Is it true that Dividend over Divisor = Quotient + Remainder?

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Is it true that Dividend over Divisor = Quotient + Remainder?

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Answer 1 · 2018-03-24T17:47:41

Please see below.

Explanation:

We often ask students to express the result of a division as the quotient and the remainder. But the word "and" here does not mean "plus".

$\frac{14}{3}$ $14/3$ has a quotient of $4$ $4$ and remainder $2$ $2$ .

The equality involving these words is

$Dividend = Quotient \times Divisor + Remainder$ $"Dividend" = "Quotient" xx "Divisor" + "Remainder"$

$14 = 4 \times 3 + 2$ $14 = 4 xx 3 + 2$

Answer 2 · 2018-03-24T17:53:37

No,

Explanation:

It is not true that Dividend over Divisor is equal to Quotient plus Remainder. For example if $37$ $37$ is divided by $8$ $8$ , then quotient is $4$ $4$ and remainder is $5$ $5$ . Observe that $37$ $37$ divided by $8$ $8$ is not equal to $4$ $4$ plus $5$ $5$ .

What is true is that Dividend is equal to Divisor multiplied by Quotient plus Remaider and in example $37 = 8 \times 4 + 5$ $37=8xx4+5$

However in terms of what is stated in question, one can say

Dividend over Divisor is equal to Quotient plus Remainder divided by Divisor i.e. $\frac{37}{8} = 4 + \frac{5}{8}$ $37/8=4+5/8$

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Is it true that Dividend over Divisor = Quotient + Remainder?

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