Integers - ACT Math

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 .

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 .

If the cost of the bag is $22.50 and the bag holds 24 oz, each ounce is worth 94 cents. If Stella sold 4 drinks with 2 oz of ice each, she has used 8 oz of ice. 8 oz of ice at 94 cents an ounce is valued at $7.52. If you subtract that from the total value of the bag of ice, that leaves $14.98 worth of ice.

If you answered $18.74, you only valued the ice in each drink at one ounce.

If you answered $7.52, you found the value of ice in the drinks but not the value of the remainder of the bag.

If you answerd $3.76, you found the value of ice in the drinks if each drink only contained 1 ounce of ice.

If you answered $16.86, you just forgot to subtract the cost of ice for all four drinks but rather only subtracted the cost of ice for three drinks.

This question is testing the order of operations. For the equation , you must do the division problem first, then addition. .

To answer this question, we must substitute our given values into an equation and solve, remembering our order of operations.

First, we must take our values for each variable and substitute them into the equation given. Therefore, since we are told that , , and ,

Now that we have our values plugged in, we need to remember the order of operations in order to solve this problem. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally addition and subtraction. The first order of operations is to carry out any operations that are within parenthesis. Therefore, for this data:

We can now simply multiply these numbers together.

Our answer is .

To answer this question, we must calculate the average of Steven's five games. After this, to maintain his average, he needs to score the same in his sixth game as his average.

To calculate the average of a set of numbers, you add all the values together (or get the sum) and divide by the total number of values. So, for this data:

We can then solve this fraction to get our average:

Steven's average over the first five games is a score of . In order to maintain his average, he must match his average in game six. So, our answer is a score of in game six.

To answer this question, we must substitute our value of into our equation for and follow our order of operations rules to solve for .

we first must substitute our known value into the equation. For this data:

We must now follow our order of operations to determine what we should do next. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally, addition and subtraction. So, for this equation, we must square the because solving for exponents comes before solving multiplication.

Note that when you square a number, you are multiplying it by itself. When we multiply two negative numbers, their product is positive.

We then multiply our two integers together and solve for :

Therefore, the answer to our question is .

To solve this question, we need to understand how absolute value works within an equation.

When numbers are within an absolute value sign (the numbers will be surrounded by ), we need to use absolute value, or how far the number inside is away from zero. We must do any operations within the absolute value sign first. Therefore, the answer inside will always be positive, despite its sign, because you can't have negative distance from zero. So, for this data:

We can then just multiply our two integers in order to get our answer:

Therefore, our answer is .

Adding to is the same as subtracting from . .

Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.

Starting at and adding is the same as subtracting . .

Starting at and adding is the same as subtracting . .

Add the ones digits:

Since there is no tens digit to carry over, proceed to add the tens digits:

The answer is .

If there are students taking Greek, then there are or students taking Latin. However, the question asks how many total students there are in the school, so you must add these two values together to get:

or total students.

Rewrite the question in a mathematical expression.

Add the ones digit.

Since this number is larger than , carry over the in tens digit when adding the next term.

Add the tens digit with the carry over.

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

In order to get an odd result from an addition, we must have one odd and one even number, thus you know from the first point about that only one of the two values is odd. Now, to get an even result, you can have two evens or two odds. So, let's presume that has two odd values, this means that must be even. Thus, you have:

Now, if we presume that has two even values, we must then know that is odd. Thus, we have:

First of all, you can eliminate the two answers that say that a given value is positive or negative. This cannot be told from our data. Next, it cannot be the case that is even. It will always be odd (hence, the correct answer is this). Finally, it cannot be that is even always. In the second case above, you will have two even numbers added together, given you an even. Then, you will add in an odd, giving you an odd.

This problem can be solved using common factors.

Rewrite using factors.

Rewrite by using factors. Simplify until the answer cannot be reduced any further.

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