they each ate.
Reena ate \( \frac {3}{5} \) of the fruit.
Kamal ate \( \frac {2}{5} \) of the fruit.
Total fruit eaten = Reena's part + Kamal's part
\( = \frac {3}{5} + \frac {2}{5} \)
Since the denominators are the same, we can simply add the numerators:
\( = \frac {3+2}{5} \)
\( = \frac {5}{5} \)
\( = 1 \)
So, together they ate 1 whole fruit. This means they finished the entire fruit.
In simple words: Reena ate three-fifths and Kamal ate two-fifths. Because the bottom numbers are the same, we just add the top numbers. \( \frac {5}{5} \) means they ate one whole fruit.

🎯 Exam Tip: When adding fractions with the same denominator, only add the numerators and keep the denominator unchanged.

Question 3. Sohan has \( \frac {5}{8} \) bananas. He gave \( \frac {1}{2 } \) bananas to Monika. How many bananas Sohan has left with?
Answer: To find out how many bananas Sohan has left, we need to subtract the bananas he gave to Monika from the total bananas he had.
Sohan had \( \frac {5}{8} \) bananas.
He gave \( \frac {1}{2} \) bananas to Monika.
Bananas left = Total bananas - Bananas given away
\( = \frac {5}{8} - \frac {1}{2} \)
First, we need a common denominator for 8 and 2. The least common multiple is 8.
We change \( \frac {1}{2} \) to an equivalent fraction with a denominator of 8:
\( \frac {1}{2} = \frac {1 \times 4}{2 \times 4} = \frac {4}{8} \)
Now, subtract the fractions:
\( = \frac {5}{8} - \frac {4}{8} \)
\( = \frac {5-4}{8} \)
\( = \frac {1}{8} \)
Sohan has \( \frac {1}{8} \) of the bananas left. This means he has only a small portion remaining.
In simple words: Sohan started with five-eighths of bananas. He gave away half, which is four-eighths. When you take four-eighths from five-eighths, he is left with one-eighth of the bananas.

🎯 Exam Tip: Always convert fractions to a common denominator before performing subtraction to ensure correct calculation.