Samacheer Kalvi Class 5 Maths Solutions Term 2 Chapter 5 Interconcept Exercise 5.4

Question 1. Answer the following
(i) 3 Km 500 m = __________
Answer:
(i) 3 Km 500 m = \( 3 + 500 \times \frac { 1 }{ 1000 } \)
= \( 3 + \frac { 1 }{ 2 } = 3\frac { 1 }{ 2 } \) km
500 meters is half of a kilometer. So, 3 kilometers and 500 meters is the same as \( 3\frac{1}{2} \) kilometers.
In simple words: To change meters to kilometers, divide the meters by 1000. Then add it to the existing kilometers.

🎯 Exam Tip: Remember the basic conversion: 1 kilometer = 1000 meters. This is crucial for converting units.

(ii) 25 Km 250 m = __________
Answer:
(ii) 25 Km 250 m = \( 25 + 250 \times \frac { 1 }{ 1000 } \)
= \( 25 + \frac { 1 }{ 4 } = 25\frac { 1 }{ 4 } \) km
250 meters is one-fourth of a kilometer. So, 25 kilometers and 250 meters equals \( 25\frac{1}{4} \) kilometers.
In simple words: Divide the meters by 1000 to get the kilometer fraction. Add this to the whole kilometers.

🎯 Exam Tip: Always remember that 1000 meters make 1 kilometer when performing unit conversions.

(iii) 17 Km 750 m = __________
Answer:
(iii) 17 Km 750 m = \( 17 + 750 \times \frac { 1 }{ 1000 } \)
= \( 17 + \frac { 3 }{ 4 } = 17\frac { 3 }{ 4 } \) km
750 meters is three-fourths of a kilometer. So, 17 kilometers and 750 meters equals \( 17\frac{3}{4} \) kilometers.
In simple words: Convert meters to kilometers by dividing by 1000. Then, express the total as a mixed number.

🎯 Exam Tip: Practice simplifying fractions to their lowest terms for a cleaner and more accurate answer.

(iv) 35 Km 250 m = __________
Answer:
(iv) 35 Km 250 m = \( 35 + 250 \times \frac { 1 }{ 1000 } \)
= \( 35 + \frac { 1 }{ 4 } = 35\frac { 1 }{ 4 } \) km
250 meters is a quarter of a kilometer. So, 35 kilometers and 250 meters can be written as \( 35\frac{1}{4} \) kilometers.
In simple words: To combine kilometers and meters, change the meters into a fraction of a kilometer and add them together.

🎯 Exam Tip: Ensure you express the fraction in its simplest form, for example, \( \frac{1}{4} \) instead of \( \frac{250}{1000} \).

(v) 45 Km 750 m = __________
Answer:
(v) 45 Km 750 m = \( 45 + 750 \times \frac { 1 }{ 1000 } \)
= \( 45 + \frac { 3 }{ 4 } = 45\frac { 3 }{ 4 } \) km
750 meters makes up three-fourths of a kilometer. Therefore, 45 kilometers and 750 meters is equal to \( 45\frac{3}{4} \) kilometers.
In simple words: Add the meters as a fraction to the kilometers. This shows the total length in kilometers.

🎯 Exam Tip: Always check your calculations, especially when simplifying fractions from meters to kilometers, to avoid errors.

Question 2. Convert into Hours: [In fraction]
(i) 10 minutes
Answer:
(i) 10 minutes = \( 10 \times \frac { 1 }{ 60 } \)
= \( \frac { 1 }{ 6 } \) hours
There are 60 minutes in one hour. So, 10 minutes is \( \frac{10}{60} \) of an hour, which simplifies to \( \frac{1}{6} \) of an hour.
In simple words: To convert minutes to hours, divide the number of minutes by 60, then simplify the fraction.

🎯 Exam Tip: Always simplify fractions to their simplest form to get full marks and make the answer clear.

(ii) 25 minutes
Answer:
(ii) 25 minutes = \( 25 \times \frac { 1 }{ 60 } \)
= \( \frac { 5 }{ 12 } \) hours
Since there are 60 minutes in an hour, 25 minutes can be written as \( \frac{25}{60} \) of an hour, which simplifies to \( \frac{5}{12} \) hours.
In simple words: Divide 25 minutes by 60 to find its value as a part of an hour, then reduce the fraction.

