Page 1 Exercise 5.1 PAGE: 5.5 1. Write the opposite of each of the following: (i) Increase in population (ii) Depositing money in a bank (iii) Earning money (iv) Going North (v) Gaining a weight of 4kg (vi) A loss of Rs 1000 (vii) 25 (viii) – 15 Solution: (i) The opposite of Increase in population is Decrease in population. (ii) The opposite of Depositing money in a bank is Withdrawing money from a bank. (iii) The opposite of earning money is Spending money. (iv) The opposite of Going North is Going South. (v) The opposite of gaining a weight of 4kg is losing a weight of 4kg. (vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000. (vii) The opposite of 25 is – 25. (viii) The opposite of – 15 is 15. 2. Indicate the following by using integers: (i) 25 o above zero (ii) 5 o below zero (iii) A profit of Rs 800 (iv) A deposit of Rs 2500 (v) 3km above sea level (vi) 2km below level Solution: (i) 25 o above zero is + 25 o . (ii) 5 o below zero is - 5 o . (iii) A profit of Rs 800 is + 800. (iv) A deposit of Rs 2500 is + 2500. (v) 3km above sea level is + 3. (vi) 2km below level is – 2. Page 2 Exercise 5.1 PAGE: 5.5 1. Write the opposite of each of the following: (i) Increase in population (ii) Depositing money in a bank (iii) Earning money (iv) Going North (v) Gaining a weight of 4kg (vi) A loss of Rs 1000 (vii) 25 (viii) – 15 Solution: (i) The opposite of Increase in population is Decrease in population. (ii) The opposite of Depositing money in a bank is Withdrawing money from a bank. (iii) The opposite of earning money is Spending money. (iv) The opposite of Going North is Going South. (v) The opposite of gaining a weight of 4kg is losing a weight of 4kg. (vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000. (vii) The opposite of 25 is – 25. (viii) The opposite of – 15 is 15. 2. Indicate the following by using integers: (i) 25 o above zero (ii) 5 o below zero (iii) A profit of Rs 800 (iv) A deposit of Rs 2500 (v) 3km above sea level (vi) 2km below level Solution: (i) 25 o above zero is + 25 o . (ii) 5 o below zero is - 5 o . (iii) A profit of Rs 800 is + 800. (iv) A deposit of Rs 2500 is + 2500. (v) 3km above sea level is + 3. (vi) 2km below level is – 2. 3. Mark the following integers on a number line: (i) 7 (ii) -4 (iii) 0 Solution: The following integers are marked on a number line as given below: 4. Which number in each of the following pairs is smaller? (i) 0, -4 (ii) -3 , 12 (iii) 8, 13 (iv) – 15, -27 Solution: (i) 0 is greater than the negative integers So we get – 4 < 0 Therefore, - 4 is smaller. (ii) 12 is greater than -3 on a number line So we get -3 < 12 Therefore, - 3 is smaller. (iii) 13 is greater than 8 on a number line So we get 8 < 13 Therefore, 8 is smaller. (iv) – 15 is greater than – 27 on a number line So we get – 27 < - 15 Therefore, - 27 is smaller. 5. Which number in each of the following pairs is larger? (i) 3, -4 (ii) – 12, - 8 (iii) 0, 7 (iv) 12, - 18 Solution: (i) We know that 3 is larger than – 4 on a number line So we get 3 > - 4 Therefore, 3 is larger. (ii) We know that – 8 is larger than – 12 on a number line So we get – 8 > - 12 Page 3 Exercise 5.1 PAGE: 5.5 1. Write the opposite of each of the following: (i) Increase in population (ii) Depositing money in a bank (iii) Earning money (iv) Going North (v) Gaining a weight of 4kg (vi) A loss of Rs 1000 (vii) 25 (viii) – 15 Solution: (i) The opposite of Increase in population is Decrease in population. (ii) The opposite of Depositing money in a bank is Withdrawing money from a bank. (iii) The opposite of earning money is Spending money. (iv) The opposite of Going North is Going South. (v) The opposite of gaining a weight of 4kg is losing a weight of 4kg. (vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000. (vii) The opposite of 25 is – 25. (viii) The opposite of – 15 is 15. 