Std 6 Mathematics · Chapter 3

3. In the World of Numbers

Solutions to Practice Set 3.1, Practice Set 3.2 and Exercise 3. Maharashtra State Board (Balbharati), Grade Six Mathematics.

About the chapter

In this chapter, we read and write large numbers up to crores. We compare them and do addition and subtraction. Then we learn about negative numbers. We show integers on a number line and add and subtract them.

Key points

In the Indian system, a number is read as crore, lakh, thousand and hundreds.
Natural numbers are 1, 2, 3, … Whole numbers are 0, 1, 2, 3, …
Positive numbers, zero and negative numbers together are called integers.
On a number line, a number on the right is always greater than a number on the left.
The sum of a number and its opposite number is zero.

Formulas and terms

Negative number – a number less than zero, like −3.
Opposite numbers – numbers like +7 and −7. (+7) + (−7) = 0
Adding integers with the same sign – add them and keep the same sign.
Adding integers with different signs – subtract the smaller from the larger. Give the sign of the larger number.
Subtracting an integer – add its opposite number. a − (−b) = a + b

Practice Set 3.1

1Write the following numbers in words.

(i) 49,38,67,521 – Forty-nine crore thirty-eight lakh sixty-seven thousand five hundred twenty-one
(ii) 28,41,57,649 – Twenty-eight crore forty-one lakh fifty-seven thousand six hundred forty-nine
(iii) 2,37,50,145 – Two crore thirty-seven lakh fifty thousand one hundred forty-five
(iv) 6,79,81,049 – Six crore seventy-nine lakh eighty-one thousand forty-nine

2Write the appropriate symbol in the box: <, = or >.

(i) 59,21,492 < 64,79,426
(ii) 7,579 > 0
(iii) 48,579 = 48,579
(iv) 0 < 700

3Solve. (i) 95,754 − 38,254 (ii) 85,39,652 + 53,27,541

(i) 95,754 − 38,254 = 57,500

(ii) 85,39,652 + 53,27,541 = 1,38,67,193

4The expenditure on school nutrition in June was ₹87,000 and in July it became ₹1,69,000. What was the total expenditure for June and July? How much more was spent in July than in June?

Expenditure in June = ₹87,000
Expenditure in July = ₹1,69,000
Total expenditure = 87,000 + 1,69,000 = ₹2,56,000
More spent in July = 1,69,000 − 87,000 = ₹82,000

The total expenditure was ₹2,56,000. ₹82,000 more was spent in July than in June.

5An organization deposited ₹9,25,498 income tax in February and ₹11,49,505 in March. How much total income tax was deposited in the two months?

Tax deposited in February = ₹9,25,498
Tax deposited in March = ₹11,49,505
Total tax = 9,25,498 + 11,49,505 = ₹20,75,003

A total income tax of ₹20,75,003 was deposited in the two months.

Practice Set 3.2

1Write the correct symbol > or < in the box below.

A number on the right is always greater than a number on the left.

(i) (−10) < 5
(ii) (−19) < (−5)
(iii) (−3) < 0
(iv) 8 < 12
(v) 5 > 0
(vi) (−3) > (−9)

Remember: −19 is less than −5. On the number line, −19 lies to the left of −5.

2Solve.

(i) 4 + 7 = 11
(ii) (−4) + (−5) = −9
(iii) (−7) + 2 = −5
(iv) 10 + (−2) = 8
(v) (−63) + (−32) = −95
(vi) (−71) + (+71) = 0

3Solve.

(i) 78 − (−45) = 78 + 45 = 123
(ii) (−19) − (−27) = (−19) + 27 = 8
(iii) 148 − (−37) = 148 + 37 = 185
(iv) (−120) − 200 = (−120) + (−200) = −320
(v) (−57) − (−48) = (−57) + 48 = −9
(vi) (−15) − (−24) = (−15) + 24 = 9

Remember: To subtract a number, add its opposite number.

Exercise 3

1Choose the correct option.

(i) −5 is …….. — c) an integer
(ii) −5 __ 0 — b) <

2Write whether the following statements are true or false.

(i) Zero is the smallest natural number. – False
The smallest natural number is 1.
(ii) All natural numbers are whole numbers. – True
(iii) All whole numbers are natural numbers. – False
0 is a whole number, but it is not a natural number.
(iv) The sum of opposite numbers is zero. – True

3Write the following four numbers in ascending order: 87,29,35,104 · 87,39,27,401 · 85,93,21,793 · 89,51,23,307

85,93,21,793 < 87,29,35,104 < 87,39,27,401 < 89,51,23,307

4Obtain five-digit numbers using the digits 1 to 9 only once. Read them, write them in words, and write the largest and the smallest numbers.

Some five-digit numbers are:

24,681 – Twenty-four thousand six hundred eighty-one
13,579 – Thirteen thousand five hundred seventy-nine
56,789 – Fifty-six thousand seven hundred eighty-nine

Largest number = 98,765 – Ninety-eight thousand seven hundred sixty-five

Smallest number = 12,345 – Twelve thousand three hundred forty-five

5(i) Draw a number line and show −5, 3, −3 and 7 on it. (ii) What are the numbers to the right of zero called? (iii) What are the numbers to the left of zero called?

Negative numbers lie to the left of 0 and positive numbers to the right.

(ii) The numbers to the right of zero are called positive numbers.

(iii) The numbers to the left of zero are called negative numbers.

6A district spent ₹69,27,762 in 2023-24 and ₹88,36,584 in 2024-25 on environmental protection. Find the total expenditure and how much more was spent in 2024-25.

Spent in 2023-24 = ₹69,27,762
Spent in 2024-25 = ₹88,36,584
Total expenditure = 69,27,762 + 88,36,584 = ₹1,57,64,346
More spent in 2024-25 = 88,36,584 − 69,27,762 = ₹19,08,822

The total expenditure was ₹1,57,64,346. ₹19,08,822 more was spent in 2024-25.

7Write the numbers 1 to 9 in the given box so that each number appears only once and the vertical, horizontal and diagonal sums are equal.

Blue cells were given in the textbook; green cells are the ones we fill in.

1 + 2 + 3 + … + 9 = 45. There are 3 rows. So each sum must be 45 ÷ 3 = 15.

The rows are 8, 1, 6 / 3, 5, 7 / 4, 9, 2. Every row, column and diagonal adds up to 15.

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