🎯 Exam Tip: Remember common factors like 5 when simplifying fractions involving minutes and hours for quicker solutions.

(iii) 36 minutes
Answer:
(iii) 36 minutes = \( 36 \times \frac { 1 }{ 60 } \)
= \( \frac { 3 }{ 5 } \) hours
To convert 36 minutes to hours, we divide by 60. This gives us \( \frac{36}{60} \), which simplifies to \( \frac{3}{5} \) of an hour.
In simple words: To change minutes into a fraction of an hour, divide by 60 and simplify the fraction.

🎯 Exam Tip: Knowing multiplication tables for numbers like 6 helps quickly simplify fractions such as \( \frac{36}{60} \).

(iv) 48 minutes
Answer:
(iv) 48 minutes = \( 48 \times \frac { 1 }{ 60 } \)
= \( \frac { 4 }{ 5 } \) hours
Converting 48 minutes to hours means dividing by 60, resulting in \( \frac{48}{60} \). This fraction can be simplified to \( \frac{4}{5} \) of an hour.
In simple words: Divide 48 by 60 to get a fraction for hours, then make the fraction as simple as possible.

🎯 Exam Tip: Look for the greatest common divisor (GCD) to simplify fractions efficiently. For \( \frac{48}{60} \), the GCD is 12.

(v) 50 minutes
Answer:
(v) 50 minutes = \( 50 \times \frac { 1 }{ 60 } \)
= \( \frac { 5 }{ 6 } \) hours
To change 50 minutes into hours, we divide 50 by 60. This gives the fraction \( \frac{50}{60} \), which simplifies to \( \frac{5}{6} \) of an hour.
In simple words: Divide minutes by 60 and simplify the fraction to show how many hours it is.

🎯 Exam Tip: Remember that \( \frac{1}{2} \) an hour is 30 minutes, and \( \frac{1}{4} \) is 15 minutes, which can help you estimate and check your answers.

Question 3. Convert into minutes:
(i) \( \frac { 5 }{ 6 } \) Hour
Answer:
(i) \( \frac { 5 }{ 6 } \) Hour = \( \frac {5}{ 6 } \times 60 \)
= 50 minutes
There are 60 minutes in an hour. To find \( \frac{5}{6} \) of an hour, we multiply \( \frac{5}{6} \) by 60, which gives us 50 minutes.
In simple words: Multiply the fraction of an hour by 60 to find the number of minutes.

🎯 Exam Tip: When multiplying fractions by whole numbers, you can divide the whole number by the denominator first to simplify the calculation.

(ii) \( \frac { 8 }{ 10 } \) Hour
Answer:
(ii) \( \frac { 8 }{ 10 } \) Hour = \( \frac { 8 }{ 10 } \times 60 \)
= 48 minutes
To convert \( \frac{8}{10} \) of an hour into minutes, we multiply it by 60 minutes. This calculation results in 48 minutes.
In simple words: Multiply the fraction of an hour by 60 to get the total minutes.

🎯 Exam Tip: Simplify the fraction \( \frac{8}{10} \) to \( \frac{4}{5} \) before multiplying by 60, as it can make the calculation easier.

(iii) \( \frac { 4 }{ 6 } \) Hour
Answer:
(iii) \( \frac { 4 }{ 6 } \) Hour = \( \frac { 4 }{ 6 } \times 60 \)
= 40 minutes
To find the number of minutes in \( \frac{4}{6} \) of an hour, we multiply the fraction by 60 minutes. This calculation shows there are 40 minutes.
In simple words: Multiply the given fraction of an hour by 60 to find the number of minutes.

🎯 Exam Tip: Always simplify the fraction (e.g., \( \frac{4}{6} \) to \( \frac{2}{3} \)) first if it makes the multiplication by 60 simpler.

(iv) \( \frac { 5 }{ 10 } \) Hour
Answer:
(iv) \( \frac { 5 }{ 10 } \) Hour = \( \frac {5}{ 10 } \times 60 \)
= 30 minutes
To convert \( \frac{5}{10} \) of an hour into minutes, we multiply the fraction by 60. This calculation shows that it is 30 minutes.
In simple words: Multiply the fraction of an hour by 60 to get the answer in minutes.

