# ACT Math : How to multiply odd numbers

## Example Questions

### Example Question #3 : How To Multiply Odd Numbers

If  and  are both odd integers, which of the following is not necessarily odd?

Explanation:

With many questions like this, it might be easier to plug in numbers rather than dealing with theoretical variables.  However, given that this question asks for the expression that is not always even or odd but only not necessarily odd, the theoretical route might be our only choice.

Therefore, our best approach is to simply analyze each answer choice.

:  Since  is odd,  is also odd, since and odd number multiplied by an odd number yields an odd product.  Since  is also odd, multiplying it by  will again yield an odd product, so this expression is always odd.

:  Since  is odd, multiplying it by 2 will yield an even number.  Subtracting this number from  will also give an odd result, since an odd number minus an even number gives an odd number.  Therefore, this answer is also always odd.

:  Since both numbers are odd, their product will also always be odd.

:  Since  is odd, multiplying it by 2 will give an even number.  Since  is odd, subtracting it from our even number will give an odd number, since an even number minus and odd number is always odd.  Therefore, this answer will always be odd.

:   Since both numbers are odd, there sum will be even.  However, dividing an even number by another even number (2 in our case) does not always produce an even or an odd number.  For example, 5 and 7 are both odd.  Their sum, 12, is even.  Dividing by 2 gives 6, an even number.  However, 5 and 9 are also both odd.  Their sum, 14, is even, but dividing by 2 gives 7, an odd number.  Therefore, this expression isn't necessarily always odd or always even, and is therefore our answer.

### Example Question #4 : How To Multiply Odd Numbers

Theodore has  jelly beans. Portia has three times that amount. Harvey has five times as many as she does. What is the total count of jelly beans in the whole group?

Explanation:

To find the answer to this question, calculate the total jelly beans for each person:

Portia:  * <Theodore's count of jelly beans>, which is  or

Harvey:  * <Portia's count of jelly beans>, which is  or

So, the total is:

(Do not forget that you need those original  for Theodore!)

### Example Question #6 : Even / Odd Numbers

Find the product of  and .

Explanation:

Rewrite the product into the expression , and multiply the ones digit of both numbers.

The ones digit of the final answer is the ones digit from the multiplication of 3 and 7 thus the 1.  The tens digit, 2, will be carried over to the next calculation.

Multiply the tens digit of 13 to 7 and add the carry over.

The value of 9 is the tens digit of the final answer.

Combine the tens digit with the ones digit.  The answer is .

### Example Question #11 : Integers

The product of two numbers is a negative odd integer. Which statement must be true about the numbers?