Question

if a natural number a is divided by 7 the remainder is 5 if a natural number b is divided by 7 the remainder is 3 the remainder is r if a + b is divided by 7 find the value of (3r+ 5 )/4 ​

Answer 1

Answer:

a=7 ✖5=35

b=7 ✖3=21

a+b ➗7

35+21➗7

56➗7=8

Answer 2

Given :  a natural number 'a' is divided by $7$, the remainder  is $5$. If a natural number 'b' is divided by $7$, the  remainder is $3$. The remainder is 'r' if $a + b$ is divided  by $7$

To Find : Value of $(3r+5)/4$

Solution:

'a' is divided by $7$, the remainder  is $5$

$= > a = 7m + 5$

'b' is divided by $7$, the  remainder is $3$

$= > b = 7n + 3$

$a + b = 7m + 5 + 7n + 3$

$= > a + b = 7m + 7n + 8$

$= > a + b = 7m + 7n + 7 + 1$

$= > a + b = 7(m + n + 1) + 1$

$= > a + b = 7k + 1$

The remainder is 'r' if $a + b$ is divided  by $7$

$= > a + b = 7k + r$

$= > r = 1$

$=(3r+5)/4 \\= (3\times 1 + 5)/4$

$= (3 + 5)/4$

$= 8/4$

$= 2$

#SPj2