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

[bobisaka]

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]

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 $$\frac37\cdot r$$ or parentheses. Nevertheless, this does not change the rule: a sequence of multiplications and divisions is evaluated left-to-right.

 

[HallsofIvy]

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 \frac{3}{7}\frac{14}{1}= \frac{42}{7}= 6 or \frac{3}{7}14= 3\frac{14}{7}= 3(2)= 6. And with s= 8, 5/8 times 8 is \frac{5}{8}8= 5\frac{8}{8}. The result is 6+ 5= 11.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> The way i solve it leads me to: 3/98 + 5/8<br /> (using this process 3/7 * 14/1 = 3/7 * 1/14 = 3/98 ) </div> </div> </blockquote> That is peculiar! I had thought you were interpreting &quot;3/7 r&quot; as &quot;3/7r&quot; where there is no space and so means \frac{3}{7r} (which is why writing fractions &quot;in line&quot; as &quot;3/7&quot; rather that &quot;\frac{3}{7}&quot; tends to be ambiguous). But why in the world would you think that &quot;<div style="text-align: left"><span style="font-family: 'Verdana'">3/7 * 14/1 = 3/7 * 1/14&quot;? <b>Multiplying</b> by a/b is NOT <b>multiplying</b> by b/a because a/b and b/a are not the same thing. Perhaps you are remembering a garbled form of &quot;to <b>divide</b> by a fraction invert and <b>multiply</b>. That is \frac{a}{b}\div \frac{c}{d}= \frac{a}{g}\cdot\frac{d}{c}. But that is changing from <b>division</b> to <b>multiplication</b>.</span>&#8203;</div><span style="font-family: 'Verdana'"><br /> However the correct solution is: 3/7(14) + 5/8(8)[/QUOTE]</span>

 

[bobisaka]

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.