NCERT Solutions Class 5 Mathematics Mela Chapter 01 We the Travellers I

 

Question 1. Fill in the blanks by continuing the pattern in each of the following sequences. Discuss the patterns in class.
(a) 456 → 567 → 678 → _____ → _____ → _____ → _____
(b) 1,050 → _____ → 3,150 → 4,200 → _____ → _____ → _____
(c) 5,501 → 6,401 → 7,301 → _____ → _____ → _____ → _____
(d) 10,100 → 10,200 → 10,300 → _____ → _____ → _____ → _____ → 10,900 → 11,000
(e) 10,105 → 10,125 → _____ → _____ → _____ → _____ → _____ → _____ → _____
(f) 10,992 → 10,993 → _____ → _____ → _____ → _____ → _____ → _____ → _____
(g) 10,794 → 10,796 → 10,798 → _____ → _____ → _____ → _____ → _____ → _____
(h) 73,005 → 72,004 → _____ → _____ → _____ → _____ → _____ → _____ → _____
(i) 82,350 → 83,350 → _____ → _____ → _____ → _____ → _____ → _____ → _____
Answer: (a) 789, 890, 1001, 1112 - each number increases by 111. (b) 2,100, 5,250, 6,300, 7,350 - the pattern alternates between adding 1,050 and adding 1,050. (c) 8,201, 9,101, 10,001, 10,901 - each number increases by 900. (d) 10,400, 10,500, 10,600, 10,700 - each number increases by 100. (e) 10,145, 10,165, 10,185, 10,205, 10,225, 10,245, 10,265, 10,285 - each number increases by 20. (f) 10,994, 10,995, 10,996, 10,997, 10,998, 10,999, 11,000, 11,001 - each number increases by 1. (g) 10,800, 10,802, 10,804, 10,806, 10,808, 10,810, 10,812 - each number increases by 2. (h) 71,003, 70,002, 69,001, 68,000, 69,999, 65,998, 64,997, 63,996 - the pattern decreases by 1,001 for the first few terms, then reverses. (i) 84,350, 85,350, 86,350, 87,350, 88,350, 89,350, 90,350, 91,350 - each number increases by 1,000.
In simple words: Look at how much each number changes from one to the next. Keep adding (or subtracting) the same amount to find the missing numbers.

Exam Tip: Always find the difference between the first two given numbers - this tells you the rule for the whole pattern. Test your answer by checking that the pattern stays the same throughout.

 

Question 2. Fill in the blanks appropriately. Use commas as required.
Answer: (a) 456, 567, 678, 789, 890, 1,001, 1,112 - this sequence grows by adding 111 each time. (b) 1,050, 2,100, 3,150, 4,200, 5,250, 6,300, 7,350 - this pattern increases by 1,050 in every step. (c) 5,501, 6,401, 7,301, 8,201, 9,101, 10,001, 10,901 - each number is 900 more than the previous one. (d) 10,100, 10,200, 10,300, 10,400, 10,500, 10,600, 10,700, 10,800, 10,900, 11,000 - all numbers rise by 100 from one term to the next. (e) 10,105, 10,125, 10,145, 10,165, 10,185, 10,205, 10,225, 10,245, 10,265, 10,285 - every number goes up by 20. (f) 10,992, 10,993, 10,994, 10,995, 10,996, 10,997, 10,998, 10,999, 11,000, 11,001 - each term is 1 more than the one before. (g) 10,794, 10,796, 10,798, 10,800, 10,802, 10,804, 10,806, 10,808, 10,810, 10,812 - numbers grow by 2 each step. (h) 73,005, 72,004, 71,003, 70,002, 69,001, 68,000, 69,999, 65,998, 64,997, 63,996 - this sequence drops by 1,001 repeatedly. (i) 82,350, 83,350, 84,350, 85,350, 86,350, 87,350, 88,350, 89,350, 90,350, 91,350 - the pattern increases by 1,000 at every step.
In simple words: Write out the numbers that fit the pattern. The pattern shows a steady jump or drop by the same amount every time.

Exam Tip: Format numbers with commas for clarity - use a comma after every group of three digits starting from the right side.

 

Question 3. Fill in the Number and Number Name columns in the table below.
Answer:

In simple words: Break the number into groups - thousands, hundreds, tens, ones - and write the name for each group, then join them together.

Exam Tip: Always name numbers starting from the largest place value on the left. Hyphens join two-word number names like "twenty-three" or "ninety-nine".

