WEBVTT
00:00:01.600 --> 00:00:08.780
Expand four-sevenths multiplied by three-quarters plus eight-ninths of 𝑥.
00:00:10.070 --> 00:00:19.460
In order to expand any bracket or parenthesis, we need to multiply the term outside of the bracket by each of the terms inside the bracket.
00:00:20.860 --> 00:00:28.960
In this case, we need to multiply four-sevenths by three-quarters and four-sevenths by eight-ninths of 𝑥.
00:00:30.250 --> 00:00:39.910
The easiest way to multiply two fractions is to multiply the two numerators — in this case, four and three — and the two denominators — seven and four.
00:00:41.500 --> 00:00:49.670
Four multiplied by three is equal to 12 and seven multiplied by four is equal to 28.
00:00:51.130 --> 00:00:57.070
This means that four-sevenths multiplied by three-quarters is equal to 12 28ths.
00:00:58.690 --> 00:01:04.380
This answer can be simplified by dividing the numerator and denominator by four.
00:01:04.830 --> 00:01:09.090
Remember whatever you do to the top, you must do to the bottom of a fraction.
00:01:10.300 --> 00:01:16.390
12 divided by four is equal to three and 28 divided by four is equal to seven.
00:01:16.740 --> 00:01:20.080
Therefore, our simplified fraction is three-sevenths.
00:01:21.430 --> 00:01:26.690
An alternative way of multiplying the two fractions would be to at first cancelled.
00:01:27.630 --> 00:01:33.350
In this case, we could have divided the four on the numerator and the four on the denominator by four.
00:01:34.080 --> 00:01:36.400
Four divided by four is equal to one.
00:01:36.810 --> 00:01:42.200
This leaves us with one-seventh multiplied by three over one or three.
00:01:43.370 --> 00:01:47.360
One-seventh multiplied by three is equal to three-sevenths.
00:01:48.490 --> 00:01:55.030
Either way by multiplying four-sevenths by three-quarters, we get an answer of three-sevenths.
00:01:56.260 --> 00:02:02.430
The second part of our expansion involves multiplying four-sevenths by eight-ninths of 𝑥.
00:02:03.410 --> 00:02:11.260
Once again, we can multiply the two fractions by multiplying the numerators and then separately multiplying the denominators.
00:02:12.330 --> 00:02:20.350
Four multiplied by eight is equal to 32 and seven multiplied by nine is equal to 63.
00:02:21.510 --> 00:02:34.540
This means that four-sevenths multiplied by eight-ninths of 𝑥 is equal to 32 over 63𝑥 or 32 63rds of 𝑥.
00:02:35.930 --> 00:02:47.540
The expansion of four-sevenths multiplied by three-quarters plus eight-ninths 𝑥 is three-sevenths plus 32 63rds 𝑥.