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What is value in math? Learn the definition of "values" in math and compare value vs. worth. See value math examples, including mean value and value of a function.Updated: 11/21/2023
Table of Contents
- What is Value in Math?
- Understanding Value: Math Example
- Place Value vs. Face Value
- Value vs. Worth
- Lesson Summary
Additional Activities
Value in Math: Problems for Additional Practice
1. There are four boxes on the table. The first box has 34 chocolates, the second box 24, the third box 43 and the fourth box 17 chocolates. Find the mean or average value of the number of chocolates in the four boxes.
2. A phone bill function for a month is expressed as a flat fee of $45 plus 50 cents for each minute x that the phone is used to call out of state. Find a function C(x) that represents the cost for using the phone for x minutes to call out of state, in dollars. Then use this cost function to find the value of using the phone for 65 minutes.
3. One pound of peas cost $2.97 while one pound of potatoes costs $1.89. Find the cost of purchasing five pounds of peas and six pounds of potatoes.
Solutions
1. The mean or average value of the number of chocolates in the boxes is given by the sum of the total number of chocolates in the boxes divided by the number of boxes. This is expressed algebraically as follows:
- Mean Value = (34 + 24 + 43 17)/4 = 118/4
- Mean Value = 29.50 chocolates.
2. The cost function in dollars can be expressed as follows, since 50 cents = 0.5 dollars:
C(x) = 45 + 0.50x
Using the function above, we can calculate the cost of using the phone for calling out of state for 65 minutes as follows:
C(65) = 45 + 0.50(65)
C = 77.50
The cost for using the phone is $77.50.
3. The total monetary value for purchasing the vegetables is based on multiplying the unit prices of peas and potatoes by the number of units or pounds of each vegetable purchased as follows:
- Total Cost = Price Per Pound of Peas x Pounds of Peas + Price Per Pound of Potatoes x Pounds of Potatoes
- Total Cost = $2.97 x 5 + $1.89 x 6
- Total Cost = $26.19.
The total cost of vegetables is $26.19.
Table of Contents
- What is Value in Math?
- Understanding Value: Math Example
- Place Value vs. Face Value
- Value vs. Worth
- Lesson Summary
It is not uncommon for math problems to ask for the "value" of a calculation or expression. For instance, a math teacher might ask for the value of {eq}a+b {/eq} when {eq}a {/eq} and {eq}b {/eq} are equal to certain numbers.
In math, the value of a calculation or expression is the number that results from the relevant calculation(s). For instance, when {eq}a=5 {/eq} and {eq}b=2 {/eq}, the value of {eq}a+b {/eq} is 7. You could be asked for the value of a calculation (like {eq}5 \times 3 {/eq}), a constant (like {eq}\pi {/eq}), a variable (like {eq}n {/eq}), an expression (like {eq}x+y {/eq}), a function (like {eq}f(3) {/eq}), and many other things. The length of this list should show you how common the concept of value is in mathematics!
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In this lesson, we will look at various uses of this word in mathematics. We will look at mean value, the value of a function, the place value and face value of a digit in a number, and the value of an object in terms of money (its "monetary value"). This is only a small sample of the ways that you might encounter the word "value" in a math problem.
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Mean Value
The mean value of a set of numbers in math is the average of those numbers. You can calculate the mean value by adding up the numbers and then dividing the result by the number of numbers. For instance, to find the mean value of 4, 1, 3, and 8, first, add up the numbers:
{eq}\hspace{2em} 4+1+3+8 = 16 {/eq}.
Then divide this sum by 4, since there are four numbers:
{eq}\hspace{2em} \frac{16}{4} = 4 {/eq}.
Therefore, the mean value of these numbers is 4.
Value of a Function
The value of a function for a given number is the number that is output by the function. It is usually found by applying the function's equation to the given number.
For instance, say that the function {eq}f {/eq} is defined by the equation {eq}f(x) = 2x-3 {/eq}. With this equation, you can calculate the value of {eq}f(5) {/eq} by substituting {eq}x=5 {/eq} into the definition and calculating the result:
{eq}\hspace{2em} \begin{align*} f(5) &= 2(5)-3 \\ &= 10-3 \\ &= 7 \end{align*} {/eq}
This tells you that if {eq}f(x) = 2x-3 {/eq}, then the value of {eq}f(5) {/eq} is 7.
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Numbers are always written using digits, which are the whole numbers from 0 to 9. There are two related ways to discuss the value of the digits in a number: place value and face value.