 

Question 4. Arrange the numbers below in increasing order. You can use the number line below, if required.
18926, 34407, 34740, 40347, 40473, 47340, 73404, 74430
Answer: The numbers in increasing order are: 18,926, 34,407, 34,740, 40,347, 40,473, 47,340, 73,404, 74,430. To arrange numbers from smallest to largest, start by looking at the leftmost digit. Numbers with fewer digits come first. Then, for numbers with the same number of digits, compare each digit position from left to right until you find a difference.
In simple words: Line up the numbers from smallest to biggest by looking at their leftmost digit first. When the first digits match, check the next digit to the right.

Exam Tip: Use a number line to plot numbers visually - it helps you see their order at a glance. Always verify by checking that each number is truly larger than the one before it.

 

Question 5. A student said 9,990 is greater than 49,014 because 9 is greater than 4. Is the student correct? Why or why not? Use the number line below to find the position of the numbers. Fill in the blanks.
Answer: No, the student is not correct. When comparing numbers, the count of digits matters more than any single digit. Since 9,990 has 4 digits while 49,014 has 5 digits, the five-digit number must be larger. On a number line, numbers grow as you move to the right, so 49,014 sits much farther to the right than 9,990. Even though the first digit 9 is bigger than 4 when taken alone, we must compare the whole numbers, not just one digit. The number with more digits is always bigger than the number with fewer digits.
In simple words: A number with more digits is always bigger than a number with fewer digits - even if the first digit looks smaller.

Exam Tip: Always count the total number of digits first before comparing individual digits. This saves time and prevents mistakes.

 

Question 6. Digit swap (a) In the number 1,478, interchanging the digits 7 and 4 gives 1,748. Now, interchange any two digits in the number 1,478 to make a number that is larger than 5,500.
Answer: Starting with 1,478, we swap two digits to get a number bigger than 5,500. Swapping 1 and 8 gives 8,471, which is greater than 5,500. Swapping 1 and 7 gives 7,418, which is also greater than 5,500. Swapping 1 and 4 gives 4,178, which is less than 5,500. The numbers larger than 5,500 are 8,471 and 7,418. To make the largest possible number, put the biggest digits in the highest place values.
In simple words: Try swapping different pairs of digits. Check which new numbers are bigger than 5,500.

Exam Tip: When making the largest number, move the biggest digit to the leftmost (highest value) position. When making the smallest, move the smallest digit there instead.

 

Question 6(b). Interchange two digits of 10,593 to make a number i) Between 11,000 and 15,000. ii) More than 35,000.
Answer: (i) To create a number between 11,000 and 15,000, we swap 0 and 3 in 10,593 to get 13,590. Checking: 11,000 - 13,590 - 15,000, so it falls in the range. Other swaps like 0 and 5 give 15,093 (too high), 1 and 3 give 30,591 (too high), and 1 and 5 give 50,193 (too high). (ii) To make a number over 35,000, swapping 1 and 5 gives 50,193 (more than 35,000). Swapping 1 and 9 gives 90,513 (more than 35,000). Swapping 0 and 9 gives 19,503 (less than 35,000). The numbers exceeding 35,000 are 50,193 and 90,513.
In simple words: Swap digits one pair at a time and check if the result fits the target range. Try different pairs until you find ones that work.

Exam Tip: Test all possible swaps systematically. Write down each new number and check it against the given condition before finalizing your answer.

 

Question 6(c). Interchange two digits of 48,247 to make a number i) As small as possible. ii) As big as possible.
Answer: (i) To find the smallest number, we put the smallest digits in the highest place values. Swapping 4 and 2 gives 28,447. Swapping 4 and 7 gives 78,247. Swapping 4 and 8 gives 84,247. Swapping 8 and 2 gives 42,847. Comparing all results, 28,447 is the smallest. (ii) To find the largest number, we put the largest digits in the highest place values. From the same swaps - swapping 4 and 2 gives 28,447, swapping 4 and 7 gives 78,247, swapping 4 and 8 gives 84,247, swapping 8 and 2 gives 42,847 - we see 84,247 is the largest. The smallest possible number is 28,447 and the largest is 84,247.
In simple words: For the smallest number, put smaller digits at the front. For the largest, put bigger digits at the front.

Exam Tip: Always swap systematically - write every possible result and compare them to identify the true minimum and maximum.

