factorise each of the following 27 - 125 a^3 -1 35 a + 225 a^2
Answers
Answer:
Okay, so first off we are referring to this is a proportion, but it can also be considered a ratio. The question we are really asking here is whether 27/35 equals 23/3 in a different proportion. Let's look at it visually and use letters to explain how proportions work:
A
B
=
C
D
Now these look like fractions and we could call the top number of each a numerator and the bottom number of each the denominator but, when working with proportions we need to refer to them differently.The numbers in the A and D positions are called the "extremes" and the numbers in the B and C position are called the "means".
So how do we know if 27/35 and 23/3 are proportional to each other? The core defining property of any proportion is that the product of the means is equal to the product of the extremes.
What does that mean? Well in simple terms it means A multiplied by D must equal B multiplied by C. You could also consider these ratios to be fractions and then simplify them down to their lowest terms and compare them. If they are equal, then they are proportional.