Samacheer Kalvi Class 5 Maths Solutions Term 1 Chapter 4 Measurements

Tamilnadu Samacheer Kalvi 5th Maths Solutions Term 1 Chapter 4 Measurements Ex 4

 

Question 1. Fill in the blanks.
a. 7m 5cm = _______ cm
Answer:
\( 7m \, 5cm = 7 \times 100 \, cm + 5 \, cm = 700 \, cm + 5 \, cm = 705 \, cm \)
So, 7m 5cm = 705 cm.
In simple words: To change meters to centimeters, multiply the meter value by 100. Then, add any extra centimeters.

🎯 Exam Tip: Remember that 1 meter is equal to 100 centimeters, which is key for such conversions.

 

b. 505 mm = _______ cm _______ mm
Answer:
\( 505 \, mm = 505 \div 10 \, cm = 50 \, cm \, 5 \, mm \)
So, 505 mm = 50 cm 5 mm.
In simple words: To change millimeters to centimeters, divide the millimeter value by 10. The remainder will be in millimeters.

🎯 Exam Tip: Keep in mind that 1 centimeter is equal to 10 millimeters when converting units.

 

c. 326m = _______ cm
Answer:
\( 326 \, m = 326 \times 100 \, cm = 32600 \, cm \)
So, 326m = 32600 cm.
In simple words: When converting meters to centimeters, simply multiply the meter value by 100. Each meter has 100 centimeters.

🎯 Exam Tip: A quick way to convert meters to centimeters is to add two zeros to the meter value.

 

d. 5km 30m = _______ m
Answer:
\( 5 \, km \, 30 \, m = 5 \times 1000 \, m + 30 \, m = 5000 \, m + 30 \, m = 5030 \, m \)
So, 5km 30m = 5030 m.
In simple words: To convert kilometers to meters, multiply by 1000. Then, add any remaining meters to get the total in meters.

🎯 Exam Tip: Remember that 1 kilometer is equal to 1000 meters, which is essential for these conversions.

 

e. 650cm: _______ m _______ cm
Answer:
\( 650 \, cm = 650 \div 100 \, m = 6 \, m \, 50 \, cm \)
So, 650cm = 6 m 50 cm.
In simple words: To change centimeters to meters, divide by 100. The whole number part is meters, and the remainder is centimeters.

🎯 Exam Tip: Understanding that 100 centimeters make 1 meter helps in quickly converting between these units.

 

Question 2. True or false.
a) 600 m is 6mm.
Answer: False.
In simple words: 600 meters is a very long distance, much longer than 6 millimeters. One meter has 1000 millimeters, so 600 meters would be 600,000 millimeters.

🎯 Exam Tip: Always think about the size difference between units to catch false statements quickly.

 

b) 7000 m is 7 km.
Answer: True.
In simple words: Since 1000 meters make 1 kilometer, 7000 meters is exactly the same as 7 kilometers. This is a correct conversion.

🎯 Exam Tip: Knowing the basic conversion factors like 1 km = 1000 m is vital for true/false questions.

 

c) 400 cm is 4 km.
Answer: False.
In simple words: 400 centimeters is equal to 4 meters, not 4 kilometers. A kilometer is much, much longer than a meter.

🎯 Exam Tip: Be careful with conversions involving large differences in unit magnitude, like centimeters to kilometers.

 

d) 770 mm is 77 cm.
Answer: True.
In simple words: Because 10 millimeters make 1 centimeter, dividing 770 millimeters by 10 gives 77 centimeters. The statement is correct.

🎯 Exam Tip: Remember the relationship: to convert mm to cm, divide by 10; to convert cm to mm, multiply by 10.

 

e) 9000m is 90 mm.
Answer: False.
In simple words: 9000 meters is a very long distance. To convert meters to millimeters, you multiply by 1000, so 9000 meters is 9,000,000 millimeters, not 90 millimeters.

🎯 Exam Tip: Always convert to the same base unit (like meters) before comparing or stating equivalences.

 

Question 3. Find the sum of the following
a. 17 m 45 cm + 52 m 30 cm
Answer:
First, add the centimeter parts: \( 45 \, cm + 30 \, cm = 75 \, cm \).
Next, add the meter parts: \( 17 \, m + 52 \, m = 69 \, m \).
So, the sum is 69 m 75 cm.

