# NCERT Math Solutions for Class 6 Chapter 1

Dear students, if you are in Class 6, mathematics may not be an easy task for you. Every day, your teacher assigns homework that needs to be solved, but you may find Class 6 Math challenging. Don’t worry if you are

## Class 6 Math Chapter 1 Solution – Knowing Our Numbers

Question 1: (Page No. 12) Fill in the blanks:

(a). 1 lakh = _________ ten thousand.

Ans: lakh =10 ten thousand

(b). 1 million = _________ hundred thousand.

Ans: lakh =10 ten thousand

(c). 1 crore = _________ ten lakh.

Ans: 1 crore = 10 ten lakh

(d). 1 crore = _________ million.

Ans: 1 crore = 10 million

(e). 1 million = _________ lakh.

Ans: 1 million = 10  lakh

#### Page No 12: Question 2:

Place commas correctly and write the numerals:

(a). Seventy-three lakh seventy-five thousand three hundred seven.

Ans: 73,75,307

(b). Nine crore five lakh forty-one.

Ans: 9,05,00,041

(c). Seven crore fifty two lakh twenty-one thousand three hundred two.

Ans: 7,52,21,302

(d). Fifty-eight million four hundred twenty-three thousand two hundred two.

Ans: 58,423,202

(e). Twenty-three lakh thirty thousand ten.

Ans: 23,30,010

#### Page No 12: Question 3:

Insert commas suitably and write the names according to the Indian System of Numeration:

(a). 87595762

Ans: Eight crore seventy-five lacks ninety-five thousand seven hundred sixty-two

(b). 8546283

Ans: Eighty-five lakh forty-six thousand two hundred eighty-three

(c). 99900046

Ans: Nine crores ninety-nine lakh forty-six

(d). 98432701

Ans: Nine crore eighty-four lakh thirty-two thousand seven hundred one

#### Page No 12: Question 4:

Insert commas suitably and write the names according to International System of Numeration:

(a). 78921092  (b). 7452283

(c). 99985102 (d). 48049831

Using the International System of Numeration and inserting commas suitably, the numbers are written as follows:

(a) 78,921,092 (b) 7,452,283 (c) 99,985,102 (d) 48,049,831

#### Page No 16: Question 1:

A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third, and final day was respectively 1094, 1812, 2050, and 2751. Find the total number of tickets sold on all four days.

Ans: To find the total number of tickets sold on all four days of the book exhibition, you simply need to add the number of tickets sold on each day:

Total = 1094 (first day) + 1812 (second day) + 2050 (third day) + 2751 (final day)

Total = 1094 + 1812 + 2050 + 2751

Total = 7707

So, the total number of tickets sold on all four days was 7,707.

#### Page No 16: Question 2:

Q. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10, 000 runs. How many more runs does he need?

Ans: To find out how many more runs Shekhar needs to reach his goal of 10,000 runs, you can follow these steps:

Step 1: Start with the number of runs Shekhar has scored so far, which is 6,980 runs.

Step 2: Determine the target number of runs Shekhar wants to achieve, which is 10,000 runs.

Step 3: Subtract the runs he has already scored from his target runs to find out how many more runs he needs:

10,000 (target runs) – 6,980 (runs scored so far) = 3,020 runs

So, Shekhar needs 3,020 more runs to complete 10,000 runs in test matches..

#### Page No 16: Question 3:

In an election, the successful candidate registered 5, 77, 500 votes and his nearest rival secured 3, 48, 700 votes. By what margin did the successful candidate win the election?

Step 2: Determine the number of votes the nearest rival secured, which is 3,48,700 votes.

Step 3: Subtract the number of votes received by the nearest rival from the number of votes received by the successful candidate to find the margin of victory:

So, the successful candidate won the election by a margin of 2,28,800 votes.

#### Page No 16: Question 4:

Kirti bookstore sold books worth Rs 2,85,891 in the first week of June and books worth Rs 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Sol: Let’s solve this step by step:

Step 1: Find the total sales for the two weeks together. Total sales = Sales in the first week + Sales in the second week Total sales = Rs 2,85,891 + Rs 4,00,768

Step 2: Add the sales figures: Total sales = Rs 2,85,891 + Rs 4,00,768 = Rs 6,86,659

So, the total sales for the two weeks together were Rs 6,86,659.

