How do you solve $\frac{9}{10} = \frac{7}{a}$ $\frac { 9} { 10} = \frac { 7} { a }$ ?

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Answer 1 · 2018-03-05T04:29:49

See a solution process below:

Because both sides of the equation are pure fractions we can "flip" or invert the fractions and not impact the solution:

$\frac{10}{9} = \frac{a}{7}$ $10/9 = a/7$

Now, multiply each side of the equation by $7$ $color(red)(7)$ to solve for $a$ $a$ while keeping the equation balanced:

$7 \times \frac{10}{9} = 7 \times \frac{a}{7}$ $color(red)(7) xx 10/9 = color(red)(7) xx a/7$

$70/9 = cancel(color(red)(7)) xx a/color(red)(cancel(color(black)(7)))$

$70/9 = a$

$a = 70/9$

How do you solve \frac { 9} { 10} = \frac { 7} { a }910=7a\frac { 9} { 10} = \frac { 7} { a }?