Question

need this explained please help will give medal
the area of this rectangle is 1/4 ft^2 find the width explain how you found your answer

Answer 1

Remember how to find area of a rectangle?

Answer 2

here is the picture

Answer 3

Area of a rectangle
\[\Large\bf\sf A=l\cdot w\]

Answer 4

Plugging in what they told us,
Area = 1/4.
length = 3/4\[\Large\bf\sf \frac{1}{4}=\frac{3}{4}w\]

Answer 5

Do you know how to solve for w, the width?

Answer 6

this is my little brother and sister work my mom just needs it explained

Answer 7

and isn't the 1/4 squared

Answer 8

We have a 3/4 multiplying the w.
To solve for w, we multiply both sides by the reciprocal of that factor.
So we'll multiply each side by 4/3.

The `units`, feet, are being squared.
But no the actual value is not being squared.

Answer 9

\[\Large\bf\sf \color{royalblue}{\frac{4}{3}}\cdot\frac{1}{4}=\frac{3}{4}w\cdot \color{royalblue}{\frac{4}{3}}\]

Answer 10

On the right side, since they're reciprocals, they'll "cancel out".

If that's too confusing, you can multiply out the numbers and then simplify them afterwards. When we multiply fractions, we simply multiply top and top, and bottom with bottom,\[\Large\bf\sf \frac{4\cdot 1}{3\cdot 4}\quad=\quad \frac{3\cdot4}{4\cdot 3}w\]Giving us,\[\Large\bf\sf \frac{4}{12}=\frac{12}{12}w\]12/12 can be simplifed to 1.
1w is the same as w, we won't write the 1.
4/12 simplifies as well,\[\Large\bf\sf \frac{4}{12}=w\]to,\[\Large\bf\sf \frac{1}{3}=w\]

Answer 11

Any of that way too confusing?
I know the reciprocal thing is a little weird, there is another approach we can do if that's too complicated.

Answer 12

it a little confusing

Answer 13

Mmm let's try it this way instead.
\[\Large\bf\sf \frac{1}{4}=\frac{3}{4}w\]See how there is a 4 in the denominator of each side?
Let's multiply each side by 4,\[\Large\bf\sf 4\cdot\frac{1}{4}=4\cdot \frac{3}{4}w\] You can think of the 4's in the denominator as division.
So we're both dividing by 4 and multiplying by 4 on each side.
Those 4's will "cancel out".\[\Large\bf\sf \cancel4\cdot\frac{1}{\cancel4}=\cancel4\cdot \frac{3}{\cancel4}w\]giving us,\[\Large\bf\sf 1=3w\]Hmm that step is a little weird isn't it? :( I can't think of the right way to explain it..

Answer 14

Then our next step would be to divide by 3 (since 3 is multiplying our w).\[\Large\bf\sf \frac{1}{3}=\frac{\cancel3w}{\cancel3}\]

Answer 15

\[\Large\bf\sf \frac{1}{3}=w\]

Answer 16

Our units that we end up with will be `ft`.

Area is length (in feet), times width (in feet).
We multiply the length and width, but we also multiply the units, feet times feet.
That's what gives us our units of ft^2 for area.

Answer 17

\[\Large\bf\sf w=\frac{1}{3}ft\]

Answer 18

@zepdrix
This is mom. In the first example how did you get 12/12

Answer 19

Hi mom c:
Using the first method?\[\Large\bf\sf \frac{3}{4}w\cdot\frac{4}{3}\]This is just a bunch of multiplication.
Multiplication is `commutative` meaning ~ we can multiply in any order that we want.
So we'll choose to multiply the fractions together first.\[\Large\bf\sf\frac{3}{4}\cdot\frac{4}{3}w\]When we multiply fractions, we simply do `top times top` and `bottom times bottom`.\[\Large\bf\sf \frac{3\cdot4}{4\cdot3}w\]Which gives us,\[\Large\bf\sf\frac{12}{12}w\]

Answer 20

Thank you!