2. Indicate the following by using integers: (i) 25 o above zero (ii) 5 o below zero (iii) A profit of Rs 800 (iv) A deposit of Rs 2500 (v) 3km above sea level (vi) 2km below level Solution: (i) 25 o above zero is + 25 o . (ii) 5 o below zero is - 5 o . (iii) A profit of Rs 800 is + 800. (iv) A deposit of Rs 2500 is + 2500. (v) 3km above sea level is + 3. (vi) 2km below level is – 2. 3. Mark the following integers on a number line: (i) 7 (ii) -4 (iii) 0 Solution: The following integers are marked on a number line as given below: 4. Which number in each of the following pairs is smaller? (i) 0, -4 (ii) -3 , 12 (iii) 8, 13 (iv) – 15, -27 Solution: (i) 0 is greater than the negative integers So we get – 4 < 0 Therefore, - 4 is smaller. (ii) 12 is greater than -3 on a number line So we get -3 < 12 Therefore, - 3 is smaller. (iii) 13 is greater than 8 on a number line So we get 8 < 13 Therefore, 8 is smaller. (iv) – 15 is greater than – 27 on a number line So we get – 27 < - 15 Therefore, - 27 is smaller. 5. Which number in each of the following pairs is larger? (i) 3, -4 (ii) – 12, - 8 (iii) 0, 7 (iv) 12, - 18 Solution: (i) We know that 3 is larger than – 4 on a number line So we get 3 > - 4 Therefore, 3 is larger. (ii) We know that – 8 is larger than – 12 on a number line So we get – 8 > - 12 Therefore, - 8 is larger. (iii) We know that 7 is larger than 0 on a number line So we get 7 > 0 Therefore, 7 is larger. (iv) We know that 12 is larger than – 18 on a number line So we get 12 > - 18 Therefore, 12 is larger. 6. Write all integers between: (i) – 7 and 3 (ii) – 2 and 2 (iii) – 4 and 0 (iv) 0 and 3 Solution: (i) The integers between – 7 and 3 are - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2 (ii) The integers between – 2 and 2 are -1, 0, 1. (iii) The integers between – 4 and 0 are -3, -2, -1 (iv) The integers between 0 and 3 are 1, 2. 7. How many integers are between? (i) – 4 and 3 (ii) 5 and 12 (iii) – 9 and – 2 (iv) 0 and 5 Solution: (i) The integers between – 4 and 3 are -3, -2, -1, 0, 1, 2 Therefore, number of integers between – 4 and 3 are 6. (ii) The integers between 5 and 12 are 6, 7, 8, 9, 10, 11 Therefore, number of integers between 5 and 12 are 6. (iii) The integers between – 9 and – 2 are -8, -7, -6, -5, -4, -3 Therefore, number of integers between -9 and -2 are 6. (iv) The integers between 0 and 5 are 1, 2, 3, 4 Page 4 Exercise 5.1 PAGE: 5.5 1. Write the opposite of each of the following: (i) Increase in population (ii) Depositing money in a bank (iii) Earning money (iv) Going North (v) Gaining a weight of 4kg (vi) A loss of Rs 1000 (vii) 25 (viii) – 15 Solution: (i) The opposite of Increase in population is Decrease in population. (ii) The opposite of Depositing money in a bank is Withdrawing money from a bank. (iii) The opposite of earning money is Spending money. (iv) The opposite of Going North is Going South. (v) The opposite of gaining a weight of 4kg is losing a weight of 4kg. (vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000. (vii) The opposite of 25 is – 25. (viii) The opposite of – 15 is 15. 2. Indicate the following by using integers: (i) 25 o above zero (ii) 5 o below zero (iii) A profit of Rs 800 (iv) A deposit of Rs 2500 (v) 3km above sea level (vi) 2km below level Solution: (i) 25 o above zero is + 25 o . (ii) 5 o below zero is - 5 o . (iii) A profit of Rs 800 is + 800. (iv) A deposit of Rs 2500 is + 2500. (v) 3km above sea level is + 3. (vi) 2km below level is – 2. 3. Mark the following integers on a number line: (i) 7 (ii) -4 (iii) 0 Solution: The following integers are marked on a number line as given below: 4. Which number in each of the following pairs is smaller? (i) 0, -4 (ii) -3 , 12 (iii) 8, 13 (iv) – 15, -27 Solution: (i) 0 is greater than the negative integers So we get – 4 < 0 Therefore, - 4 is smaller. (ii) 12 is greater than -3 on a number line So we get -3 < 12 Therefore, - 3 is smaller. (iii) 13 is greater than 8 on a number line So we get 8 < 13 Therefore, 8 is smaller. (iv) – 15 is greater than – 27 on a number line So we get – 27 < - 15 Therefore, - 27 is smaller. 