Pythagoras Maths Questions

1. Is This Always True?

Please provide 2-3 mathematical examples to prove or disprove these statements.

1. Patti says that if you add the same negative integer five times, the sign of the sum is negative and its size is five times the size of the original integer.

For example:

–7 + (–7) + (–7) + (–7) + (–7)

= –(5 × 7) [7 is the size of –7]

= –35

Is Patti’s statement true for all negative integers?

2. Dina says that if you add a negative integer to a positive integer, the sum is zero or less.  

Is Dina’s statement true for all integers?

3. Suman says that if you subtract any two negative integers, the difference is always negative.

Is Suman’s statement true for all integers?

4. Lisa says that if you add two opposite integers, the sum is zero.

Is Lisa’s statement true for all integers?

5. Christopher says that if the mean (average) of a data set of integers is a negative integer, then there must be more negative integers than positive integers in the data set.

Is Christopher’s statement always true?

2. Is This Always True?

Name:

Date:

1. Bert says that to subtract one integer from another, simply add to the first number the opposite of the one you are subtracting.

For example:

9 – 5

= 9 + (–5)

= 4

Is Bert’s statement true for all integers?

2. Emmanuelle says that if you divide two negative integers, the quotient is a positive integer.  Is

Emmanuelle’s statement true for all negative integers?

3. Sandra says that any negative rational number, say negative one-half, can be represented in 3 equal ways:

Is Sandra’s statement always true?