# Thread: Hard fraction question (Homework)

1. ## 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)

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

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

See a.

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

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

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

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)

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

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

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

b)

same thing as for a)

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

P.S. you should post work, that you have been trying to do, don't ask to someone do your homework for you ...

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

5. 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

2 and 1/7 ......

you are probably right

sorry

P.S. Edited that one up there ...

6. Its ok.

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

7. Hi

I will attempt to walk you through the second example.

You have the following problem:

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

So you rearrange to get:

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

First lets change into an improper fraction(s):

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

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

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

Which gives a result of:

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

You can now divide top and bottom to give:

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

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