 

Question 7. Vijay rounded off a number to the nearest hundred. Suma rounded off the same number to the nearest thousand. Both got the same result. Circle the numbers they might have used.
7,126 7,835 7,030 6,999
Answer: Testing each option: For 7,126, the nearest hundred is 7,100 and the nearest thousand is 7,000 - these don't match. For 7,835, the nearest hundred is 7,800 and the nearest thousand is 8,000 - these don't match. For 7,030, the nearest hundred is 7,000 and the nearest thousand is 7,000 - they match! For 6,999, the nearest hundred is 7,000 and the nearest thousand is 7,000 - they match! The correct numbers are 7,030 and 6,999.
In simple words: Round each number both ways - to the nearest hundred and nearest thousand. If both roundings give the same answer, that number works.

Exam Tip: Remember: to round to the nearest hundred, look at the tens digit; to round to the nearest thousand, look at the hundreds digit. A number works if both rounding methods give the same result.

 

Question 8. Think and write two numbers that have the same - (a) Nearest ten.
Answer: Two numbers that round to the same nearest ten are 38 and 42. Both of these numbers round up or down to 40 when rounding to the nearest ten.
In simple words: Pick any two numbers that are close to the same ten value. They both round to that ten.

Exam Tip: For rounding to the nearest ten, look at the ones digit. If it's 5 or higher, round up; if it's lower than 5, round down.

 

Question 8(b). Think and write two numbers that have the same - (b) Nearest hundred.
Answer: Two numbers that round to the same nearest hundred are 248 and 198. Both of these numbers round to 200 when rounding to the nearest hundred.
In simple words: Pick two different numbers that both round to the same hundred. They don't have to be close to each other.

Exam Tip: When rounding to the nearest hundred, look at the tens digit. If it's 5 or more, round the hundreds digit up; otherwise, keep it the same.

 

Question 9. Think and write the numbers that have the same - (a) Nearest ten and nearest hundred.
Answer: Two numbers with the same nearest ten and nearest hundred are 195 and 204. Both round to 200 when rounded to the nearest ten, and both also round to 200 when rounded to the nearest hundred.
In simple words: Find numbers that give the same answer whether you round them to the nearest ten or to the nearest hundred.

Exam Tip: These numbers must be in a narrow range - close enough so that both rounding methods point to the same value.

 

Question 9(b). Think and write the numbers that have the same - (b) Nearest hundred and nearest thousand.
Answer: Two numbers with the same nearest hundred and nearest thousand are 949 and 915. Both round to 1,000 when rounded to the nearest thousand, and both also round to 1,000 when rounded to the nearest hundred.
In simple words: Pick numbers that round to the same value no matter whether you round to the nearest hundred or nearest thousand.

Exam Tip: These numbers fall in a tight band - they must be close enough that the two different rounding methods produce the same result.

 

Question 9(c). Think and write the numbers that have the same - (c) Nearest ten, hundred and thousand.
Answer: Two numbers with the same nearest ten, hundred, and thousand are 1,000 and 1,004. Both round to 1,000 for the nearest ten, the nearest hundred, and the nearest thousand.
In simple words: Find numbers that give 1,000 no matter which rounding method you use - nearest ten, nearest hundred, or nearest thousand.

Exam Tip: Numbers very close to round values (like 1,000) often satisfy this condition - they're far enough from competing rounding targets that all three methods agree.

 

Question 10. A cyclist can cover 15 km in one hour. How much distance will she cover in 4 hours, if she maintains the same speed?
Answer: If the cyclist travels 15 kilometres every hour, then in 4 hours she will travel 15 × 4 = 60 kilometres. Since her speed stays the same throughout, we simply multiply the distance per hour by the number of hours.
In simple words: The cyclist goes 15 km each hour. In 4 hours, she goes 15 times 4, which is 60 km.

Exam Tip: For distance, speed, and time problems, use multiplication: distance = speed × time. If the speed doesn't change, multiply the distance for one hour by the total number of hours.

 

Question 11. A school has 461 girls and 439 boys. How many vehicles are needed for all of them to go on a trip using the following modes of travel? The numbers in the bracket indicates the number of people that can travel in one vehicle.
(a) Bicycle (2)
(b) Autorickshaw (3)
(c) Car (4)
(d) Big car (6)
(e) Tempo traveller (10)
(f) Boat (20)
(g) Minibus (25)
(h) Aeroplane (180)
Answer: First, find the total number of students: 461 girls + 439 boys = 900 students. Then, divide 900 by the capacity of each vehicle to find how many are needed. If there's a remainder, add one more vehicle.
(a) Bicycle (2 people): 900 ÷ 2 = 450 bicycles
(b) Autorickshaw (3 people): 900 ÷ 3 = 300 autorickshaws
(c) Car (4 people): 900 ÷ 4 = 225 cars
(d) Big car (6 people): 900 ÷ 6 = 150 big cars
(e) Tempo traveller (10 people): 900 ÷ 10 = 90 tempo travellers
(f) Boat (20 people): 900 ÷ 20 = 45 boats
(g) Minibus (25 people): 900 ÷ 25 = 36 minibuses
(h) Aeroplane (180 people): 900 ÷ 180 = 5 aeroplanes
In simple words: Add the girls and boys to get 900 total. Divide 900 by how many fit in each type of vehicle to find how many vehicles you need.

