Multiply mixed fractions

B

bobisaka

Junior Member
Joined
Dec 25, 2019
Messages
115
Hi all,


1578774759593.png


For this particular question I do in two ways (i did it both ways cause the answers are not correct and i am getting confused):
If i flip over to its reciprocal i get the answer 48/7
If i multiply it without flipping over the 2nd fraction I get the answer 27/25
However in the textbook the answer is -16/3
How do i come to this answer?

Now, i have done all the questions in the 'multiply and divide mixed numbers and complex fractions', and solved them all correctly or at least understand it if I have made mistakes.


However when it comes to the end practice questions, I am getting different answers to the solutions given. What am i doing wrong?
 
bobisaka said:
… What am i doing wrong?
Click to expand...

Hello bobisaka. We can't tell what a student may have done wrong, when they don't show their work. (Please see the forum guidelines.)

We don't use a reciprocal when multiplying two fractions.

Written as improper fractions, (2+2/5) is 12/5 and -(2+2/9) is -20/9.

So we're multiplying 12/5 times -20/9.

Is that what you tried?

?
 
I would first write each mixed number as an improper fraction:
[MATH]\frac{\frac{12}{5}\cdot -\frac{20}{9}}{\frac{-16}{3}} = \frac{12}{5}\cdot \frac{20}{9} \cdot \frac {3}{16}[/MATH]and start cancelling factors. I think you will get a different answer.

Edit: Seeing Otis's post I see I apparently misinterpreted the posted problem as a big fraction.
 
bobisaka said:
Hi all,


View attachment 16000


For this particular question I do in two ways (i did it both ways cause the answers are not correct and i am getting confused):
If i flip over to its reciprocal i get the answer 48/7
If i multiply it without flipping over the 2nd fraction I get the answer 27/25
However in the textbook the answer is -16/3
How do i come to this answer?

Now, i have done all the questions in the 'multiply and divide mixed numbers and complex fractions', and solved them all correctly or at least understand it if I have made mistakes.

However when it comes to the end practice questions, I am getting different answers to the solutions given. What am i doing wrong?
Click to expand...
Please show us step-by-step - how you derived the answers. First thing to do would be to convert all the "mixed fractions" to ordinary improper fraction.
\(\displaystyle \dfrac{2\frac{2}{5} \ * \ \left(-2\frac{2}{9}\right )}{-\frac{16}{3}}\)

= \(\displaystyle \dfrac{\frac{12}{5} \ * \ \left(-\frac{20}{9}\right )}{-\frac{16}{3}}\)

continue.....
 
Thanks for the quick reply Otis, i believe i solved it.

Okay I made a mistake on the 3rd step, instead of -240/45, i put 35 for the denominator which is incorrect.

These questions take so much attention to detail, that i miss it alot of the time.. but it is refreshing to see!

edit:Thanks for all the help guys, I am going to continue on with the rest of the questions. If i have any more related problems, i will post it on this thread.
 
I think the problem is being misread. It simply is

[MATH]2\frac{2}{5} * \left (-\ 2\frac{2}{9} \right ).[/MATH]
The correct answer is indeed [MATH]-\ \dfrac{16}{3}.[/MATH]
What the OP is doing is a mystery.

EDIT: Mystery explained.
 
JeffM said:
I think the problem is being misread. It simply is

[MATH]2\frac{2}{5} * \left (-\ 2\frac{2}{9} \right ).[/MATH]
The correct answer is indeed [MATH]-\ \dfrac{16}{3}.[/MATH]
What the OP is doing is a mystery.

EDIT: Mystery explained.
Click to expand...
I think you are correct in your interpretation. Of course, it would have been clear if we were shown the steps in OP......
 
bobisaka said:
… I made a mistake on [my] 3rd step, instead of -240/45, i put 35 for the denominator …
Click to expand...
Hi. I'm glad you were able to locate your mistake. In post #3, professor Kurtz suggested cancelling common factors, before multiplying fractions. Doing that produces smaller numbers to multiply and makes reducing an answer to lowest terms easier (or unnecessary). Here's how it looks.

\(\displaystyle \displaystyle \dfrac{12}{5} × \dfrac{-20}{9} \;\; = \;\; \dfrac{\cancel{12}^{4}}{\cancel{5}_{1}} × \dfrac{\cancel{-20}^{-4}}{\cancel{9}_{3}} \;\; = \;\; -\dfrac{4×4}{1×3} \; = \; -\dfrac{16}{3}\)

Let us know, if you need help understanding those cancellations.

… These questions take so much attention to detail, that i miss it alot of the time …
Click to expand...
All math problems require some attention. If you find yourself making a lot of simple mistakes, try double-checking what you write down after each step. (That helps me catch errors, and it saves time.)

Everything gets better with practice, so do as many extra problems as you can. You'll see things improve. Cheers.

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