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Evaluate 3/7 r + 5/8 s when r = 14 and s = 8

bobisaka

New member
Dec 25, 2019
3
Hi all,

I'm currently on khan academy and am stuck at solving the following question. I try to use the 'multiply fraction by whole number' solution, however the correct solution is different. What is the correct way to solving this?

3/7 r + 5/8 s when r = 14 and s = 8

The way i solve it leads me to: 3/98 + 5/8
(using this process 3/7 * 14/1 = 3/7 * 1/14 = 3/98 )



However the correct solution is: 3/7(14) + 5/8(8)
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,488
Hello, and welcome to the forum.

using this process 3/7 * 14/1 = 3/7 * 1/14 = 3/98
You cannot simply change 14/1 to 1/14.

When you have a sequence of multiplications and divisions with no parentheses, they should be evaluated left-to-right. So $3/7r$ means $(3/7)\cdot r=3r/7$. Therefore,
\[
\frac37\cdot\frac{14}{1}+\frac58\cdot\frac81=3\cdot2+5=11.
\]

Edit: In fact $3/7r$ does look confusing and I understand people who take it for $3/(7r)$. Therefore, such notation should be avoided by using fractions like \(\displaystyle \frac37\cdot r\) or parentheses. Nevertheless, this does not change the rule: a sequence of multiplications and divisions is evaluated left-to-right.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Hi all,

I'm currently on khan academy and am stuck at solving the following question. I try to use the 'multiply fraction by whole number' solution, however the correct solution is different. What is the correct way to solving this?

3/7 r + 5/8 s when r = 14 and s = 8
Notice the space between the "7" and the "r" and the space between the "8" and the "s". That indicates that this is the fraction 3/7 times the number r and the fraction 5/8 times the number s. With r= 14, 3/7 times 14 is the same as [tex]\frac{3}{7}\frac{14}{1}= \frac{42}{7}= 6[/tex] or [tex]\frac{3}{7}14= 3\frac{14}{7}= 3(2)= 6. And with s= 8, 5/8 times 8 is [tex]\frac{5}{8}8= 5\frac{8}{8}[/tex]. The result is 6+ 5= 11.

The way i solve it leads me to: 3/98 + 5/8
(using this process 3/7 * 14/1 = 3/7 * 1/14 = 3/98 )
That is peculiar! I had thought you were interpreting "3/7 r" as "3/7r" where there is no space and so means [tex]\frac{3}{7r}[/tex] (which is why writing fractions "in line" as "3/7" rather that "[tex]\frac{3}{7}[/tex]" tends to be ambiguous). But why in the world would you think that "
3/7 * 14/1 = 3/7 * 1/14"? Multiplying by a/b is NOT multiplying by b/a because a/b and b/a are not the same thing. Perhaps you are remembering a garbled form of "to divide by a fraction invert and multiply. That is [tex]\frac{a}{b}\div \frac{c}{d}= \frac{a}{g}\cdot\frac{d}{c}[/tex]. But that is changing from division to multiplication.



However the correct solution is: 3/7(14) + 5/8(8)[/QUOTE]
 

bobisaka

New member
Dec 25, 2019
3
Hi all,

Thanks for the feedback. You stand correct in that I got confused with dividing fraction by whole number.

That clears everything. Thank you.