Perform the indicated operations:9+6, (mod 5)7-11,(mod 12)4*3,(mod 5)1 div 2,(mod 5)

Answer and Explanation:To find : Perform the indicated operations?Solution : Modular math is defined as [tex]\frac{A}{B}=Q\text{ remainder } R[/tex]or [tex]A\times Q+R=B[/tex]Where, A is the dividend B is the divisor Q is the quotient R is the remainder   The solution is [tex]A mod B = R[/tex]Now, We perform same in every case1) [tex](9+6), \mod 5[/tex]We can direct add the term, [tex]15 \mod 5[/tex]Now, we divide 15 by 5 and see the remainder[tex]5\times 3+0=15[/tex]Remainder is 0.So,  [tex]15 \mod 5=0[/tex]2) [tex](7-11), \mod 12[/tex]We can direct subtract the term, [tex]-4 \mod 12[/tex]Now, we divide -4 by 12 and see the remainder[tex]12\times (-1)+8=-4[/tex]Remainder is 8.So,  [tex]-4 \mod 12=8[/tex]3) [tex](4\times 3), \mod 5[/tex]We can direct multiply the term, [tex]12 \mod 5[/tex]Now, we divide 12 by 5 and see the remainder[tex]5\times 2+2=12[/tex]Remainder is 2.So, [tex]12 \mod 5=2[/tex]4) [tex](1\div 2), \mod 5[/tex]We can direct divide the term, [tex]0.5 \mod 5[/tex]Now, we divide 0.5 by 5 and see the remainder[tex]5\times 0+0.5=0.5[/tex]Remainder is 0.5.So,  [tex]0.5 \mod 5=0.5[/tex]