Face value is actually the easier one to explain. The face value of a digit is just the number itself. For instance, in the number 723, the face value of the first digit is 7. Pretty simple.
Place value, on the other hand, is what you get when you multiply this number by the value of the place. For example, in the number 723, the first digit is in the hundreds place, which means that the value of its place is 100. Therefore, the place value of the 7 in this number is
{eq}\hspace{2em} 7 \times 100 = 700 {/eq}.
In other words, the first digit is worth 7 hundreds, so its place value is 700.
Examples
As further examples, the table below gives the face value and place value of the digits in the number 9,614.
| Digit | Place value | Face value |
| 9 | 9,000 | 9 |
| 6 | 600 | 6 |
| 1 | 10 | 1 |
| 4 | 4 | 4 |
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Finally, notice that we have only discussed value in a theoretical, mathematical sense so far. In everyday language, however, when people discuss value, they often mean how much something is worth, often in terms of money, which is sometimes called its "monetary value".
You may encounter problems in which you are asked for the value of something in money. For example, say you purchase a bracelet for $2,000 and a necklace for $1,500. To calculate the total value of the bracelet and necklace, you would just add these two dollar values:
{eq}\hspace{2em} \$ 2{,}000 + \$ 1{,}500 = \$ 3{,}500 {/eq}.
Thus, the total value of the bracelet and necklace is $3,500.
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The value of a calculation or expression is the number that results from the relevant calculation(s).
The mean value of a set of numbers is the average of those numbers.
The value of a function for a given number is the number that is output by the function. It is usually found by applying the function's equation to the given number.
There are two ways to discuss the value of a digit in a number. The face value of a digit is the actual value of the digit, irrespective of its place. The place value is what you get when you multiply the digit by the value of the place. That is, {eq}\text{Place value} = \text{Face value} \times \text{Value of place} {/eq}. For example, in the number 412, the first digit has a face value of 4 and a place value of 400.
In certain scenarios, when people ask for the value of something, they mean how much it is worth in money.
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Video Transcript
Definition of Value
In math class, your teacher may ask questions like 'What is the value of 5 x 6?' or 'What is the value of x + y if x = 6 and y = 3?' In math, value is a number signifying the result of a calculation or function. So, in the example above, you could tell your teacher that the value of 5 x 6 is 30 or the value of x + y if x = 6 and y = 3 is 9.
Value can also refer to a variable or constant. What is a variable in math? A variable is a letter used to signify an unknown number. Common variables are x or y. What is a constant in math? A constant is a fixed or well-defined number.
The term value can also be used in different ways in math. Let's take a look at mean value, the value of a function at a certain point, and value as worth.
Mean Value
One of the common uses of the term value is as mean value. Mean value is the average of a set of numbers divided by the number of numbers in the set. For example, we have this set of numbers {4, 5, 6, 5}. To find the mean, we do the following:
4 + 5 + 6 + 7 = 20
We then need to divide by the number of numbers in the set, which is 4, so we have:
20 / 4 = 5
The mean of the above set of numbers would be 5.
Value of a Function at a Certain Point
Another common instance of the term value is when we are referring to the value of a function at a certain point. For example, we are given this function and x value:
f(x) = 6x + 7
x = 4
We are asked to find the value of the function with x being 4, so we plug in our x value and get the value of the function as 31:
f(x) = (6 x 4) + 7
f(x) = 24 + 7
f(x) = 31
Value as Worth
We have learned that value is a number indicating a result of a calculation or a variable or constant; but sometimes value means what something is worth. When we speak of worth, we are often speaking of money.
So, let's take a look at a couple of examples.
Example 1: We are going to the movies and need to figure out how much a night out to the movies for two people with a candy bar and popcorn would value. We have the following information:
Candy bar = $1.50
Popcorn = $6.00
Movie ticket = $10
Doing the calculations, we end up with the answer that this date is going to cost $35:
(1.50 + 6 + 10) x 2 = 35
Example 2: The jeweler told Eleanor that her diamond earrings valued at $200 and her diamond bracelet valued at $500. How much value does Eleanor's diamond earrings and bracelet have in total?
200 + 500 = 700
After doing the calculations, we discover Eleanor's jewelry is valued at $700.
Lesson Summary
In math, value can either refer to the result of a calculation or a variable or constant. Mean value is the average of a set of numbers. You can find this by adding the numbers in a set and dividing it by the number of numbers in that set. The value of a function at a certain point refers to the value of a function if you plug in the values given for the variables in the function. Value can also refer to worth of an object in math. In this case, value usually refers to money.
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