All courses. Pre-Algebra Explore and understand integers Overview Absolute value Adding and subtracting integers Multiplying and dividing with integers. Pre-Algebra Inequalities and one-step equations Overview Different ways to solve equations Calculating the area and the perimeter Solving inequalities Understanding inequalities and equations.
Pre-Algebra Discover fractions and factors Overview Monomials and adding or subtracting polynomials Powers and exponents Multiplying polynomials and binomials Factorization and prime numbers Finding the greatest common factor Finding the least common multiple. All constant terms are also like terms. So among the terms. Terms that are either constants or have the same variables with the same exponents are like terms. Look at the variables and exponents.
The expression contains and constants. The terms and are like terms because they both have. The terms and are like terms because they are both constants. The term does not have any like terms in this list since no other terms have the variable raised to the power of. The expression contains the terms.
The terms are like terms because they all have. The term has no like terms in the given expression because no other terms contain the two variables. We can simplify an expression by combining the like terms. What do you think would simplify to? If you thought you would be right! Add the coefficients and keep the same variable. If you have of something and add more of the same thing, the result is of them.
For example, oranges plus oranges is oranges. We will discuss the mathematical properties behind this later. The expression has only two terms. When an expression contains more terms, it may be helpful to rearrange the terms so that like terms are together. The Commutative Property of Addition says that we can change the order of addends without changing the sum. So we could rearrange the following expression before combining like terms.
Simplify the expression:. These are not like terms and cannot be combined. So is in simplest form. In the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences.
They are summarized in Figure. Each phrase tells you to operate on two numbers. Look for the words of and and to find the numbers. Look for the words of and and to find the numbers to subtract. This can also be written as. How old will you be in eight years? What age is eight more years than your age now? Did you add to your present age? Eight more than means eight added to your present age. How old were you seven years ago? This is seven years less than your age now.
You subtract from your present age. Seven less than means seven subtracted from your present age. They tell us the operation is addition. They tell us the operation is subtraction. Because we are multiplying times the sum, we need parentheses around the sum of and.
Here we are taking the sum of five times and. Notice how the use of parentheses changes the result. The height of a rectangular window is inches less than the width. Let represent the width of the window. Write an expression for the height of the window.
The length of a rectangle is inches less than the width. Let represent the width of the rectangle. Write an expression for the length of the rectangle.
The width of a rectangle is meters greater than the length. Let represent the length of the rectangle. Write an expression for the width of the rectangle. Blanca has dimes and quarters in her purse. The number of dimes is less than times the number of quarters. Let represent the number of quarters. Write an expression for the number of dimes. Here's a formal definition:. Given variable [ index ] , where index must be of integer int type, read a value from or store a value into variable 's storage element at location index.
Example: temperatures[1]. The value passed to index is a bit integer that is either 0 or a positive value ranging to one less than the array's length, which is indicated by appending.
For example, grades. Listing 2 presents the source code to an example application that lets you play with the array index operator.
Listing 2 is somewhat more interesting than Listing 1. After creating a five-element, one-dimensional array of integers via an array initializer and assigning the array's reference to grades , main proceeds to access various elements.
Two items are of special interest:. The final example, which passes 1D as an index to the array index operator, is commented out because it will not compile. If you uncomment the line and attempt to compile Listing 2, you will receive an error message about incompatible types: "possible lossy conversion from double to int. Compile Listing 2 javac ArrayIndexOp. You should observe the following output:. The expression and variable must be assignment compatible , meaning their types must agree.
For example, you cannot assign a string literal to an integer variable. I'll explain more about this when we discuss type conversions. Each expression and variable must be assignment compatible. Each operator serves as a useful shortcut. Here are the latest Insider stories. More Insider Sign Out. Sign In Register. Sign Out Sign In Register.
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