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what is a/b equal to..

Schüler

Tags: Mathematik

RASTA aktiv_icon

20:27 Uhr, 23.11.2022

Tag,
need help with this

I started with the original equation and took the reciprocal of both sides to solve for

b

\frac{a}{b} = \frac{3}{5}

\frac{b}{a} = \frac{5}{3}

b = \frac{5 a}{3}

now I have the value of

b,

what can I do now,

Vielen Dank!

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pivot aktiv_icon

21:00 Uhr, 23.11.2022

Hello,

now you can insert

\frac{5 a}{3}

into

\frac{b}{c} = \frac{7}{9}

\frac{\frac{5 a}{3}}{c} = \frac{7}{9}

\frac{5 a}{3 c} = \frac{7}{9}

...

Solve the equation for

\frac{a}{c}

Alternatively you can calculate

\frac{a}{b} \cdot \frac{b}{c}

, with the given values.

greetings,
pivot

RASTA aktiv_icon

21:29 Uhr, 23.11.2022

okay, let me try that, thanks.

\frac{5 a}{3 c} = \frac{7}{9}

now

i

will multiply both sides by

3 c

to clear the a variable on the left side.

3 c (\frac{5 a}{3 c}) = 3 c (\frac{7}{9})

5 a = \frac{7 c}{3}

now

i

will divide both sides by 5 to clear variable

a,

\frac{\frac{5}{a}}{5} = \frac{\frac{7 c}{3}}{5}

a = \frac{7 c}{3} \cdot \frac{1}{5}

a = \frac{7 c}{15}

now that I have the value of a and

b,

what can I do to find the equivalent fraction to a over

b

this is where I am really lost.

pivot aktiv_icon

21:33 Uhr, 23.11.2022

Your transformation is right, but you have gone a little bit too far. Remember that is aksed for the value of

\frac{a}{c}

Dividing your result by

c

you get

\frac{a}{c} = \frac{7}{15}

RASTA aktiv_icon

21:41 Uhr, 23.11.2022

Don't understand well,
do you mean this is the operation that

i

need to do ?.

\frac{a}{b} \cdot \frac{b}{c}

\frac{3}{5} = \frac{\frac{7 c}{15}}{c}

RASTA aktiv_icon

21:44 Uhr, 23.11.2022

or this one?

\frac{3}{5} \cdot \frac{7}{9} = \frac{21}{45}

RASTA aktiv_icon

21:46 Uhr, 23.11.2022

but they are asking what the value of

\frac{a}{c}

is.

pivot aktiv_icon

22:01 Uhr, 23.11.2022

>>Don't understand well, do you mean this is the operation that i need to do ? ...<<

This is one (second) approach. It is a little bit easier than your approach.
Have you notice that b is cancelling out?

>>or this one?<<

That is right. Finally you can cancel the fraction by

3

.

>>but they are asking what the value of a/c is<<
I know.

RASTA aktiv_icon

22:03 Uhr, 23.11.2022

Ohh,

i

see it now,
you mean having the value of a then

i

can substitute

a \in \frac{a}{c}

and just simplifiy it to get

\frac{7}{15}

\frac{a}{c} = 7 \frac{c}{15} / c = \frac{7}{15}

\frac{a}{c} = \frac{7}{15}

is it correct?

thanks

pivot aktiv_icon

22:38 Uhr, 23.11.2022

That's right.

RASTA aktiv_icon

22:46 Uhr, 23.11.2022

Thanks.

walbus aktiv_icon

05:16 Uhr, 24.11.2022

my approach:

\frac{a}{b} = \frac{3}{5}

a = \frac{3}{5} b

\frac{b}{c} = \frac{7}{9}

c = \frac{9}{7} b

\frac{\frac{3}{5} b}{\frac{7}{9} b} = \frac{3}{5} \cdot \frac{9}{7} = \frac{27}{35}

Roman-22

05:36 Uhr, 24.11.2022

There are so many ways to skin a cat and as we seem to start to collect different ways, here are my two cents:

1)

a : b = 3 : 5 = 21 : 35

b : c = 7 : 9 = 35 : 45

(the point is to generate the same number at "equal" positions

\to

least common multiple)
So we see

a : b : c = 21 : 35 : 45

and therefore

a : c = 21 : 45 = 7 : 15

2)

\frac{a}{c} = \frac{a}{b} \cdot \frac{b}{c} = \frac{3}{5} \cdot \frac{7}{9} = \frac{1}{5} \cdot \frac{7}{3} = \frac{7}{15}

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