Question

what is the largest four digit number,which when divided by 19 leaves a reminder of 7.
here are the option:a.9972 b.9976 c.9978 d.9982

Answer 1

What is the largest four digit number, which when divided by 19 leaves a remainder of 7.

Here are the options: $a.9972$ $b.9976$ $c.9978$ $d.9982$

Solution:

Division with remainder is finding the largest integer that is the product of a divider provides value not greater than the dividend. The required number is called incomplete quotient. The difference between the dividend and the product of a divider on a partial quotient is called the remainder, is always less than the divisor. The general form of a linear equation can be expressed as $a = b \times q + r$. In this equation, q can be referred to as the quotient and d as the divisor, while r as the remainder. The equation can be transformed to find the remainder as: $r = a - b \times q$. Additionally, a and b must be natural numbers, with b being non-zero. The quotient is the integer result (rounded down) of the division of a by b. The remainder must also be an integer. If a and b are natural numbers, with d non-zero, it can be proven that there exist unique integers q and r, such that $a = b \times q + r$ and $0 \leq r < b$. The number q is called the quotient, while r is called the remainder.

Firstly we divide to get a whole number and a decimal for each option:

$$\begin{array}{l} a. \frac{9972}{19} = 524,8421053 \\ b. \frac{9976}{19} = 525,0526316 \\ c. \frac{9978}{19} = 525,1578947 \\ d. \frac{9982}{19} = 525,3684211 \\ \end{array}$$

Subtract the whole number part for each option:

a. Subtract 524 get 0,8421053, multiply the above by 19 to get 16.0000007 rounding gives the remainder of 16.

b. Subtract 525 get 0,0526316, multiply the above by 19 to get 1.0000004 rounding gives the remainder of 1.

c. Subtract 525 get 0,1578947, multiply the above by 19 to get 2.9999993 rounding gives the remainder of 3.

d. Subtract 525 get 0,3684211, multiply the above by 19 to get 7.0000009 rounding gives the remainder of 7.

**Answer**: the largest four digit number, which when divided by 19 leaves a remainder of 7 is option d.9982.