Negative Numbers and Integers
EXERCISE 6
Question. Fill in the blanks :
(i) Negative of \( -20 \) is ……….
(ii) Negative of \( 0 \) is …………
(iii) Negative of \( 8 \) is ………..
(iv) If \( 10 \) represents gain of Rs. \( 10 \), then \( -10 \) represents …………..
(v) If going south is negative then going north is …………
(vi) Because \( 5 < 7 \), therefore \( -5 \) ……….. \( -7 \).
(vii) If \( 3 > -2 \), then \( 3 \) is on the ………….. of \( -2 \).
(viii) If \( -8 < -6 \), then \( -8 \) is on the …………. of \( -6 \).
Answer: (i) \( 20 \)
(ii) \( 0 \)
(iii) \( -8 \)
(iv) loss of Rs. \( 10 \)
(v) positive
(vi) less than
(vii) right side
(viii) left side
Question. Use a number line to write the following integers in ascending (increasing) order :
(i) \( -5, 8, 0, -9, 4, -14 \) and \( 12 \)
(ii) \( -6, 7, 0, -9, 5 \) and \( 9 \)
Answer: (i) \( -5, 8, 0, -9, 4, -14 \) and \( 12 \)
Draw a number line for integers,, as shown below, and mark on it all the given integers.
Clearly, the given integers in the ascending order are :
\( -14 < -9 < -5 < 0 < 4 < 8 < 12 \)
(ii) \( -6, 7, 0, -9, 5 \) and \( 9 \)
Draw a number line for integers, as shown below, and mark on it all the given integers.
Clearly, the given integers in the ascending order are :
\( -9 < -6 < 0 < 5 < 7 < 9 \)
Question. Use a number line to write the following integers in descending (decreasing) order :
(i) \( -10, 0, 3, -4, 12, 11, -1 \) and \( 5 \)
(ii) \( -4, 3, -8, -12, -7 \) and \( 6 \).
Answer: (i) \( -10, 0, 3, -4, 12, 11, -1 \) and \( 5 \)
Draw a number line for integers, as shown below, and mark on it all the given integers.
Clearly, the given integers in the descending order are :
\( 12 > 11 > 5 > 3 > 0 > -1 > -4 > -10 \)
(ii) \( -4, 3, -8, -12, -7 \) and \( 6 \).
Draw a number line for integers, as shown below, and mark on it all the given integers.
Clearly, the given integers in the descending order are :
\( 6 > 3 > -4 > -7 > -8 > -12 \)
Question. Add:
(i) \( 13 \) and \( 15 \)
(ii) \( -13 \) and \( 15 \)
(iii) \( 13 \) and \( -15 \)
(iv) \( -13 \) and \( -15 \)
Answer: (i) \( 13 \) and \( 15 \)
\( 13 + 15 = 28 \)
(ii) \( -13 \) and \( 15 \)
\( (-13) + 15 = 2 \)
(iii) \( 13 \) and \( -15 \)
\( = (13)+ (-15) \)
\( = 13 - 15 = -2 \)
(iv) \( -13 \) and \( -15 \)
\( = (-13) + (-15) \)
\( = -13 - 15 = -28 \)
Question. Add:
(i) \( 259 \) and \( 214 \)
(ii) \( -528 \) and \( -243 \)
(iii) \( -623 \) and \( 326 \)
(iv) \( 258 \) and \( -473 \)
(v) \( -622 \) and \( -254 \)
(vi) \( 257 \) and \( -254 \)
Answer: (i) \( 259 \) and \( 214 \)
\( = 259 + 214 = 473 \)
(ii) \( -528 \) and \( -243 \)
\( = -528 + (-243) \)
\( = -528 - 243 \)
\( = -771 \)
