what is the answer to 1/4[7(7-1/4)]

Question

need help on this question really bad

Answer 1

Hi Deez!

So to attack this problem, we need to remember PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction, in order left to right!) Which is a way to remember which part of the problem we solve first!

So! Let's go through PEMDAS with 1/4[7(7-1/4)]

Step one: Are there any parentheses? YES! In fact, there are two sets. When there are two sets of parentheses, you want to start with the inside set. Or, you can think of it as what, starting from the inside is in between the first LEFT ( and RIGHT ) parentheses.

So for us, (7-1/4). THIS IS WHERE HOW IT IS WRITTEN IS REALLY IMPORTANT!!!! If it is written as (7-1/4) we will first DIVIDE because that comes first in PEMDAS. Then, we need to do 7 - 1/4. To subtract, these need to have equivalent (meaning the same, denominators) so we multiply 7* (4/4). We can do this because 4/4=1 so we aren't changing the value. SO now we have 28/4 - 1/4 = giving us 27/4

So now, we can replace the first parentheses with 27/4 Now, we go to the next parentheses.

1/4[7(27/4)] (where 27/4 is what we got from the step above.) Because this is MULTIPLICATION, we do not need the same denominators. So we can simply multiply 27*7, then divide by 4 (we only have to worry about one denominator because 7= 7/1). Giving us 189/4 to replace EVERYTHING in the parentheses.

So now, all we have is 1/4 * 189/4.... which gives us 189 / 16 as your final answer

Answer 2

We start with the innermost parenthesis first.

1/4*[7*(7-1/4)]

=1/4*[7*(28/4-1/4)] since 28/4=7

=1/4*[7*((28-1)/4)] by combining two fractions

=1/4*[7*27/4]

=1/4*[(7*27)/4] since this is how you multiply a fraction by an integer

=1/4*189/4

=(1*189)/(4*4) since when multiplying two fractions, you need to multiply the numerators together and use the result as the new numerator, and multiply the denominators together as use the result as the new denominator.

=189/16