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Fill in the blanks with \( \rangle,< \) or \( = \) sign.
(a) $(-3)+(-6)$___$(-3)-(-6)$
(b) $(– 21) – (– 10)$ _____ $(– 31) + (– 11)$
(c) $45 – (– 11)$ ______ $57 + (– 4)$
(d) $(– 25) – (– 42)$ _____ $(– 42) – (– 25)$
To do :
We have to fill in the blanks with \( \rangle,< \) or \( = \) sign.
Solution :
We know that,
$(+) \times (-) = (-)$
$(+) \times (+) = (+)$
$(-) \times (-) = (+)$
$(-) \times (+) = (-)$
(a) $(-3)+(-6)=-3-6$
$=-(3+6)$
$=-9$
$(-3)-(-6)=-3+6$
$=6-3$
$=3$
$-9<3$
Therefore,
$(-3)+(-6) < (-3)-(-6)$
(b) $(-21)-(-10)=-21+10$
$=-(21-10)$
$=-11$
$(-31)+(-11)=-31-11$
$=-(31+11)$
$=-42$
$-11>-42$
Therefore,
$(-21)-(-10)>(-31)+(-11)$
(c) $45-(-11)=45+11$
$=56$
$57+(-4)=57-4$
$=53$
$56>53$
Therefore,
$45-(-11)>57+(-4)$
(d) $(-25)-(-42)=-25+42$
$=42-25$
$=17$
$(-42)-(-25)=-42+25$
$=-(42-25)$
$=-17$
$17>-17$
Therefore,
$(-25)-(-42)>(-42)-(-25)$