Three-fourths of a number is 7/8. How do you find the number in lowest terms?

Question

Three-fourths of a number is 7/8.  How do you find the number in lowest terms?

Eva Adamson · Accepted Answer

See the enter solution process below:

First, let's call the number we are looking for #n#/ In this problem the word "of" means to multiply or times. "three fourths of a number is 7/8" can then be rewritten as: #3/4 xx n = 7/8# We can now solve for #n# by multiplying each side of the equation by #color(red)(4)/color(blue)(3)# while keeping the equation balanced: #color(red)(4)/color(blue)(3) xx 3/4 xx n = color(red)(4)/color(blue)(3) xx 7/8# #cancel(color(red)(4))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(4))) xx n = color(red)(4)/color(blue)(3) xx 7/(4 xx 2)# #n = cancel(color(red)(4))/color(blue)(3) xx 7/(color(red)(cancel(color(black)(4))) xx 2)# #n = 7/(3 xx 2)# #n = 7/6#

Isaiah Anthony · Answer

undefined To find the number in lowest terms, you can set up an equation and solve for the unknown number $ x $:

$$ \frac{3}{4}x = \frac{7}{8} $$

To solve for $ x $, multiply both sides of the equation by the reciprocal of $ \frac{3}{4} $, which is $ \frac{4}{3} $:

$$ x = \frac{7}{8} \times \frac{4}{3} = \frac{7 \times 4}{8 \times 3} = \frac{28}{24} $$

Now, simplify the fraction $ \frac{28}{24} $ to lowest terms by dividing both the numerator and denominator by their greatest common divisor, which is 4:

$$ \frac{28}{24} = \frac{7}{6} $$

So, the number in lowest terms is $ \frac{7}{6} $.