🎯 Exam Tip: Recognizing that \( \frac{5}{10} \) is equal to \( \frac{1}{2} \) helps quickly solve that half an hour is 30 minutes.

(v) \( \frac { 6 }{ 10 } \) Hour
Answer:
(v) \( \frac { 6 }{ 10 } \) Hour = \( \frac { 6 }{ 10 } \times 60 \)
= 36 minutes
To find the minutes in \( \frac{6}{10} \) of an hour, we multiply the fraction by 60. This calculation results in 36 minutes.
In simple words: Multiply the given fraction of an hour by 60 to find the total minutes.

🎯 Exam Tip: Simplify the fraction \( \frac{6}{10} \) to \( \frac{3}{5} \) before multiplying by 60 for easier calculation.

Question 4. Match the following
(i) \( \frac { 1 }{ 2 } \) part of Rs. 1 - 50 paise
(ii) \( \frac { 1 }{ 4 } \) part of Rs. 4 - Rs. 1
(iii) \( \frac { 1 }{ 2 } \) part of Rs. 10 - Rs. 5
(iv) \( \frac { 3 }{ 4 } \) part of Rs. 100 - Rs. 75
(v) \( \frac { 1 }{ 2 } \) part of Rs. 200 - Rs. 100
Answer:
(i) \( \frac { 1 }{ 2 } \) part of Rs. 1 = 50 paise
(ii) \( \frac { 1 }{ 4 } \) part of Rs. 4 = Rs. 1
(iii) \( \frac { 1 }{ 2 } \) part of Rs. 10 = Rs. 5
(iv) \( \frac { 3 }{ 4 } \) part of Rs. 100 = Rs. 75
(v) \( \frac { 1 }{ 2 } \) part of Rs. 200 = Rs. 100
Half of 1 Rupee is 50 paise. One-fourth of 4 Rupees is 1 Rupee. Half of 10 Rupees is 5 Rupees. Three-fourths of 100 Rupees is 75 Rupees. Half of 200 Rupees is 100 Rupees. Remember that 1 Rupee is 100 paise, which helps with the first conversion.
In simple words: These are direct conversions of fractional parts of currency amounts. You divide the total amount by the denominator and multiply by the numerator to find the part.

🎯 Exam Tip: Remember that 1 Rupee is equal to 100 paise, which is essential for accurate currency fraction calculations.

Question 5. Write the \( \frac { 1 }{ 4 } \), \( \frac { 1 }{ 2 } \) and \( \frac { 3 }{ 4 } \) parts of the following
(i) Rs. 200
Answer:
(i) \( \frac { 1 }{ 4 } \) part of Rs. 200 = \( \frac { 1 }{ 4 } \times 200 = \frac { 200 }{ 4 } \) = Rs. 50
\( \frac { 1 }{ 2 } \) part of Rs. 200 = \( \frac { 1 }{ 2 } \times 200 = \frac { 200 }{ 2 } \) = Rs. 100
\( \frac { 3 }{ 4 } \) part of Rs. 200 = \( \frac { 3 }{ 4 } \times 200 = \frac { 600 }{ 4 } \) = Rs. 150
To find the parts of Rs. 200: \( \frac{1}{4} \) of Rs. 200 is Rs. 50. Half of Rs. 200 is Rs. 100. And \( \frac{3}{4} \) of Rs. 200 is Rs. 150. These calculations show how different fractions relate to a whole amount.
In simple words: Divide Rs. 200 by 4 to get one-fourth, by 2 for half, and by 4 then multiply by 3 for three-fourths.

🎯 Exam Tip: Always show your calculations for each fractional part to ensure clarity and accuracy in your answer.

(ii) Rs. 10,000
Answer:
(ii) \( \frac { 1 }{ 4 } \) part of Rs. 10,000 = \( \frac { 1 }{ 4 } \times 10,000 = \frac { 10000 }{ 4 } \) = Rs. 2500
\( \frac { 1 }{ 2 } \) part of Rs. 10,000 = \( \frac { 1 }{ 2 } \times 10,000 = \frac { 10000 }{ 2 } \) = Rs. 5000
\( \frac { 3 }{ 4 } \) part of Rs. 10,000 = \( \frac { 3 }{ 4 } \times 10,000 = \frac { 30000 }{ 4 } \) = Rs. 7500
For Rs. 10,000: \( \frac{1}{4} \) is Rs. 2500, \( \frac{1}{2} \) is Rs. 5000, and \( \frac{3}{4} \) is Rs. 7500. This shows how to break down larger amounts into specific fractions, which is useful in many real-life situations.
In simple words: Find one-fourth, one-half, and three-fourths of Rs. 10,000 by dividing and multiplying correctly.