Exam Tip: Always remember to round up if there's a remainder - even one extra person needs a vehicle. Write out all parts clearly to show your division logic.

 

Question 12. Write 5 numbers between the numbers 23,568 and 24,234.
Answer: Five numbers that fall between 23,568 and 24,234 are: 23,600, 23,750, 23,890, 24,000, and 24,123. These numbers are chosen so that each one is larger than 23,568 and smaller than 24,234. You can pick any numbers within this range - there are many possible correct answers.
In simple words: Pick any five numbers that are bigger than 23,568 but smaller than 24,234. Many different answers work.

Exam Tip: Always check that each number you write is truly between the given limits. You can spread them out evenly or bunch them closer together - both approaches work.

 

Question 13. Write 5 numbers that are more than 38,125 but less than 38,600.
Answer: Five numbers in the range from 38,125 to 38,600 are: 38,200, 38,310, 38,420, 38,500, and 38,590. Each number is strictly greater than 38,125 and strictly less than 38,600. Many other numbers would also work - this is just one example set.
In simple words: Pick any five numbers larger than 38,125 but smaller than 38,600.

Exam Tip: Space your numbers out or cluster them - both work fine. Just make sure each one is definitely bigger than the lower limit and smaller than the upper limit.

 

Question 14. Ravi's car has been driven for 56,987 km till now. Sheetal's car has been driven 67,543 km. Whose car has been driven more?
Answer: Comparing the two distances: Ravi's car has 56,987 km and Sheetal's car has 67,543 km. Since 67,543 is greater than 56,987, Sheetal's car has been driven more. To find how much more, we subtract: 67,543 - 56,987 = 10,556 km. Therefore, Sheetal's car has been driven 10,556 km more than Ravi's car.
In simple words: Look at which number is bigger. Sheetal's is bigger, so her car has been driven more. Subtract to find the difference.

Exam Tip: Always compare numbers by looking at the same place values from left to right. Once you identify the larger number, subtract to find the difference if the question asks for it.

 

Question 15. The following are the prices of different electric bikes. Arrange the prices in ascending (increasing) order.
Rs.90000, Rs.89999, Rs.94983, Rs.49900, Rs.93743, Rs.39999
Answer: Arranging these prices from lowest to highest: Rs.39999, Rs.49900, Rs.89999, Rs.90000, Rs.93743, Rs.94983. Start by comparing the first digits - 3, 4, 8, 9 - to group them. Then, for prices starting with the same digit, compare the next digits moving left to right. The smallest price is Rs.39999 and the largest is Rs.94983.
In simple words: Line up the prices from smallest to biggest by looking at the leftmost digit first. Then check the next digit if the first one matches.

Exam Tip: Write prices in a vertical list to compare them more easily. Check your work by making sure each price is truly smaller than the one after it.

 

Question 16. The following table shows the population of some towns. Arrange them in a descending (decreasing) order.
Answer:

The towns in descending order of population are: Town 6 (66,540), Town 1 (65,232), Town 3 (56,380), Town 2 (53,231), Town 4 (51,336), Town 5 (45,858). To arrange from largest to smallest, compare the numbers by looking at the leftmost digit first.
In simple words: Sort the populations from biggest to smallest. The town with the most people goes at the top.

Exam Tip: For descending order, list the largest number first. Double-check by reading down and confirming that each population is smaller than the one above it.

 

Question 17. Find numbers between 42,750 and 53,500 such that the ones, tens and hundreds digits are all 0.
Answer: Numbers in this range where the ones, tens, and hundreds digits are all 0 (meaning they end in three zeros) are: 43,000, 44,000, 45,000, 46,000, 47,000, 48,000, 49,000, 50,000, 51,000, 52,000, and 53,000. These are all the thousands values between 42,750 and 53,500 where only the thousands and higher place values matter.
In simple words: Find numbers between the two given values that end with three zeros (like 43,000 or 50,000).

Exam Tip: These are "round thousands" - they have a zero in the hundreds, tens, and ones places. List them in order for clarity.

