ACT Math : Integers

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Multiply Odd Numbers

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

Possible Answers:

Correct answer:

Explanation:

For the product of two numbers to be even, one number must be even. For the product of two numbers to be odd, both numbers must be odd.

Remember:

Example Question #1 : How To Subtract Even Numbers

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

First solve by evaluating the ones digit.  Carry over a 1 from the  so that the value of the ones digit can be evaluated.

After the carry over, the  becomes a .  This value will be used for the tens digit of the next term.  The hundreds digit will become zero.

Evaluate the tens digit.

Combine the tens digit and the ones digit.

The final answer is .

Example Question #1 : How To Subtract Even Numbers

Solve:

Possible Answers:

Correct answer:

Explanation:

1. First subtract the ones digits:

So the ones digit will be a 0.

2. Next subtract the tens digit borrowing the 1 from the hundreds digit:

So the tens digit will be a 6.

3. Add the tens and ones digits together:

Example Question #2 : How To Subtract Even Numbers

Solve:

Possible Answers:

Correct answer:

Explanation:

1. First subtract the ones digits borrowing a 1 from the tens digit:

So the ones digit will be a 6.

2. Next subtract the tens digit borrowing the 1 from the hundreds digit:

So the tens digit will be a 8.

3. Next add the hundreds, tens and ones digits together:

Example Question #1 : How To Add Even Numbers

Which of the following expressions is odd for any integers  and ?

Possible Answers:

All the expressions can be even for some combination of  and 

Correct answer:

Explanation:

The key here is for any integers  and , that means that no matter what you set  and  equal to you will get an odd number. An odd number is not divisible by 2, also it is an even number plus and odd number. The only expression that satisfies this is  will always be even, so will , but  is always odd so the combination gives us an odd number, always.

Example Question #2 : How To Add Even Numbers

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

For this problem, align and solve by adding the ones digit , tens digit , and hundreds digit . This also means that you have to add  to the  in the thousands place to get 

Example Question #3 : How To Add Even Numbers

Find the sum of 12 and 42.

Possible Answers:

Correct answer:

Explanation:

Rewrite the question into a mathematical expression.

Add the ones digit. 

Add the tens digit.

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

Example Question #11 : Integers

Solve:  

Possible Answers:

Correct answer:

Explanation:

This problem can be solved using common factors.  

Rewrite  using factors.  

Example Question #12 : Integers

Divide: 

Possible Answers:

Correct answer:

Explanation:

Rewrite   by using common factors. Reduce to the simplest form.

Example Question #13 : Integers

Divide:  

Possible Answers:

Correct answer:

Explanation:

Rewrite  and use common factors to simplify.

 

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