Step 3: Determine which week had the greater sales and find the difference. Sales in the first week = Rs 2,85,891 Sales in the second week = Rs 4,00,768

To find which week had the greater sales, compare the two sales figures:

• Sales in the first week: Rs 2,85,891
• Sales in the second week: Rs 4,00,768

Clearly, the second week had the greater sales.

Step 4: Find the difference in sales between the two weeks: Difference = Sales in the second week – Sales in the first-week Difference = Rs 4,00,768 – Rs 2,85,891

Step 5: Calculate the difference: Difference = Rs 1,14,877

So, the sale in the second week was greater than the sale in the first week by Rs 1,14,877.

#### Page No 17: Question 5:

Find the difference between the greatest and the least number that can be written using the digits 6, 2, 7, 4, 3 each only once.

To find the difference between the greatest and least numbers using the digits 6, 2, 7, 4, and 3:

Greatest number: 76432 Least number: 23467

Difference = 52965

#### Page No 17: Question 6:

A machine, on average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?

Sol:

Step 1: Identify the number of days in January 2006.

• January typically has 31 days.

Step 2: Determine the average daily production of screws.

• The machine manufactures 2,825 screws per day.

Step 3: Calculate the total production for the month of January 2006.

• Multiply the average daily production by the number of days in January: Total production = Average daily production x Number of days Total production = 2,825 screws/day x 31 days

Step 4: Calculate the total production:

• Total production = 87,575 screws

So, the machine produced a total of 87,575 screws in the month of January 2006.

#### Page No 17: Question 7:

A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?

Sol:

• Cost per radio set = Rs 1200
• Number of radio sets = 40

Total cost = Cost per radio set x Number of radio sets Total cost = Rs 1200 x 40

Step 2: Calculate the total cost: Total cost = Rs 48,000

Step 3: Subtract the total cost from the initial amount the merchant had.

• Initial amount = Rs 78,592
• Total cost of radio sets = Rs 48,000

Remaining amount = Initial amount – Total cost of radio sets Remaining amount = Rs 78,592 – Rs 48,000

Step 4: Calculate the remaining amount: Remaining amount = Rs 30,592

So, the merchant will have Rs 30,592 left after purchasing 40 radio sets at Rs 1200 each.

#### Page No 17: Question 8:

A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications?)

Sol:

You don’t need to do both multiplications to find the difference between the student’s answer and the correct answer. You can calculate it directly.

Student’s multiplication: 7236 x 65 Correct multiplication: 7236 x 56

Now, calculate the difference:

Difference = (Student’s multiplication) – (Correct multiplication) Difference = (7236 x 65) – (7236 x 56)

You can see that both expressions have a common factor of 7236, so you can factor it out:

Difference = 7236 x (65 – 56)

Now, calculate the difference:

Difference = 7236 x (9) = 65,124

So, the student’s answer was greater than the correct answer by 65,124.

#### Page No 17: Question 9:

To stitch a shirt, 2m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint: convert data in cm.)

Sol:

2 meters 15 centimeters = 215 centimeters (1 meter = 100 centimeters)

40 meters = 40 x 100 = 4000 centimeters

Cloth needed for one shirt = 215 centimeters

Number of shirts that can be made from 4000 centimeters = 4000 ÷ 215

Therefore, 18 shirts can be made, and there will be 130 centimeters (or 1 meter 30 centimeters) of cloth remaining.

#### Page No 17: Question 10:

Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a van that cannot carry beyond 800 kg?

Sol:

Each box weighs 4 kg 500 g, which is equivalent to 4.5 kg.

Now, calculate how many such boxes can be loaded:

Number of boxes = Total weight the van can carry / Weight of each box

Number of boxes = 800 kg / 4.5 kg per box

Number of boxes = 177.78

Since you cannot have a fraction of a box, you can load a maximum of 177 boxes in the van without exceeding the weight limit of 800 kg.

#### Page No 17: Question 11:

The distance between the school and the house of a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.

Sol:

To find the total distance covered by the student in six days, we’ll first calculate the distance covered in one round trip (to school and back) and then multiply it by the number of days.

