WEBVTT
00:00:00.560 --> 00:00:06.510
A mirror’s length is two-thirds of a foot, and its width is three-eighths of a foot less than its length.
00:00:06.960 --> 00:00:09.700
Determine the width of the mirror in fraction form.
00:00:10.380 --> 00:00:13.720
So here, we have our mirror with the length and the width labelled.
00:00:14.200 --> 00:00:17.400
We’re told the length is two-thirds of a foot.
00:00:18.040 --> 00:00:23.140
So this entire question references a foot, so let’s go ahead and let 𝑥 represent a foot.
00:00:24.350 --> 00:00:35.230
So if the length is two-thirds of a foot, the length would be equal to two-thirds times 𝑥 because the word of, in mathematical word problems, means to multiply.
00:00:35.480 --> 00:00:37.600
So the length is two-thirds 𝑥.
00:00:38.330 --> 00:00:42.250
Now the width is three-eighths of a foot less than its length.
00:00:42.990 --> 00:00:47.130
So if it’s less than its length, we need to subtract away from the length.
00:00:47.580 --> 00:00:52.440
So 𝑊 equals the length minus three-eighths of a foot.
00:00:53.020 --> 00:00:56.700
And it asks us to determine the width of the mirror in fraction form.
00:00:57.070 --> 00:00:58.850
So this is our equation for the width.
00:00:59.090 --> 00:01:06.260
Now we can replace 𝐿 with two-thirds 𝑥, and now it’s all in terms of 𝑥, which is a foot.
00:01:07.000 --> 00:01:08.850
So now we need to combine like terms.
00:01:09.370 --> 00:01:11.910
So the fraction part can make it seem a little tricky.
00:01:12.290 --> 00:01:20.080
If we were to subtract five 𝑥 and three 𝑥, we would take five minus three to get two, and then we bring down our 𝑥.
00:01:20.530 --> 00:01:26.520
So we need to do the exact same thing with the fractions; we need to subtract the fractions and then bring down the 𝑥.
00:01:26.930 --> 00:01:35.480
So to subtract our fractions, we need a common denominator, the smallest number that three and eight both go into, which will be 24.
00:01:35.770 --> 00:01:42.670
So now that we have our denominator, we have to change our numerators because we can’t just change the denominators without changing the numerator.
00:01:43.370 --> 00:01:46.320
So how do we get from three to 24?
00:01:46.450 --> 00:01:47.570
We multiply it by eight.
00:01:47.630 --> 00:01:49.690
So we need to do the same thing to the numerator.
00:01:49.880 --> 00:01:51.540
And two times eight is 16.
00:01:52.100 --> 00:01:55.420
Now to get from eight to 24, we multiply it by three.
00:01:55.510 --> 00:01:58.290
So on the numerator, three times three is nine.
00:01:58.790 --> 00:02:02.940
So now we keep our common denominator and subtract the numerators.
00:02:03.030 --> 00:02:07.510
So 16 minus nine is seven, and then we bring down our 𝑥.
00:02:08.270 --> 00:02:11.940
So it says determine the width of the mirror in fraction form, which we’ve done.
00:02:12.470 --> 00:02:24.460
Now the only thing we should do is — we introduced 𝑥, we let 𝑥 represent a foot, so the question uses the words “of a foot” — so let’s replace 𝑥 with “of a foot”.
00:02:24.850 --> 00:02:28.070
So our final answer would be: seven twenty-fourths of a foot.