In simple words: To add measurements with different units, add the same units separately. Meters with meters and centimeters with centimeters.

🎯 Exam Tip: When adding mixed units, always align the units properly and add them column by column, starting from the smallest unit.

 

b. 75 km 400 m + 37 km 300 m + 52 km 750 m
Answer:
First, add all the meter parts:
\( 400 \, m + 300 \, m + 750 \, m = 1450 \, m \).
We know that \( 1000 \, m = 1 \, km \), so \( 1450 \, m = 1 \, km \, 450 \, m \).
Carry over the 1 km to the kilometer column.
Next, add all the kilometer parts, including the carried over 1 km:
\( 75 \, km + 37 \, km + 52 \, km + 1 \, km = 165 \, km \).
So, the total sum is 165 km 450 m.

In simple words: Add the meters first. If the sum is 1000 meters or more, convert it to kilometers and carry that over. Then add the kilometers, including any carried-over amounts.

🎯 Exam Tip: Always perform unit conversions (like m to km) before adding the larger units, carrying over any excess to the next column.

 

c. 4 cm 8 mm + 5 cm 9 mm
Answer:
First, add the millimeter parts: \( 8 \, mm + 9 \, mm = 17 \, mm \).
Since \( 10 \, mm = 1 \, cm \), \( 17 \, mm \) is \( 1 \, cm \, 7 \, mm \).
Carry over the 1 cm to the centimeter column.
Next, add the centimeter parts, including the carried over 1 cm:
\( 4 \, cm + 5 \, cm + 1 \, cm = 10 \, cm \).
So, the total sum is 10 cm 7 mm.

In simple words: Add the millimeters first and convert any value over 10 mm into centimeters to carry over. Then add the centimeters, including the carry-over.

🎯 Exam Tip: When adding, always remember the conversion factor for the units (e.g., 10 mm = 1 cm) to correctly carry over values.

 

Question 4. Subtract the following
a. 15 km 450 m - 13 km 200 m.
Answer:
First, subtract the meter parts: \( 450 \, m - 200 \, m = 250 \, m \).
Next, subtract the kilometer parts: \( 15 \, km - 13 \, km = 2 \, km \).
So, the difference is 2 km 250 m.

In simple words: Subtract the smaller units first, then the larger units. Make sure to subtract from the corresponding unit.

🎯 Exam Tip: When subtracting mixed units, always start with the smallest unit column, borrowing from the larger unit if needed.

 

b. 750 m 840 mm – 370m 480 mm.
Answer:
First, subtract the millimeter parts: \( 840 \, mm - 480 \, mm = 360 \, mm \).
Next, subtract the meter parts: \( 750 \, m - 370 \, m = 380 \, m \).
So, the difference is 380 m 360 mm.

In simple words: Subtract the millimeters, then subtract the meters. Ensure you subtract numbers in the same unit column.

🎯 Exam Tip: If the smaller unit in the top number is less than the smaller unit in the bottom number, you'll need to borrow from the larger unit, remembering its conversion factor (e.g., 1 m = 1000 mm).

 

c. 5 km 400 m – 3 km 350 m
Answer:
First, subtract the meter parts: \( 400 \, m - 350 \, m = 50 \, m \).
Next, subtract the kilometer parts: \( 5 \, km - 3 \, km = 2 \, km \).
So, the difference is 2 km 50 m.

In simple words: When subtracting, always handle the smaller unit (meters) first, then the larger unit (kilometers).

🎯 Exam Tip: Double-check your subtraction, especially when numbers are close, to avoid simple arithmetic errors.

 

Question 5. Multiply the following.
a. 350 m 45 cm × 7
Answer:
First, multiply the centimeter part by 7:
\( 45 \, cm \times 7 = 315 \, cm \).
Convert 315 cm to meters and centimeters: \( 315 \, cm = 3 \, m \, 15 \, cm \).
Carry over the 3 m to the meter column.
Next, multiply the meter part by 7 and add the carried-over meters:
\( 350 \, m \times 7 = 2450 \, m \).
Add the carried over 3 m: \( 2450 \, m + 3 \, m = 2453 \, m \).
So, the total product is 2453 m 15 cm.

In simple words: Multiply the smaller unit first. Convert any larger amount into the next unit and carry it over. Then multiply the larger unit and add what you carried over.