Distance between school and home = 1 km 875 m = 1875 meters (1 km = 1000 m)

Distance covered in one round trip (to school and back) = 2 times the distance between school and home: 2 * 1875 meters = 3750 meters

Now, calculate the total distance covered by the student in six days: Total distance covered = Distance covered in one round trip * Number of round trips in six days

Total distance covered = 3750 meters * 6 days

Total distance covered = 22,500 meters

Therefore, distance covered in 6 days = 22,500 m

= 22.5 km or 22 km 500 m

#### Page No 17: Question 12:

A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?

Sol:

To find out how many glasses, each with a 25 ml capacity, can be filled with 4 litres and 500 ml of curd, you need to convert the volume of curd to milliliters and then divide it by the capacity of each glass.

1 liter = 1000 ml

So, 4 liters = 4 x 1000 ml = 4000 ml

Now, add 500 ml to this:

4000 ml + 500 ml = 4500 ml

Now, divide the total volume of curd (4500 ml) by the capacity of each glass (25 ml):

Number of glasses = Total volume of curd / Capacity of each glass Number of glasses = 4500 ml / 25 ml/glass

Number of glasses = 180

So, you can fill 180 glasses, each with a 25 ml capacity, with 4 liters and 500 ml of curd.

#### Page No 23: Question 1:

To estimate the following calculations using the general rule: Make ten more such examples of addition, subtraction, and estimation of their outcome.

(a) 730 + 998

• Estimate: 700 + 1000
• Result: 1700

(b) 796 – 314

• Estimate: 800 – 300
• Result: 500

(c) 12,904 + 2,888

• Estimate: 13,000 + 3,000
• Result: 16,000

(d) 28,292 – 21,496

• Estimate: 28,000 – 21,000
• Result: 7000

So, the estimated results are: (a) 1700 (b) 500 (c) 16,000 (d) 7000

#### Page No 23: Question 2:

Give a rough estimate (by rounding off to the nearest hundreds) and also a closer estimate (by rounding off to the nearest tens):

(a) 439 + 334 + 4317

Rounding off to the nearest hundreds, 439, 334, and 4317 can be rounded off to 400, 300, and 4300 respectively.

So, 400+300+4300= 5000

Rounding off to the nearest tens, 439, 334, and 4317 can be rounded off to 440, 330, and 4320 respectively.

so, 440+330+4320= 5090

(b) 1,08,734 − 47,599

Rounding off to hundreds, 1,08,734 and 47,599 can be rounded off to 1,08,700 and 47,600 respectively.

So, 1,08,700 – 47,600 = 61100

Rounding off to tens, 1,08,734 and 47,599 can be rounded off to 1,08,730 and 47,600 respectively.

So, 1,08,730 – 47,600 = 61130

(c) 8325 − 491

Rounding off to hundreds, 8325 and 491 can be rounded off to 8300 and 500 respectively.

So, 8300 – 500 = 7800

Rounding off to tens, 8325 and 491 can be rounded off to 8330 and 490 respectively.

So, 8330 – 490 = 7840

(d) 4,89,348 − 48,365

Rounding off to hundreds, 4,89,348 and 48,365 can be rounded off to 4,89,300 and 48,400 respectively.

So, 4,89,300 – 48,400 =440900

Rounding off to tens, 4,89,348 and 48,365 can be rounded off to 4,89,350 and 48,370 respectively.

So, 4,89,350 – 48,370 = 440980

#### Page No 23: Question 3:

Estimate the following products using the general rule:

(a) 578 Ã— 161

(b) 5281 Ã— 3491

(c) 1291 Ã— 592

(d) 9250 Ã— 29

Sol:

(a) 578 × 161

Rounding off using the general rule, 578 and 161 can be rounded off to 600 and 200 respectively.

so, 600 × 200 = 120000.

(b) 5281 × 3491

Rounding off using the general rule, 5281 and 3491 can be rounded off to 5000 and 3000 respectively.

So 5000 × 3000 = 15,000,000

(c) 1291 × 592

Rounding off using the general rule, 1291 and 592 can be rounded off to 1000 and 600 respectively.

So, 1000 × 600 = 600,000

(d) 9250 × 29

Rounding off using the general rule, 9250 and 29 can be rounded off to 9000 and 30 respectively.

So, 9000 × 30 = 270000