Grades 7-8 Video Solutions 2021-video 2021 7-8/21

Video Transcription

Question 21. In a particular fraction, the numerator and denominator are both positive. The numerator of this fraction is increased by 40%. By what percentage should the denominator  be decreased so that the new fraction is double the original fraction? Let's start off with a hypothetical fraction. 100 divided by 100. This is equal to 1. Now  we want to find a way to double this. We also know that the numerator is increased by 40%. When we increase 100 by 40%, we get 140. Now since we want it to be doubled from 1 to 2,  we have to figure out how much to decrease the denominator by. To do this, we go down to 70, and then we get the fraction of 2. 140 divided by 70. To get to 70 from 100,  we have to decrease it by C, 30%.

Video Summary

To solve the problem of doubling a fraction, the transcript used a hypothetical example where both the numerator and denominator are initially 100. Increasing the numerator by 40% gives 140. To double the fraction from 1 to 2 with the new numerator of 140, the denominator needs to be decreased to 70. The calculation shows that this requires a decrease of 30% from the original denominator of 100. Therefore, the denominator should be decreased by 30% to achieve the desired outcome.

Keywords

fraction doubling

numerator increase

denominator decrease

percentage calculation

mathematical problem