# Hard fraction question (Homework)

• Sep 13th 2010, 11:52 PM
Kick
Hard fraction question (Homework)
a) What must 2 1/7 be divided by to give 1 3/7 ?
b) What must 3 4/5 be multiplied by to give 10 2/5?

It's a pre-algebra, no calculator allowed question.

Do i have to just keep guessing and substituting guesses until i get the answers? Or are there exact formulas for solving these problems? (You cant use an algebra formula because its from a pre-algebra book and algebra has not even been covered yet)
• Sep 14th 2010, 12:21 AM
MathoMan
a) What must 2 1/7 be divided by to give 1 3/7 ?
$\displaystyle 2\frac{1}{7}=\frac{15}{7}$ and $\displaystyle 1\frac{3}{7}=\frac{10}{7}$. Since $\displaystyle \frac{15}{7}\cdot \frac{2}{3}=\frac{10}{7}$ and $\displaystyle \frac{15}{7}\cdot \frac{2}{3} =\frac{15}{7}:\frac{3}{2}$ the answer is $\displaystyle \frac{3}{2}.$

b) What must 3 4/5 be multiplied by to give 10 2/5?

See a.
• Sep 14th 2010, 12:43 AM
yeKciM
Quote:

Originally Posted by MathoMan
a) What must 2 1/7 be divided by to give 1 3/7 ?
$\displaystyle 2\frac{1}{7}=\frac{15}{7}$ and $\displaystyle 1\frac{3}{7}=\frac{10}{7}$. Since $\displaystyle \frac{15}{7}\cdot \frac{2}{3}=\frac{10}{7}$ and $\displaystyle \frac{15}{7}\cdot \frac{2}{3} =\frac{15}{7}:\frac{3}{2}$ the answer is $\displaystyle \frac{3}{2}.$

b) What must 3 4/5 be multiplied by to give 10 2/5?

See a.

$\displaystyle \displaystyle 2\cdot \frac {1}{7} \neq \frac {15}{7}$
$\displaystyle \displaystyle 2+ \frac {1}{7} = \frac {15}{7}$
$\displaystyle \displaystyle 2\cdot \frac {1}{7} = \frac {2}{7}$

Quote:

Originally Posted by Kick
a) What must 2 1/7 be divided by to give 1 3/7 ?
b) What must 3 4/5 be multiplied by to give 10 2/5?

It's a pre-algebra, no calculator allowed question.

Do i have to just keep guessing and substituting guesses until i get the answers? Or are there exact formulas for solving these problems? (You cant use an algebra formula because its from a pre-algebra book and algebra has not even been covered yet)

as far as the problem goes ... (because you didn't wrote 2+1/7 ... you wrote 2 1/7 same as 2/7 )

a)

$\displaystyle \displaystyle \frac {\frac {2}{7}}{x} = \frac {3}{7} \Rightarrow \frac {2}{7x} = \frac {3}{7} ... . . . . . . . . . . \Rightarrow x= \frac {2}{3}$

(if it's 2 and 1/7 .... and 1 and 3/7 than.... )

$\displaystyle \displaystyle \frac {\frac {15}{7}}{x} = \frac {10}{7} \Rightarrow \frac {15}{7x} = \frac {10}{7} . . . . . . . . . . . . . . . \Rightarrow x =\frac {3}{2}$

b)

same thing as for a)

but if you mean 2 + 1/7 than just enter different values (instead of $\displaystyle \frac {2}{7}$ is $\displaystyle \frac {15}{7}$ )... but procedure is the same :D

P.S. you should post work, that you have been trying to do, don't ask to someone do your homework for you ...
• Sep 14th 2010, 12:54 AM
MathoMan
Quote:

Originally Posted by yeKciM
$\displaystyle \displaystyle 2\cdot \frac {1}{7} \neq \frac {15}{7}$
$\displaystyle \displaystyle 2+ \frac {1}{7} = \frac {15}{7}$
$\displaystyle \displaystyle 2\cdot \frac {1}{7} = \frac {2}{7}$....

When one writes 2 1/7 it is more common to accept it as a mixed number 'cause multiplication is usually denoted with an *. But who knows, maybe you're right.
• Sep 14th 2010, 12:57 AM
yeKciM
Quote:

Originally Posted by MathoMan
When one writes 2 1/7 it is more common to accept it as a mixed number 'cause multiplication is usually denoted with an *. But who knows, maybe you're right.

aaahhhh lol :D:D:D:D

2 and 1/7 ......

you are probably right :D

sorry :D

P.S. Edited that one up there ... :D
• Sep 14th 2010, 01:05 AM
MathoMan
Its ok. (Nod)

I know how hard it can be to spot a tree in a forest, eh?! Happens to me all the time and then I go (Angry)
• Sep 14th 2010, 04:34 AM
RHandford
Hi

I will attempt to walk you through the second example.

You have the following problem:

$\displaystyle 3\tfrac{4}{5} \cdot x= 10\tfrac{2}{5}$

So you rearrange to get:

$\displaystyle x= \frac{10\tfrac{2}{5}}{3\tfrac{4}{5}}$

First lets change into an improper fraction(s):

$\displaystyle x= \frac{\tfrac{52}{5}}{\tfrac{19}{5}}$

To divide a fraction you turn one side upside down and multiply, which gives:

$\displaystyle x= \frac{52}{5}\cdot \frac{5}{19}$

Which gives a result of:

$\displaystyle x= \frac{260}{95}$

You can now divide top and bottom to give:

$\displaystyle x= \frac{260}{95} \equiv \frac{52}{19} \equiv 2\tfrac{14}{19}$

$\displaystyle 3\tfrac{4}{5} \cdot 2\tfrac{14}{10} = 10\tfrac{2}{5}$