(iii) \( -623 \) and \( 326 \)
\( = -623 + 326 = -297 \)
(iv) \( 258 \) and \( -473 \)
\( = 258 + (-473) \)
\( = 258 - 473 \)
\( = -215 \)
(v) \( -622 \) and \( -254 \)
\( = -622 + (-254) \)
\( = -622 - 254 \)
\( = -876 \)
(vi) \( 257 \) and \( -254 \)
\( = 257 + (-254) \)
\( = 257 - 254 \)
\( = 3 \)
Question. Subtract :
(i) \( 5 \) from \( 8 \)
(ii) \( -5 \) from \( 8 \)
(iii) \( 4 \) from \( -7 \)
(iv) \( -8 \) from \( -2 \)
(v) \( -3 \) from \( 12 \)
(vi) \( -6 \) from \( -3 \)
Answer: (i) \( 5 \) from \( 8 \)
\( = 8 - 5 = 3 \)
(ii) \( -5 \) from \( 8 \)
\( = 8 - (-5) \)
\( = 8 + 5 = 13 \)
(iii) \( 4 \) from \( -7 \)
\( = -7 - 4 \)
\( = -11 \)
(iv) \( -8 \) from \( -2 = -2 - (-8) \)
\( = -2 + 8 \)
\( = 6 \)
(v) \( -3 \) from \( 12 \)
\( = 12 - (-3) = 15 \)
(vi) \( -6 \) from \( -3 \)
\( = -3 - (-6) \)
\( = -3 + 6 = + 3 \)
Question. Subtract:
(i) \( -123 \) from \( 453 \)
(ii) \( -78 \) from \( -12 \)
(iii) \( 329 \) and \( -124 \)
(iv) \( -222 \) from \( 0 \)
Answer: (i) \( -123 \) from \( 453 \)
\( = + 453 - (-123) \)
\( = 453 + 123 = 576 \)
(ii) \( -78 \) from \( -12 \)
\( = -12 - (-78) \)
\( = -12 + 78 = 66 \)
(iii) \( 329 \) and \( -124 \)
\( = + 329 - 124 = 205 \)
(iv) \( -222 \) from \( 0 \)
\( = 0 - (-222) \)
\( = 0 + 222 = 222 \)
Question. Using a number line, find the integer which is :
(i) \( 3 \) more than \( -1 \)
(ii) \( 5 \) less than \( 2 \)
(iii) \( 5 \) more than \( -9 \)
(iv) \( 4 \) less than \( -4 \)
(v) \( 7 \) more than \( 0 \)
(vi) \( 7 \) less than \( -8 \)
Answer: (i) To get \( 3 \) more than \( -1 \), start from \( -1 \) and than move \( 3 \) units to the right of \( -1 \) to get \( 2 \).
\( \therefore 3 \) more than \( -1 \) is \( 2 \) Ans.
(ii) To get \( 5 \) less than \( 2 \), start from \( 2 \) and then move \( 5 \) units to the left of \( 2 \) to get \( -3 \).
\( \therefore 5 \) more than \( 2 \) is \( -3 \) Ans.
(iii) To get \( 5 \) more than \( -9 \), start from \( -9 \) and then move \( 5 \) units to the right of \( -9 \) to get \( -4 \).
\( \therefore 5 \) more than \( -9 \) is \( -4 \) Ans.
(iv) To get \( 4 \) less than \( -4 \), start from \( -4 \) and then move \( 4 \) units to the left of \( -4 \) to get \( -8 \).
\( \therefore 4 \) less than \( -4 \) is \( -8 \) Ans.
(v) To get \( 7 \) more than \( 0 \), start from \( 0 \) and then move \( 7 \) units to the right of \( 0 \) to get \( 7 \).
\( \therefore 7 \) more than \( 0 \) is \( 7 \) Ans.
(vi) To get \( 7 \) less than \( -8 \), start from \( -8 \), start from \( -8 \) and then move \( 7 \) units to the left of \( -8 \) to get \( -15 \).
\( \therefore 7 \) less than \( -8 \) is \( -15 \) Ans.
