Is there a difference between 'subtract' and 'subtract by'?

Question

A basic terminology question for a foreign speaker.

Please correct me if wrong. (Let's ignore the commutative property of + and * here)

5 add by 10 is 5 + 10
5 add 10 is 10 + 5
5 subtract by 10 is 5 - 10
5 subtract 10 is 10 - 5 
5 multiply by 10 is 5 * 10
5 multiply 10 is 10 * 5
5 times 10 is 5 * 10
5 divide by 10 is 5 / 10
5 divide 10 is 10 / 5

Also, do we only say 'plus' and 'minus', never 'plus by' or 'minus by'?

Answer 1

We don't say "subtract by" or "add by". 'by' is used with the verbs multiply and divide in sentences like:

• Divide 6 by 3 -> 6/3
• 6 divided by 3 -> 6/3
• multiply 5 by 4 -> 5*4
• 5 multiplied by 4 -> 5*4

On the other hand, we can use 'to' and 'from' with the verbs add and subtract:

• Subtract 5 from 10 -> 10-5
• Add 5 to 10 -> 10+5

The above ways of giving the expressions are verb-based. We can also use other words to make them 'operator-based', where there is no verb, but an English word to replace the operator:

• 6 divided by 3 -> 6/3
• 5 times 4 -> 5*4
• 10 minus 5, or 10 take away 5 -> 10-5
• 10 plus 5 -> 10+5

Answer 2

This should probably be moved to math.SE, since I don't see anything here about teaching. But almost every line you wrote is incorrect English.

"Add by" is gramatically incorrect. It should be "plus."

"5 add 10" should be "5 plus 10" (or "5 and 10").

subtract by -> minus

5 subtract 10 -> 5 subtracted from 10 (if you want it to mean 10-5)

5 multiply by 10 -> 5 multiplied by 10

5 divide by 10 -> 5 divided by 10

5 divide 10 is incorrect English.