🎯 Exam Tip: When multiplying mixed units, carefully manage carry-overs from smaller units to larger units using the correct conversion factor.

 

b. 25 km 300 m × 6
Answer:
First, multiply the meter part by 6:
\( 300 \, m \times 6 = 1800 \, m \).
Convert 1800 m to kilometers and meters: \( 1800 \, m = 1 \, km \, 800 \, m \).
Carry over the 1 km to the kilometer column.
Next, multiply the kilometer part by 6 and add the carried-over kilometers:
\( 25 \, km \times 6 = 150 \, km \).
Add the carried over 1 km: \( 150 \, km + 1 \, km = 151 \, km \).
So, the total product is 151 km 800 m.

In simple words: Multiply the meters by the number, then convert any amount over 1000m to km and carry it. Then multiply the kilometers by the number and add the carried-over kilometers.

🎯 Exam Tip: Always remember that 1000 meters makes 1 kilometer when performing multiplication with carry-overs.

 

c. 37 m 350 mm × 8
Answer:
First, multiply the millimeter part by 8:
\( 350 \, mm \times 8 = 2800 \, mm \).
Convert 2800 mm to meters and millimeters: \( 2800 \, mm = 2 \, m \, 800 \, mm \).
Carry over the 2 m to the meter column.
Next, multiply the meter part by 8 and add the carried-over meters:
\( 37 \, m \times 8 = 296 \, m \).
Add the carried over 2 m: \( 296 \, m + 2 \, m = 298 \, m \).
So, the total product is 298 m 800 mm.

In simple words: Multiply the millimeters first, converting any excess into meters and carrying it over. Then multiply the meters and add the carried-over meters.

🎯 Exam Tip: Remember that 1000 millimeters make 1 meter, which is vital for correctly managing carry-overs in multiplication.

 

Question 6. Divide the following
a. 950 km 800 m ÷ 5
Answer:
Divide the kilometer part by 5 first.
\( 950 \, km \div 5 = 190 \, km \). There is no remainder in kilometers.
Next, divide the meter part by 5.
\( 800 \, m \div 5 = 160 \, m \).
So, the result is 190 km 160 m.

In simple words: Divide the kilometers part first, then the meters part. If there is a remainder from the kilometers, convert it to meters and add it to the existing meters before dividing.

🎯 Exam Tip: When dividing mixed units, always divide the larger unit first. If there's a remainder, convert it to the smaller unit and add it before dividing the smaller unit.

 

b. 49 m 770 mm ÷ 7
Answer:
Divide the meter part by 7 first.
\( 49 \, m \div 7 = 7 \, m \). There is no remainder in meters.
Next, divide the millimeter part by 7.
\( 770 \, mm \div 7 = 110 \, mm \).
So, the result is 7 m 110 mm.

In simple words: Divide the meters by the number. Then divide the millimeters by the same number. Combine the results.

🎯 Exam Tip: Ensure that all steps of the division are shown clearly, especially if there are remainders that need to be converted.

 

c. 172 m 48 cm ÷ 4
Answer:
Divide the meter part by 4 first.
\( 172 \, m \div 4 = 43 \, m \). There is no remainder in meters.
Next, divide the centimeter part by 4.
\( 48 \, cm \div 4 = 12 \, cm \).
So, the result is 43 m 12 cm.

In simple words: First, divide the meters by the given number. Then, divide the centimeters by the same number. Put the results together.

🎯 Exam Tip: Pay attention to remainders; if a remainder exists from the larger unit, convert it to the smaller unit before continuing the division.

Life Related Problems

 

Question 7. Answer the following:
a. Saravanan had chosen to drive his vehicle from Puducherry to Chennai for a distance of 165 Km. While starting his vehicle, the odometer showed 000157 Km. Find the reading of the odometer, when he reached Chennai?
Answer:
Distance from Puducherry to Chennai = 165 km
Odometer reading at the start = 000157 km
To find the reading upon reaching Chennai, we add the distance traveled to the starting reading:
Reading of odometer after reaching Chennai = Starting reading + Distance traveled
\( = 157 \, km + 165 \, km = 322 \, km \)
So, the odometer will show 000322 km when he reaches Chennai.
In simple words: To find the new odometer reading, add the distance traveled to the starting odometer reading.

