When dividing the number "a" by 9, the remainder is 5. What condition must the number "b" satisfy in order for the difference a-b to be a multiple of 9?

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When dividing the number &quot;a&quot; by 9, the remainder is 5. What condition must the number &quot;b&quot; satisfy in order for the difference a-b to be a multiple of 9?

tranciarebt · Accepted Answer

When dividing the number &quot;a&quot; by 9, the remainder is 5So the number a can be written asa=9k+5Now let&#039;s use the divisibility property:&quot;If both the minuend and the subtrahend are divisible by some number, then the difference is also divisible by that number&quot;write down our differencea-b=9m(9k+5)-b=9mnote that the number b can also be divided by 9 with a remainderso let&#039;s write it asb=9n+xand now our difference will look like thisa-b=9m(9k+5)-(9n+x)=9m9(k-n)+(5-x)=9mso that this equality holds x=5And then the number b must be divisible by 9 with a remainder of 5let&#039;s give an example:50:9= 5*9+541:9=4*9+550-41=9 and it&#039;s a multiple of 9***************221:9=24*9+5140:9=15*5+5221-140=81and it is a multiple of 9

When dividing the number "a" by 9, the remainder is 5. What condition must the number "b" satisfy in order for the difference a-b to be a multiple of 9?

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