https://www.gregmat.com/quizzes/quiz/im-overwhelmed-arithmetic-progress-quiz-7 (Question 5)
I’m not clear from the video explainer why .5/7 would be a fraction. The steps that were shown were to multiply each by 2/2, but there wasn’t a proper explanation as to why one would do that
Idk if it helps, but 0.5 can be written as 1/2
So, the fraction can be rewritten as (1/2)/7, which would simplify to 1/14.
I’m not sure why they multiply by 2/2 though.
It is a “manipulation” to turn the 0.5 into an integer.
That is multiply by \frac{\text{2}}{\text{2}} to convert the numerator into an integer.
We could have multiplied by \frac{\text{4}}{\text{4}} for example to get \frac{\text{2}}{\text{28}}
In other words, we could have multiplied the numerator and denominator by any multiple of 2 (it has to be same number though so that we don’t change the original fraction)
Another example, if we had say \frac{\text{0.73}}{\text{3}} we can do \frac{\text{0.73 * 100}}{\text{3 * 100}}
Notice that \frac{\text{2}}{\text{2}}=\frac{\text{4}}{\text{4}}=\frac{\text{100}}{\text{100}}=1 so we are essentially multiplying by “1” and that preserves the original fraction.
@user12334 This is why we did that “manipulation”