🎯 Exam Tip: For odometer problems, remember to add the new distance to the previous reading to find the final reading.

 

b. Karthik Raja decided to travel from A. He moves 1 Km in east to reach B. Then he goes 2 Km towards north and reaches C. Then he goes 1 Km towards west and reaches D. If he goes 2 Km towards South, Where would he reach? Draw a suitable diagram and calculate the total distance travelled by him.
Answer:

Starting from A, Karthik travels:
1. A to B: 1 km (East)
2. B to C: 2 km (North)
3. C to D: 1 km (West)
4. D to A: 2 km (South)
After traveling 2 Km towards South from D, he would reach point A again.
Total Distance = Distance A-B + Distance B-C + Distance C-D + Distance D-A
Total Distance = \( 1 \, km + 2 \, km + 1 \, km + 2 \, km = 6 \, km \)
So, he would reach point A, and the total distance traveled is 6 km.
In simple words: Karthik travels in a square shape, returning to his starting point. To find the total distance, add up the length of each part of his journey.

🎯 Exam Tip: For directional travel problems, drawing a simple diagram helps visualize the path and calculate the total distance and final position accurately.

 

c. Sangeetha has just finished building a new house with garden area. She measured the garden area and found it to be 6m x 6m. Suppose she has to put a pole every 1m, how many poles are required? What should be the total length of the fencing material to fence the garden?
Answer:
The garden is a square with a side length of 6m.
The perimeter of the garden = \( 4 \times \text{Side} = 4 \times 6 \, m = 24 \, m \).
If a pole is required every 1m, then the number of poles needed is equal to the perimeter.
Number of poles required = \( 24 \div 1 = 24 \) poles.
The total length of the fencing material to fence the garden is given by multiplying the perimeter by a factor (likely height of the fence, in this case, 1.5):
Length of fencing material = Perimeter \( \times \) 1.5
\( = 24 \, m \times 1.5 = 36 \, m \)
So, 24 poles are required, and the total length of fencing material is 36 m.
In simple words: First, find the total length around the garden. This is how many poles are needed if they are 1 meter apart. Then, multiply this length by 1.5 to find the total fencing material needed.

🎯 Exam Tip: When calculating fencing, remember to find the perimeter first. If a height or multiple layers are implied, factor that into the total material needed.

 

d. One student needs 1 m 25 cm cloth to stitch a shirt. What is the total length of clothes need to stitch a class of 22 students?
Answer:
Cloth needed for one student = 1 m 25 cm
To find the total cloth needed for 22 students, we multiply the cloth per student by 22:
Total cloth needed for 22 students = \( 1 \, m \, 25 \, cm \times 22 \).
Convert 1 m 25 cm to centimeters: \( 1 \, m = 100 \, cm \), so \( 100 \, cm + 25 \, cm = 125 \, cm \).
Multiply 125 cm by 22:
\( 125 \, cm \times 22 = 2750 \, cm \).
Convert 2750 cm back to meters and centimeters:
\( 2750 \, cm = 27 \, m \, 50 \, cm \).
So, 27 m 50 cm of cloth is needed for 22 students.
In simple words: First, change the cloth needed for one student into only centimeters. Then multiply this total by the number of students. Finally, change the answer back to meters and centimeters.

🎯 Exam Tip: For multiplication with mixed units, convert everything to the smallest unit first, multiply, and then convert the result back to mixed units.

 

e. The distance from village A to village B is 3 km 450 m. The distance from village B to village C is 5 km 350 m. What will be the total length of the road, if the road is laid from village A to village C?
Answer:
Distance from village A to Village B = 3 km 450 m
Distance from village B to village C = 5 km 350 m
To find the total length of the road from A to C, we add these two distances:
Total distance from A to C = \( (3 \, km \, 450 \, m) + (5 \, km \, 350 \, m) \).
First, add the meter parts: \( 450 \, m + 350 \, m = 800 \, m \).
Next, add the kilometer parts: \( 3 \, km + 5 \, km = 8 \, km \).
So, the total length of the road from A to C is 8 km 800 m.

In simple words: To find the total length of the road, add the kilometer parts together and the meter parts together separately.

🎯 Exam Tip: For distance problems involving segments, simply add the lengths of each segment to find the total distance, ensuring units are aligned.