🎯 Exam Tip: When working with large numbers, double-check your division and multiplication to avoid simple errors in your calculations.

(iii) Rs. 8,000
Answer:
(iii) \( \frac { 1 }{ 4 } \) part of Rs. 8,000 = \( \frac { 1 }{ 4 } \times 8,000 = \frac { 8000 }{ 4 } \) = Rs. 2000
\( \frac { 1 }{ 2 } \) part of Rs. 8,000 = \( \frac { 1 }{ 2 } \times 8,000 = \frac { 8000 }{ 2 } \) = Rs. 4000
\( \frac { 3 }{ 4 } \) part of Rs. 8,000 = \( \frac { 3 }{ 4 } \times 8,000 = \frac { 24000 }{ 4 } \) = Rs. 6000
To find the parts of Rs. 8,000: \( \frac{1}{4} \) of Rs. 8,000 is Rs. 2000. Half of Rs. 8,000 is Rs. 4000. And \( \frac{3}{4} \) of Rs. 8,000 is Rs. 6000. Practicing these fractional calculations helps improve number sense.
In simple words: Calculate one-fourth, one-half, and three-fourths of Rs. 8,000 by using multiplication and division.

🎯 Exam Tip: Practice mental math with common fractions like quarters and halves to quickly estimate and verify your answers.

(iv) Rs. 24,000
Answer:
(iv) \( \frac { 1 }{ 4 } \) part of Rs. 24,000 = \( \frac { 1 }{ 4 } \times 24,000 = \frac { 24000 }{ 4 } \) = Rs. 6000
\( \frac { 1 }{ 2 } \) part of Rs. 24,000 = \( \frac { 1 }{ 2 } \times 24,000 = \frac { 24000 }{ 2 } \) = Rs. 12000
\( \frac { 3 }{ 4 } \) part of Rs. 24,000 = \( \frac { 3 }{ 4 } \times 24,000 = \frac { 72000 }{ 4 } \) = Rs. 18000
For Rs. 24,000: \( \frac{1}{4} \) is Rs. 6000, \( \frac{1}{2} \) is Rs. 12000, and \( \frac{3}{4} \) is Rs. 18000. This shows how fractions can be applied to larger monetary values efficiently.
In simple words: Find the quarter, half, and three-quarter parts of Rs. 24,000 accurately.

🎯 Exam Tip: Remember that finding \( \frac{1}{2} \) is the same as dividing by 2, and finding \( \frac{1}{4} \) is like dividing by 4, simplifying the calculation process.

(v) Rs. 50,000
Answer:
(v) \( \frac { 1 }{ 4 } \) part of Rs. 50,000 = \( \frac { 1 }{ 4 } \times 50,000 = \frac { 50000 }{ 4 } \) = Rs. 12500
\( \frac { 1 }{ 2 } \) part of Rs. 50,000 = \( \frac { 1 }{ 2 } \times 50,000 = \frac { 50000 }{ 2 } \) = Rs. 25000
\( \frac { 3 }{ 4 } \) part of Rs. 50,000 = \( \frac { 3 }{ 4 } \times 50,000 = \frac { 150000 }{ 4 } \) = Rs. 37500
To find the parts of Rs. 50,000: \( \frac{1}{4} \) of Rs. 50,000 is Rs. 12500. Half of Rs. 50,000 is Rs. 25000. And \( \frac{3}{4} \) of Rs. 50,000 is Rs. 37500. This demonstrates how to calculate fractions of large sums of money.
In simple words: Calculate one-fourth, one-half, and three-fourths of Rs. 50,000 clearly.

🎯 Exam Tip: Always double-check your multiplication for fractions like \( \frac{3}{4} \), ensuring you multiply by the numerator and then divide by the denominator.