How do you simplify #(17 * 4 + 17 *9 + 17 *7)/(2+34 + 5*34 + 3*34)# ?

Question

Avery Alexander · Accepted Answer

#color(brown)(=> 12/11 = 1(1/11)#

#(17*4 + 17*9 + 17*7) / (2 + 34 + 5 * 34 + 3 * 34)#

#=>(64 + 153 + 119) / (2 + 34 + 170 + 102), color(brown)("Multiplication"#

#=> (336 / 308), color(brown)("Addition"#

#=> cancel(336)^color(red)(84) / cancel(308)^color(red)(77)#

#=>cancel(84)^color(green)(12) / cancel(77)^(color(green)(11)#

#color(brown)(=> 12/11 = 1(1/11)#

Jace Anderson · Answer

undefined To simplify the expression $ \frac{17 \times 4 + 17 \times 9 + 17 \times 7}{2 + 34 + 5 \times 34 + 3 \times 34} $, first, compute the numerator and denominator separately:

Numerator:
$$ 17 \times 4 + 17 \times 9 + 17 \times 7 = 68 + 153 + 119 = 340 $$

Denominator:
$$ 2 + 34 + 5 \times 34 + 3 \times 34 = 2 + 34 + 170 + 102 = 308 $$

Now, substitute the simplified values into the fraction:

$$ \frac{340}{308} $$

This fraction can be further simplified by finding the greatest common divisor (GCD) of the numerator and denominator, which is $ 4 $:

$$ \frac{340 \div 4}{308 \div 4} = \frac{85}{77} $$

Therefore, the simplified expression is $ \frac{85}{77} $.