$3 \frac12$ divided by $\frac45\,$ ; why do I get 4.3?

Question

This has been bothering me a lot, this is my thinking:

$3\dfrac12 \implies \dfrac72 \implies \dfrac{35}{10}$

similarly $\dfrac45 \implies \dfrac{8}{10}$

So

$$\dfrac{\dfrac{35}{10}}{\dfrac{8}{10}}=\dfrac{35}{8}=4.375$$

but... 35 % 8 = 3 ; 3/10? What's wrong with 4 and 3/10?

Do you ALWAYS just discard the denominator in division, is that where I'm failing?

"but... 35 % 8 = 3 ; 3/10? What's wrong with 4 and 3/10?".I didn't get what is here "3;3/10" ? — iostream007, May 18 '13 at 14:07
Remember that mathematics is not a programming language. $%$ is not the symbol for division, it's the symbol for percentage. — Asaf Karagila, May 18 '13 at 15:26
@AsafKaragila and anyway in C-derived programming languages, % is typically integer-modulus. — geometrian, Oct 21 '14 at 18:25
@GraphicsResearch: I am well aware of that. I do believe that the banner on top says "MATHEMATICS" not "PROGRAMMERS" or "STACKOVERFLOW", though. — Asaf Karagila, Oct 21 '14 at 18:27
Why are you using $\implies$ when $=$ is the appropriate symbol to express equality? — Matthew Leingang, Feb 09 '15 at 22:37

score 5 · Answer 1 · answered Mar 31 '13 at 03:55

5

I don't know if I understand your question, but for any numbers $a$, $b$, and $c$, it is true that $$\frac{a/c}{b/c}=\frac{a}{b}$$ (as long as neither $b$ nor $c$ is zero, so that we're not dividing by zero anywhere).

answered Mar 31 '13 at 03:55

Zev Chonoles

129,973

That would make sense, the answer would be 4.375/1 or 4.375 if that method was used. – FeelingSilly Mar 31 '13 at 03:58

score 5 · Answer 2 · answered Mar 31 '13 at 03:59

5

35 div 8 is 4, 35 mod 8 = 3, so the answer is $4 + 3/8$ (not $4 + 3/10$).

answered Mar 31 '13 at 03:59

Yoni Rozenshein

6,817

1

This is the explanation they're looking for in terms I very much doubt they'll understand. Why not just say something like "the remainder of 3 means 'and three eighths' since you're dividing by 8, not 'and three tenths'." – Mark S. May 18 '13 at 15:32

score 2 · Answer 3 · answered Mar 31 '13 at 03:59

2

$$ 3.5=\frac{7}{2}\Longrightarrow \frac{7}{2}\div\frac{4}{5}=\frac{7}{2}\cdot\frac{5}{4}=\frac{35}{8}= 4\small{\frac{3}{8}}$$

answered Mar 31 '13 at 03:59

DonAntonio

211,718
17
136
287

score 0 · Answer 4 · answered Feb 09 '15 at 22:31

First, turn it into a multiplication problem by putting in the reciprocal of the second fraction: $3$$1\over 2$$\times$$5\over 4$. Now write the mixed number as an improper fraction: $7\over 2$$\times$$5\over 4$. Now multiply the numerators and the denominators together to get the result: ${7\times 5}\over{2\times 4}$, which evaluates to $35\over 8$. You can write this as a mixed number as $4$$3\over 8$, which can be written as a decimal as $4.375$, and that's why you get it.

$3 \frac12$ divided by $\frac45\,$ ; why do I get 4.3?

4 Answers4