﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:01.13,0:00:05.07,Default,,0000,0000,0000,,We have to rewrite the following fractions Dialogue: 0,0:00:05.07,0:00:09.73,Default,,0000,0000,0000,,with fraction with least common denominator Dialogue: 0,0:00:09.73,0:00:16.20,Default,,0000,0000,0000,,So LCD of the 2 fractions is going to be the LCM Dialogue: 0,0:00:16.20,0:00:21.13,Default,,0000,0000,0000,,of both of these denominators over here. Dialogue: 0,0:00:21.13,0:00:25.47,Default,,0000,0000,0000,,and if we can make this as common denominators Dialogue: 0,0:00:25.47,0:00:29.13,Default,,0000,0000,0000,,we can add the two fractions Dialogue: 0,0:00:29.13,0:00:31.80,Default,,0000,0000,0000,,First let us find the LCM, Dialogue: 0,0:00:31.80,0:00:49.20,Default,,0000,0000,0000,,let me write it out LCD of 8 & 6 Dialogue: 0,0:00:49.20,0:00:58.13,Default,,0000,0000,0000,,is going to be the LCM of 8 & 6 Dialogue: 0,0:00:58.13,0:01:00.80,Default,,0000,0000,0000,,and a couple of ways to think about the LCM Dialogue: 0,0:01:00.80,0:01:03.27,Default,,0000,0000,0000,,you could really take the multiples of 8 & 6 Dialogue: 0,0:01:03.27,0:01:08.60,Default,,0000,0000,0000,,and see what their smallest common multiple is. Dialogue: 0,0:01:08.60,0:01:20.87,Default,,0000,0000,0000,,Multiples of 6 - 6,12,18,24,30... i can keep going Dialogue: 0,0:01:20.87,0:01:27.27,Default,,0000,0000,0000,,and the multiples of 8 are 8,16,24,. looks like Dialogue: 0,0:01:27.27,0:01:32.73,Default,,0000,0000,0000,,we are done. I have found a common multiple Dialogue: 0,0:01:32.73,0:01:35.47,Default,,0000,0000,0000,,it is the smallest multiple they have other Dialogue: 0,0:01:35.47,0:01:39.87,Default,,0000,0000,0000,,common multiples like 48,72 and we can go on Dialogue: 0,0:01:39.87,0:01:43.40,Default,,0000,0000,0000,,but this is their smallest common multiple Dialogue: 0,0:01:43.40,0:01:50.93,Default,,0000,0000,0000,,So it is 24. Another way to find the LCM is Dialogue: 0,0:01:50.93,0:01:55.80,Default,,0000,0000,0000,,take the prime factorization of 6 - 2x3 Dialogue: 0,0:01:55.80,0:02:02.60,Default,,0000,0000,0000,,and the LCM of 6 must have one 2 & one 3 Dialogue: 0,0:02:02.60,0:02:13.67,Default,,0000,0000,0000,,what is the prime factorization of 8 is 2x2x2. Dialogue: 0,0:02:13.67,0:02:16.47,Default,,0000,0000,0000,,Inorder to be divisible by 8 we need to have three 2's Dialogue: 0,0:02:16.47,0:02:19.13,Default,,0000,0000,0000,,in the prime factorization. To be divisible by 6 Dialogue: 0,0:02:19.13,0:02:23.80,Default,,0000,0000,0000,,we need to have 2,3 and to be divisible by 8 we need Dialogue: 0,0:02:23.80,0:02:28.87,Default,,0000,0000,0000,,three 2's, we have only one 2 so we add a couple more Dialogue: 0,0:02:28.87,0:02:42.13,Default,,0000,0000,0000,,so thsi is now divisible by 6 & 8 Dialogue: 0,0:02:42.13,0:02:49.73,Default,,0000,0000,0000,,So 2x2x2x3 = 24. So LCM of 8 & 6 Dialogue: 0,0:02:49.73,0:02:54.20,Default,,0000,0000,0000,,which is the LCD also is 24 Dialogue: 0,0:02:54.20,0:02:58.20,Default,,0000,0000,0000,,So we want to write each of this fractions as Dialogue: 0,0:02:58.20,0:03:01.60,Default,,0000,0000,0000,,24 as their denominator. Dialogue: 0,0:03:01.60,0:03:09.73,Default,,0000,0000,0000,,So lets start with 2/8, i want to write that as / 24 Dialogue: 0,0:03:09.73,0:03:13.40,Default,,0000,0000,0000,,so get the denominator as 24, Dialogue: 0,0:03:13.40,0:03:17.53,Default,,0000,0000,0000,,we need to multiply the denominator by 3 Dialogue: 0,0:03:17.53,0:03:19.40,Default,,0000,0000,0000,,inorder not to change the fraction, we need to Dialogue: 0,0:03:19.40,0:03:24.07,Default,,0000,0000,0000,,multiply the numerator also by the same number Dialogue: 0,0:03:24.07,0:03:28.60,Default,,0000,0000,0000,,so we will multiply numerator by 3 ; 2x3=6 Dialogue: 0,0:03:28.60,0:03:33.40,Default,,0000,0000,0000,,so 2/8 = 6/24 Dialogue: 0,0:03:33.40,0:03:43.27,Default,,0000,0000,0000,,2/8 x 3/3 = 6/24 Dialogue: 0,0:03:46.87,0:03:59.80,Default,,0000,0000,0000,,and lets do the same things with 5/6 Dialogue: 0,0:03:59.80,0:04:09.53,Default,,0000,0000,0000,,5/6 = / 24, i will do it in a different colour, blue Dialogue: 0,0:04:09.53,0:04:13.07,Default,,0000,0000,0000,,to get the denominator from 6 to 24, we need Dialogue: 0,0:04:13.07,0:04:17.67,Default,,0000,0000,0000,,to multiply by 4, so we need to multiply Dialogue: 0,0:04:17.67,0:04:24.80,Default,,0000,0000,0000,,numerator also by 4 so 5x4 = 20 Dialogue: 0,0:04:24.80,0:04:28.13,Default,,0000,0000,0000,,5/6 = 20/24 Dialogue: 0,0:04:28.13,0:04:33.40,Default,,0000,0000,0000,,so we have written both the fractions with common denominator Dialogue: 0,0:04:33.40,9:59:59.99,Default,,0000,0000,0000,,So we are done