RBSE Solutions Class 6 Maths Chapter 5 Fractions Exercise 5.4

Fractions Ex 5.4

Question 1. Solve the following.
Answer:
(iv) To add \( \frac{4}{7} \) and \( \frac{3}{14} \), we first find a common denominator for 7 and 14, which is 14. We convert \( \frac{4}{7} \) to an equivalent fraction with denominator 14.
\( \frac{4}{7} + \frac{3}{14} = \frac{4 \times 2}{7 \times 2} + \frac{3}{14} = \frac{8}{14} + \frac{3}{14} \)
Now, we can add the numerators:
\( \frac{8+3}{14} = \frac{11}{14} \)
The sum of the fractions is \( \frac{11}{14} \).
In simple words: When adding fractions, make sure the bottom numbers are the same. If they are not, change one or both fractions to have a common bottom number, then add the top numbers.

🎯 Exam Tip: Always look for the Least Common Multiple (LCM) of the denominators to simplify calculations and avoid larger numbers.

Question 1. Solve the following.
Answer:
(v) To add \( \frac{2}{5} \), \( \frac{3}{4} \), and \( \frac{5}{3} \), we need to find the Least Common Multiple (LCM) of the denominators 5, 4, and 3. The LCM of 5, 4, and 3 is 60. Now, we convert each fraction to an equivalent fraction with a denominator of 60.
\( \frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60} \)
\( \frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60} \)
\( \frac{5}{3} = \frac{5 \times 20}{3 \times 20} = \frac{100}{60} \)
Now, add the equivalent fractions:
\( \frac{24}{60} + \frac{45}{60} + \frac{100}{60} = \frac{24+45+100}{60} = \frac{169}{60} \)
The sum of the fractions is \( \frac{169}{60} \).
In simple words: When adding many fractions, find the smallest number that all bottom numbers can divide into. Change each fraction to have this new bottom number, then add all the top numbers together.

🎯 Exam Tip: When finding the LCM for multiple numbers, it's helpful to list the multiples or use prime factorization to ensure accuracy.

Question 1. Solve the following.
Answer:
(vi) To add \( \frac{17}{6} \) and \( \frac{18}{5} \), we find the Least Common Multiple (LCM) of the denominators 6 and 5. The LCM of 6 and 5 is 30. We convert each fraction to an equivalent fraction with a denominator of 30.
\( \frac{17}{6} = \frac{17 \times 5}{6 \times 5} = \frac{85}{30} \)
\( \frac{18}{5} = \frac{18 \times 6}{5 \times 6} = \frac{108}{30} \)
Now, we add the numerators:
\( \frac{85}{30} + \frac{108}{30} = \frac{85+108}{30} = \frac{193}{30} \)
The sum of the fractions is \( \frac{193}{30} \).
In simple words: To add fractions with different bottom numbers, first find the smallest common number they both divide into. Make both fractions have this new bottom number, then add the top numbers.

🎯 Exam Tip: Always double-check your multiplication when converting fractions to equivalent forms to avoid errors in the numerator.

Question 1. Solve the following.
Answer:
(vii) To add \( 4\frac{1}{3} \) and \( 3\frac{1}{3} \), we first convert these mixed numbers into improper fractions. For \( 4\frac{1}{3} \), we multiply the whole number (4) by the denominator (3) and add the numerator (1), keeping the same denominator: \( \frac{(4 \times 3) + 1}{3} = \frac{12+1}{3} = \frac{13}{3} \). Similarly, for \( 3\frac{1}{3} \), it becomes \( \frac{(3 \times 3) + 1}{3} = \frac{9+1}{3} = \frac{10}{3} \).
Now that both fractions have the same denominator, we can add the numerators:
\( \frac{13}{3} + \frac{10}{3} = \frac{13+10}{3} = \frac{23}{3} \)
The sum is \( \frac{23}{3} \).
In simple words: To add numbers like "4 and a third," first turn them into fractions where the top number is bigger than the bottom. Then, if the bottom numbers are the same, just add the top numbers.

🎯 Exam Tip: Converting mixed numbers to improper fractions before adding them simplifies the process, especially when denominators are already the same or easily made common.

Question 1. Solve the following.
Answer:
(viii) To add \( 5\frac{3}{5} \) and \( 3\frac{5}{7} \), we first convert these mixed numbers to improper fractions.
For \( 5\frac{3}{5} \): \( \frac{(5 \times 5) + 3}{5} = \frac{25+3}{5} = \frac{28}{5} \)
For \( 3\frac{5}{7} \): \( \frac{(3 \times 7) + 5}{7} = \frac{21+5}{7} = \frac{26}{7} \)
Now we need to add \( \frac{28}{5} \) and \( \frac{26}{7} \). The Least Common Multiple (LCM) of the denominators 5 and 7 is 35. We convert each fraction to an equivalent fraction with a denominator of 35.
\( \frac{28}{5} = \frac{28 \times 7}{5 \times 7} = \frac{196}{35} \)
\( \frac{26}{7} = \frac{26 \times 5}{7 \times 5} = \frac{130}{35} \)
Now, we add the numerators:
\( \frac{196}{35} + \frac{130}{35} = \frac{196+130}{35} = \frac{326}{35} \)
The sum of the fractions is \( \frac{326}{35} \).
In simple words: First, change the mixed numbers into fractions where the top part is bigger. Then, find a common bottom number for these fractions, change them again, and finally add their top parts.

🎯 Exam Tip: Always convert mixed numbers to improper fractions before finding a common denominator for addition or subtraction, as this reduces errors.