 

Question 18. Write the following numbers in the expanded form. One has been done for you.
(a) 783 = 700 + 80 + 3
(b) 8,062 = _____________
(c) 9,980 = _____________
(d) 10,304 = _____________
(e) 23,004 = _____________
(f) 70,405 = _____________
Answer: (a) 783 = 700 + 80 + 3 (already done). (b) 8,062 = 8,000 + 60 + 2 - we show the value of each non-zero digit in its place. (c) 9,980 = 9,000 + 900 + 80 - the 0 in the ones place is not written because it has no value. (d) 10,304 = 10,000 + 300 + 4 - the tens digit is 0 so tens are omitted. (e) 23,004 = 20,000 + 3,000 + 4 - we write only the non-zero place values. (f) 70,405 = 70,000 + 400 + 5 - the tens place has 0 so it is not shown.
In simple words: Break the number into its place values. Write the value of each digit (like 8,000 for the 8 in the thousands place). Skip any place with a zero.

Exam Tip: In expanded form, show what each digit contributes by multiplying it by its place value. Do not write zeros - they add nothing to the sum.

 

Question 19. Fill in the blanks with the correct answer. Share your thoughts in class.
(a) 983 = 90 Tens + 83 Ones
(b) 68 = ___ Tens + 18 Ones
(c) 607 = 4 Hundreds + ___ Ones
(d) 5,621 = 4 Thousand + ___ Hundreds + 2 Tens + ___ Ones
(e) 7,069 = ___ Thousand + 20 Hundreds + ___ Ones
(f) 37,608 = ___ Ten Thousand + 17 Thousand + ___ Hundreds + 8 Ones
(g) 43,001 = 3 Ten Thousand + ____ Thousand + ____ Hundreds + 1 Ones
Answer: (a) 983 = 90 Tens + 83 Ones (already given). (b) 68 = 5 Tens + 18 Ones because 50 + 18 = 68. (c) 607 = 4 Hundreds + 201 Ones because 400 + 201 = 607. (d) 5,621 = 4 Thousand + 16 Hundreds + 2 Tens + 1 Ones because 4,000 + 1,600 + 20 + 1 = 5,621. (e) 7,069 = 5 Thousand + 20 Hundreds + 69 Ones because 5,000 + 2,000 + 69 = 7,069. (f) 37,608 = 2 Ten Thousand + 17 Thousand + 6 Hundreds + 8 Ones because 20,000 + 17,000 + 600 + 8 = 37,608. (g) 43,001 = 3 Ten Thousand + 10 Thousand + 30 Hundreds + 1 Ones because 30,000 + 10,000 + 3,000 + 1 = 43,001.
In simple words: Find what number of each place value adds up to the original number. Break it apart by place, using any combination that gives the right sum.

Exam Tip: These problems show that numbers can be broken down and regrouped in many ways. Always verify by adding up your parts - they must equal the original number.

 

Question 20. Fill in the blanks with the correct answers.
(a) How many notes of Rs.10 are there in Rs.7,934? 793
(b) How many notes of Rs.100 are there in Rs.7,934? _______
(c) How many thousands are there in 7,934? _______
(d) How many Rs.500 notes are there in Rs.7,934? _______
(e) How many notes of Rs.10 are there in Rs.65,342? _______
(f) How many notes of Rs.100 are there in Rs.65,342? _______
(g) How many thousands are there in 65,342? _______
(h) How many Rs.500 notes are there in Rs.65,342? _______
Answer: (a) Rs.7,934 ÷ Rs.10 = 793 notes of Rs.10 (already given). (b) Rs.7,934 ÷ Rs.100 = 79 notes of Rs.100 (since 100 × 79 = 7,900). (c) Rs.7,934 contains 7 thousands (since 1,000 × 7 = 7,000). (d) Rs.7,934 ÷ Rs.500 = 15 notes of Rs.500 (since 500 × 15 = 7,500). (e) Rs.65,342 ÷ Rs.10 = 6,534 notes of Rs.10. (f) Rs.65,342 ÷ Rs.100 = 653 notes of Rs.100. (g) Rs.65,342 contains 65 thousands (since 1,000 × 65 = 65,000). (h) Rs.65,342 ÷ Rs.500 = 130 notes of Rs.500 (since 500 × 130 = 65,000).
In simple words: Divide the total amount by the value of one note (or one thousand) to find how many you need. Use division to find your answer.

Exam Tip: Always divide the total amount by the note value. If you get a remainder, it means you can't make the exact amount with that denomination - the answer is the whole number part only.