5. Which number in each of the following pairs is larger? (i) 3, -4 (ii) – 12, - 8 (iii) 0, 7 (iv) 12, - 18 Solution: (i) We know that 3 is larger than – 4 on a number line So we get 3 > - 4 Therefore, 3 is larger. (ii) We know that – 8 is larger than – 12 on a number line So we get – 8 > - 12 Therefore, - 8 is larger. (iii) We know that 7 is larger than 0 on a number line So we get 7 > 0 Therefore, 7 is larger. (iv) We know that 12 is larger than – 18 on a number line So we get 12 > - 18 Therefore, 12 is larger. 6. Write all integers between: (i) – 7 and 3 (ii) – 2 and 2 (iii) – 4 and 0 (iv) 0 and 3 Solution: (i) The integers between – 7 and 3 are - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2 (ii) The integers between – 2 and 2 are -1, 0, 1. (iii) The integers between – 4 and 0 are -3, -2, -1 (iv) The integers between 0 and 3 are 1, 2. 7. How many integers are between? (i) – 4 and 3 (ii) 5 and 12 (iii) – 9 and – 2 (iv) 0 and 5 Solution: (i) The integers between – 4 and 3 are -3, -2, -1, 0, 1, 2 Therefore, number of integers between – 4 and 3 are 6. (ii) The integers between 5 and 12 are 6, 7, 8, 9, 10, 11 Therefore, number of integers between 5 and 12 are 6. (iii) The integers between – 9 and – 2 are -8, -7, -6, -5, -4, -3 Therefore, number of integers between -9 and -2 are 6. (iv) The integers between 0 and 5 are 1, 2, 3, 4 Therefore, number of integers between 0 and 5 are 4. 8. Replace * in each of the following by < or > so that the statement is true: (i) 2 * 5 (ii) 0 * 3 (iii) 0 * - 7 (iv) – 18 * 15 (v) – 235 * - 532 (vi) – 20 * 20 Solution: (i) 2 < 5 (ii) 0 < 3 (iii) 0 > - 7 (iv) – 18 < 15 (v) – 235 > - 532 (vi) – 20 < 20 9. Write the following integers in increasing order: (i) – 8, 5, 0, -12, 1, -9, 15 (ii) – 106, 107, - 320, - 7, 185 Solution: (i) – 8, 5, 0, -12, 1, -9, 15 can be written in increasing order as - 12, - 9, - 8, 0, 1, 5, 15 (ii) – 106, 107, - 320, - 7, 185 can be written in increasing order as -320, - 106, - 7, 107, 185. 10. Write the following integers in decreasing order: (i) – 15, 0, -2, -9, 7, 6, -5, 8 (ii) -154, 123, -205, -89, -74 Solution: (i) – 15, 0, -2, -9, 7, 6, -5, 8 can be written in decreasing order as 8, 7, 6, 0, -2, -5, -9, -15 (ii) -154, 123, -205, -89, -74 can be written in decreasing order as 123, - 74, - 89, - 154, - 205 11. Using the number line, write the integer which is: (i) 2 more than 3 (ii) 5 less than 3 (iii) 4 more than – 9 Solution: Page 5 Exercise 5.1 PAGE: 5.5 1. Write the opposite of each of the following: (i) Increase in population (ii) Depositing money in a bank (iii) Earning money (iv) Going North (v) Gaining a weight of 4kg (vi) A loss of Rs 1000 (vii) 25 (viii) – 15 Solution: (i) The opposite of Increase in population is Decrease in population. (ii) The opposite of Depositing money in a bank is Withdrawing money from a bank. (iii) The opposite of earning money is Spending money. (iv) The opposite of Going North is Going South. (v) The opposite of gaining a weight of 4kg is losing a weight of 4kg. (vi) The opposite of a loss of Rs 1000 is a gain of Rs 1000. (vii) The opposite of 25 is – 25. (viii) The opposite of – 15 is 15. 2. Indicate the following by using integers: (i) 25 o above zero (ii) 5 o below zero (iii) A profit of Rs 800 (iv) A deposit of Rs 2500 (v) 3km above sea level (vi) 2km below level Solution: (i) 25 o above zero is + 25 o . (ii) 5 o below zero is - 5 o . (iii) A profit of Rs 800 is + 800. (iv) A deposit of Rs 2500 is + 2500. (v) 3km above sea level is + 3. (vi) 2km below level is – 2. 