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Mathematics Question on Subtraction of Integers with the help of a Number Line

Fill in the blanks with >, < or = sign.
(a) (– 3) + (– 6) ______ (– 3) – (– 6)
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
(c) 45 – (– 11) ______ 57 + (– 4)
(d) (– 25) – (– 42) _____ (– 42) – (– 25)

Answer

(a) LHS=(−3)+(−6)=−3−6=–(3+6)=–9LHS= (-3) + (-6) = - 3 - 6 = – (3 + 6) = – 9
RHS=(−3)–(−6)=(−3)+6=3RHS = (-3) – (-6) = (-3) + 6 = 3
Here, –9<3– 9 < 3
Therefore, (−3)+(−6)<(−3)–(−6)(- 3) + (- 6) < (- 3) – (- 6)

**(b) **LHS=(−21)–(−10)=(−21)+10=−11LHS = (-21) – (-10) = (-21) + 10 = -11
RHS=(−31)+(−11)=–(31+11)=–42RHS = (-31) + (-11) = – (31 + 11) = – 42
Here,−11>\-42 -11 > \- 42
Therefore, (−21)−(−10)>(−31)+(−11)(-21) - (-10) > (-31) + (-11)

(c) LHS=45–(−11)=45+11=56LHS = 45 – (-11) = 45 + 11 = 56
RHS=57+(−4)=57−4=53RHS = 57 + (- 4) = 57 - 4 = 53
Here, 56>5356 > 53
Therefore, 45–(−11)>57+(−4)45 – (-11) > 57 + ( -4)

(d) LHS=(−25)–(−42)=−25+42=17LHS = (-25) – (-42) = - 25 + 42 = 17
RHS=(−42)–(−25)=−42+25=−17RHS = (- 42) – (-25) = - 42 + 25 = -17
Here, 17>−1717 > -17
Therefore, (−25)–(−42)>(−42)–(−25).(- 25) – (- 42) > (- 42) – (- 25).