Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.

We'll let $x=7.\overline{6}$ . We want to cut the $0.\overline{6}$ bit off completely, so let's create the scalpel that'll let us do that. If $x=7.\overline{6}$ , then we can also say that $10x=76.\overline{6}$ . Maybe I was lying a bit: the $x$ is our real scalpel here, and $10x$ is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting $x$ off of $10x$ ) leaves us with:

$10x-x=76.\overline{6}-7.\overline{6}\\9x=69$

The operation was a success! We can now simply divide either side by 9 to find $x = 69/9$ , which, when reduced by dividing the numerator and denominator by 3, gives us $x=23/3$

7 0

3 years ago

Volunteers helped clean up 8.2 kg of trash in one neighborhood and 11 1/2 kg in another. They sent 1 1/4 kg to be recycled and t

Ivan

Answer: $18.45\ kg$ or $18\frac{9}{20}\ kg$

Step-by-step explanation:

We can convert from mixed numbers to decimal numbers:

$11\frac{1}{2}\ kg=(11+0.5)\ kg=11.5\ kg\\\\1\frac{1}{4}\ kg=(1+0.25)\ kg=1.25\ kg$

Since they cleaned up 8.2 kilograms of trash in one neighborhood and 11.5 kilograms in another neighborhood, the total trash they cleaned up was:

$Total=8.2\ kg+11.5\ kg\\\\Total=19.7\ kg$

We know that they sent 1.25 kilograms to be recycled. Then, in order to calculate how many kilograms of trash they threw away, we must subtract the total kilograms of trash they cleaned up and the kilograms they sent to be recycled.

Then:

$19.7\ kg-1.25\ kg=18.45\ kg$ or $18\frac{9}{20}\ kg$

8 0

4 years ago

Read 2 more answers

-16 + 5x = -7(-6 + 8x) + 3 solvde for x

Angelina_Jolie [31]

Answer:

X=1

Step-by-step explanation:

3 0

3 years ago