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I want to translate these mathematical equations into common English, but I am having a problem translating when I use the "less than" statement in certain contexts.

Suppose x = 5 and y = 15
The following should be equivalent statements:
y = 3x
3x = y
x = 1/3 y

When I verbally speak about this math problem I could say:

y is more than x
y is 3 times x
y is 10 more than x
y is 3 of x
y is 3 times more than x <-- This feels instinctively right in a mathematical sense but off in a linguistic sense.

x times 3 is y
x is 1/3 of y
x is less than y
x is 10 less than y

But how many times less than is x compared to y?
Which of the following is the correct English representation?

x is 3 times less than y
x is 1/3 times less than y
x is 2/3 times less than y

I feel like each statement has reasons as to why it should be expressed verbally in the following ways but each one just feels wrong.

x is 3 times less than y

Would express 3x = y because x is less than y by three times.

x is 1/3 times less than y

Would express x = 1/3y because x is less than y and y times 1/3 is equal to x.

x is 2/3 times less than y

This could be accurate in the context of comparing proportions because if x = 5 and y = 15 the proportion of their difference is 2/3 (15*(2/3)= 10). Which is y - x = 10. This should be the equivalent of saying x is 10 less than y. This one feels like a stretch.

"X is (fill-in-the-blank) times less than y" has what English and mathematical meaning? Also, when the fill-in-the-blank is a fraction it confuses my mind much more than if it was an integer. Does anyone have an idea as to why that is?

mathewbruens
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1 Answers1

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When spoken, "$x$ is $N$ times less than $y$" means:

$$x = \frac{1}{N}y$$

This is due to the fact that I said "less than". Had I said "greater than", I would write:

$$x = Ny$$

The confusion coming from fractions rather than integers would be because rather than saying "$x$ is 1/2 times less than $y$", one would more commonly say "$x$ is 2 times greater than $y$".

Confusing? Definitely. Unfortunately language is not nearly as elegant as mathematics so translating between the two can often prove quite difficult. Hope this helped!

Crystal
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