3. Mark the following integers on a number line: (i) 7 (ii) -4 (iii) 0 Solution: The following integers are marked on a number line as given below: 4. Which number in each of the following pairs is smaller? (i) 0, -4 (ii) -3 , 12 (iii) 8, 13 (iv) – 15, -27 Solution: (i) 0 is greater than the negative integers So we get – 4 < 0 Therefore, - 4 is smaller. (ii) 12 is greater than -3 on a number line So we get -3 < 12 Therefore, - 3 is smaller. (iii) 13 is greater than 8 on a number line So we get 8 < 13 Therefore, 8 is smaller. (iv) – 15 is greater than – 27 on a number line So we get – 27 < - 15 Therefore, - 27 is smaller. 5. Which number in each of the following pairs is larger? (i) 3, -4 (ii) – 12, - 8 (iii) 0, 7 (iv) 12, - 18 Solution: (i) We know that 3 is larger than – 4 on a number line So we get 3 > - 4 Therefore, 3 is larger. (ii) We know that – 8 is larger than – 12 on a number line So we get – 8 > - 12 Therefore, - 8 is larger. (iii) We know that 7 is larger than 0 on a number line So we get 7 > 0 Therefore, 7 is larger. (iv) We know that 12 is larger than – 18 on a number line So we get 12 > - 18 Therefore, 12 is larger. 6. Write all integers between: (i) – 7 and 3 (ii) – 2 and 2 (iii) – 4 and 0 (iv) 0 and 3 Solution: (i) The integers between – 7 and 3 are - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2 (ii) The integers between – 2 and 2 are -1, 0, 1. (iii) The integers between – 4 and 0 are -3, -2, -1 (iv) The integers between 0 and 3 are 1, 2. 7. How many integers are between? (i) – 4 and 3 (ii) 5 and 12 (iii) – 9 and – 2 (iv) 0 and 5 Solution: (i) The integers between – 4 and 3 are -3, -2, -1, 0, 1, 2 Therefore, number of integers between – 4 and 3 are 6. (ii) The integers between 5 and 12 are 6, 7, 8, 9, 10, 11 Therefore, number of integers between 5 and 12 are 6. (iii) The integers between – 9 and – 2 are -8, -7, -6, -5, -4, -3 Therefore, number of integers between -9 and -2 are 6. (iv) The integers between 0 and 5 are 1, 2, 3, 4 Therefore, number of integers between 0 and 5 are 4. 8. Replace * in each of the following by < or > so that the statement is true: (i) 2 * 5 (ii) 0 * 3 (iii) 0 * - 7 (iv) – 18 * 15 (v) – 235 * - 532 (vi) – 20 * 20 Solution: (i) 2 < 5 (ii) 0 < 3 (iii) 0 > - 7 (iv) – 18 < 15 (v) – 235 > - 532 (vi) – 20 < 20 9. Write the following integers in increasing order: (i) – 8, 5, 0, -12, 1, -9, 15 (ii) – 106, 107, - 320, - 7, 185 Solution: (i) – 8, 5, 0, -12, 1, -9, 15 can be written in increasing order as - 12, - 9, - 8, 0, 1, 5, 15 (ii) – 106, 107, - 320, - 7, 185 can be written in increasing order as -320, - 106, - 7, 107, 185. 10. Write the following integers in decreasing order: (i) – 15, 0, -2, -9, 7, 6, -5, 8 (ii) -154, 123, -205, -89, -74 Solution: (i) – 15, 0, -2, -9, 7, 6, -5, 8 can be written in decreasing order as 8, 7, 6, 0, -2, -5, -9, -15 (ii) -154, 123, -205, -89, -74 can be written in decreasing order as 123, - 74, - 89, - 154, - 205 11. Using the number line, write the integer which is: (i) 2 more than 3 (ii) 5 less than 3 (iii) 4 more than – 9 Solution: (i) 2 more than 3 In order to get the integer 2 more than 3 We draw a number line from 2 and proceed 3 units to the right to obtain 5 Therefore, 2 more than 3 is 5. (ii) 5 less than 3 In order to get the integer 5 less than 3 We draw a number line from 3 and proceed 5 units to the left to obtain – 2 Therefore, 5 less than 3 is – 2. (iii) 4 more than – 9 In order to get the integer 4 more than – 9 We draw a number line from – 9 and proceed 4 units to the right to obtain -5 Therefore, 4 more than – 9 is – 5. 12. Write the absolute value of each of the following: (i) 14 (ii) – 25 (iii) 0 (iv) – 125 (v) – 248 (vi) a – 7, if a is greater than 7 (vii) a – 7, if a - 2 is less than 7 (viii) a + 4, if a is greater than -4 (ix) a + 4 if a is less than – 4 (x) |-3| (xi) -|-5| (xii) |12 – 5| Solution: (i) The absolute value of 14 is |14| = 14Read More

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