Question 2. Sunitha got \( \frac { 1 }{ 4 } \) part and Marry got \( \frac { 1 }{ 4 } \) parts of a mango. Both will get how much part of mango all together.
Answer: Sunitha received \( \frac { 1 }{ 4 } \) of the mango. Marry also received \( \frac { 1 }{ 4 } \) of the mango. To find the total part of mango they both got, we add their parts. Since the denominators are already the same, we just add the numerators.
Total part of mango = \( \frac { 1 }{ 4 } + \frac { 1 }{ 4 } = \frac { 1+1 }{ 4 } = \frac { 2 }{ 4 } \)
This fraction can be simplified by dividing both the numerator and the denominator by 2.
\( \frac { 2 }{ 4 } = \frac { 1 }{ 2 } \)
So, together they got \( \frac { 1 }{ 2 } \) part of the mango. This means they shared half of the mango.
In simple words: Sunitha got a quarter of a mango, and Marry also got a quarter. Together, they got two quarters, which is the same as half a mango.

🎯 Exam Tip: Always simplify your final fraction answer to its lowest terms unless the question specifically asks for an unsimplified form.

Question 3. Reabna purchased \( \frac { 1 }{ 3 } \) meter and Jaya purchased \( \frac { 3 }{ 5 } \) meter of ribbon. Find out the total length of ribbon they purchased.
Answer: Reabna bought \( \frac { 1 }{ 3 } \) meter of ribbon. Jaya bought \( \frac { 3 }{ 5 } \) meter of ribbon. To find the total length, we need to add the lengths they both bought. First, we find the Least Common Multiple (LCM) of the denominators, 3 and 5, which is 15. Then we convert each fraction to an equivalent fraction with a denominator of 15.
Reabna's ribbon = \( \frac { 1 }{ 3 } = \frac { 1 \times 5 }{ 3 \times 5 } = \frac { 5 }{ 15 } \) meter
Jaya's ribbon = \( \frac { 3 }{ 5 } = \frac { 3 \times 3 }{ 5 \times 3 } = \frac { 9 }{ 15 } \) meter
Now, we add the equivalent fractions:
Total length = \( \frac { 5 }{ 15 } + \frac { 9 }{ 15 } = \frac { 5+9 }{ 15 } = \frac { 14 }{ 15 } \) meter
Therefore, they purchased a total of \( \frac { 14 }{ 15 } \) meter of ribbon. Combining lengths requires this common unit.
In simple words: Reabna bought a part of ribbon and Jaya bought another part. To know how much ribbon they bought in total, we add their lengths by first making the bottom numbers of the fractions the same.

🎯 Exam Tip: Clearly state the individual quantities before performing the addition, and remember to include the correct units (e.g., meters) in your final answer.

Question 4. Ramesh covered \( 4\frac{1}{4} \) km of distance by bus and he walked \( \frac{3}{4} \) km distance to reach school from home. How much total distance he covered to reach school?
Answer: Ramesh travelled \( 4\frac{1}{4} \) km by bus. He then walked \( \frac{3}{4} \) km. To find the total distance, we add the distance covered by bus and the distance he walked. First, convert the mixed number \( 4\frac{1}{4} \) into an improper fraction: \( \frac{(4 \times 4) + 1}{4} = \frac{16+1}{4} = \frac{17}{4} \) km.
Now, add the two distances:
Total distance = Distance by bus + Distance walked
Total distance = \( \frac{17}{4} + \frac{3}{4} \) km
Since the denominators are already the same, we just add the numerators:
Total distance = \( \frac{17+3}{4} = \frac{20}{4} \) km
This fraction can be simplified by dividing both the numerator and the denominator by 4.
Total distance = \( 5 \) km
So, Ramesh covered a total of 5 km to reach school. This daily journey combines travel methods.
In simple words: Ramesh went some distance by bus and some by walking. To find the total distance, we add these two distances together.

🎯 Exam Tip: Always convert mixed numbers to improper fractions before performing addition or subtraction, especially when dealing with word problems involving distances or quantities.

Question 5. Amit took \( \frac{1}{2} \) litre milk first day, \( \frac{3}{4} \) litre second day and \( 1\frac{1}{4} \) litre third day. Find out how much total milk he took in these three days.
Answer: Amit consumed different amounts of milk over three days. We need to find the total quantity of milk consumed by adding the amounts from each day.
Milk on the first day = \( \frac{1}{2} \) litre
Milk on the second day = \( \frac{3}{4} \) litre
Milk on the third day = \( 1\frac{1}{4} \) litre
First, convert the mixed number \( 1\frac{1}{4} \) to an improper fraction: \( \frac{(1 \times 4) + 1}{4} = \frac{4+1}{4} = \frac{5}{4} \) litre.
Now, we add the three quantities: \( \frac{1}{2} + \frac{3}{4} + \frac{5}{4} \)
To add these, we find the Least Common Multiple (LCM) of the denominators 2, 4, and 4, which is 4. Convert \( \frac{1}{2} \) to an equivalent fraction with a denominator of 4:
\( \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \)
Now, add all the fractions:
Total milk = \( \frac{2}{4} + \frac{3}{4} + \frac{5}{4} = \frac{2+3+5}{4} = \frac{10}{4} \) litre
This fraction can be simplified by dividing both the numerator and denominator by 2:
Total milk = \( \frac{5}{2} \) litre, which can also be written as \( 2\frac{1}{2} \) litre. So, Amit drank two and a half liters of milk in total. This helps track daily intake.
In simple words: Amit drank milk on three days. To find out how much he drank in total, we add the amounts from each day. We make sure all the fractions have the same bottom number before adding them up.

🎯 Exam Tip: When dealing with multiple fractions, convert any mixed numbers first, then find the LCM of all denominators before adding to ensure a smooth calculation.