WEBVTT

00:00:00.500 --> 00:00:03.868
Welcome to GCSE Edexcel Maths revision.

00:00:04.018 --> 00:00:07.635
Topic M 3: Fractions, decimals and percentages.

00:00:07.785 --> 00:00:09.940
This video covers Higher tier.

00:00:10.090 --> 00:00:14.080
It includes the shared content and the labelled Higher extensions.

00:00:16.733 --> 00:00:22.033
The numerator counts parts; the denominator tells how many equal parts make one whole.

00:00:22.183 --> 00:00:26.998
Equivalent fractions have the same value: 3 over 4 equals 6 over 8 .

00:00:27.148 --> 00:00:32.438
Multiply or divide numerator and denominator by the same non-zero number.

00:00:32.588 --> 00:00:34.508
Three quarters of a whole

00:00:39.167 --> 00:00:45.704
Simplify a fraction by dividing by its H C F to 18 over 24 equals 3 over 4 .

00:00:45.854 --> 00:00:48.051
A denominator cannot be zero.

00:00:50.733 --> 00:01:01.037
An improper fraction has a numerator at least as large as its denominator. 11 over 4 equals 2 and 3 over 4 , because 11 divided by 4 is 2 remainder 3.

00:01:01.187 --> 00:01:05.815
Convert mixed numbers to improper fractions before multiplication or division.

00:01:08.467 --> 00:01:16.441
To convert a fraction to a decimal, divide numerator by denominator. 3 over 8 equals 0.375.

00:01:16.591 --> 00:01:24.058
A percentage is a fraction out of 100, so 0.375 equals 37.5 percent.

00:01:26.733 --> 00:01:29.677
To convert a terminating decimal to a fraction,

00:01:29.827 --> 00:01:41.975
use its place value and simplify: 0.24 equals 24 over 100 equals 6 over 25 . 125 percent equals 1.25 equals 5 over 4 ;

00:01:42.125 --> 00:01:44.951
a percentage can exceed 100 percent.

00:01:47.633 --> 00:01:58.011
For addition and subtraction, use a common denominator: 2 over 3 plus 1 over 4 equals 8 over 12 plus 3 over 12 equals 11 over 12 .

00:01:58.161 --> 00:02:00.166
Do not add denominators.

00:02:02.833 --> 00:02:06.722
For multiplication, multiply numerators and denominators.

00:02:06.872 --> 00:02:14.061
Cancel common factors first if helpful: 3 over 5 multiplied by 10 over 21 equals 2 over 7 .

00:02:16.733 --> 00:02:29.595
For division, multiply by the reciprocal of the divisor: 3 over 4 divided by 2 over 5 equals 3 over 4 multiplied by 5 over 2 equals 15 over 8 equals 1 and 7 over 8 .

00:02:32.267 --> 00:02:41.438
Signs work as in ordinary multiplication: open bracket minus 2 over 3 close bracket multiplied by 3 over 4 equals minus 1 over 2 .

00:02:41.588 --> 00:02:44.977
Put the sign outside the fraction to keep notation clear.

00:02:47.633 --> 00:02:56.795
To find a fraction of an amount, divide by the denominator then multiply by the numerator: 3 over 5 of 80 pounds equals 48 pounds.

00:02:56.945 --> 00:03:00.951
This is the same as multiplying 80 pounds by 3 over 5 .

00:03:03.633 --> 00:03:05.980
To find 15 percent of 60,

00:03:06.130 --> 00:03:10.226
pounds use 0.15 multiplied by 60 equals 9,

00:03:10.376 --> 00:03:18.694
pounds or combine 10 percent open bracket 6 pounds close bracket and 5 percent open bracket 3 pounds close bracket .

00:03:18.844 --> 00:03:21.340
Always keep units attached to the answer.

00:03:24.000 --> 00:03:27.633
In a ratio 2 to 3, there are five parts in total.

00:03:27.783 --> 00:03:31.687
The first share is 2 over 5 of the total, not 2 over 3 .

00:03:31.837 --> 00:03:35.743
The fraction comparing first share to second share is 2 over 3 .

00:03:38.400 --> 00:03:43.114
Keep exact fractions during calculations when an exact answer is requested.

00:03:43.264 --> 00:03:47.829
Rounding 1 over 3 to 0.33 too early loses accuracy.

00:03:50.500 --> 00:03:52.911
A recurring decimal repeats forever.

00:03:53.061 --> 00:04:06.031
Write the repeating block with a bar, for example 0 point repeating digits 2 7 equals 0.272727 and so on; this is different from the terminating decimal 0.27.

00:04:08.700 --> 00:04:15.591
Worked example: Let x equals 0.272727 and so on.

00:04:15.741 --> 00:04:22.845
Then 100 x equals 27.272727 and so on.

00:04:22.995 --> 00:04:30.503
Subtract x to 99 x equals 27, so x equals 27 over 99 equals 3 over 11 .

00:04:33.167 --> 00:04:46.329
Worked example: For x equals 0.16666 and so on, 10 x equals 1.6666 and so on and 100 x equals 16.6666 and so on.

00:04:46.479 --> 00:04:51.034
Subtract to get 90 x equals 15, so x equals 1 over 6 .

00:04:51.184 --> 00:04:53.957
Align the repeating tails before subtracting.

00:04:56.633 --> 00:04:59.747
That completes Fractions, decimals and percentages.

00:04:59.897 --> 00:05:03.242
Revisit the notes and test yourself on the revision website.