The integer is implicitly converted to a floating-point number before the operation takes place. The following table summarizes the data type returned by the arithmetic operators, based on the data type of the operands.
The necessary conversions take place before the operation is performed. The boldface line of code declares an array referred to by arrayOfInts , creates the array, and puts ten integer values into it. The program uses arrayOfInts. The remaining three-fourths are shown. Dotted lines indicate where the cake can be cut to divide it into equal parts. The first rule of adding fractions is to start by adding fractions that contain like denominators—for example, multiple fourths, or quarters.
Imagine one pocket containing two quarters, and another pocket containing three quarters. In total, there are five quarters. Since four quarters is equivalent to one dollar , this can be represented as follows:. To add fractions that contain unlike denominators e. One easy way to to find a denominator that will give you like quantities is simply to multiply together the two denominators of the fractions.
It is important to remember that each numerator must also be multiplied by the same value its denominator is being multiplied by in order for the fraction to represent the same ratio. This method always works. However, sometimes there is a faster way—a smaller denominator, or a least common denominator—that can be used. What if a fraction is being added to a whole number? The process for subtracting fractions is, in essence, the same as that for adding them. Find a common denominator, and change each fraction to an equivalent fraction using that common denominator.
Then, subtract the numerators. For instance:. To subtract a fraction from a whole number or to subtract a whole number from a fraction, rewrite the whole number as a fraction and then follow the above process for subtracting fractions. Unlike with addition and subtraction, with multiplication the denominators are not required to be the same.
To multiply fractions, simply multiply the numerators by each other and the denominators by each other. If any numerator and denominator shares a common factor, the fractions can be reduced to lowest terms before or after multiplying. Alternatively, the fractions in the initial equation could have been reduced, as shown below, because 2 and 4 share a common factor of 2 and 3 and 3 share a common factor of To multiply a fraction by a whole number, simply multiply that number by the numerator of the fraction:.
A common situation where multiplying fractions comes in handy is during cooking. The reciprocal is simply the fraction turned upside down such that the numerator and denominator switch places. A complex fraction is one in which the numerator, denominator, or both are fractions, which can contain variables, constants, or both. A complex fraction, also called a complex rational expression, is one in which the numerator, denominator, or both are fractions.
When dealing with equations that involve complex fractions, it is useful to simplify the complex fraction before solving the equation. From previous sections, we know that dividing by a fraction is the same as multiplying by the reciprocal of that fraction. Therefore, we use the cancellation method to simplify the numbers as much as possible, and then we multiply by the simplified reciprocal of the divisor, or denominator, fraction:.
Start with Step 1 of the combine-divide method above: combine the terms in the numerator. To do so, we multiply the fractions in the denominator together and simplify the result by reducing it to lowest terms:. Recall, again, that dividing by a fraction is the same as multiplying by the reciprocal of that fraction:. Exponentiation is a mathematical operation that represents repeated multiplication. Here, the exponent is 3, and the expression can be read in any of the following ways:. Some exponents have their own unique pronunciations.
Operands for the arithmetic operators can be integers or real numbers. The plus operator is the equivalent of the SetUnion and SetAddMember functions; it performs the union of two sets:. SuperSet contains all members of both subsets with no duplicates.
However, division, when both operands are of the integer data type, may act differently. Their usage can be explained in terms of the assignment operator and the arithmetic operators. In the table, we will use the variable age and you can assume that it is of integer data type. Skip to content Overview The basic arithmetic operations are addition, subtraction, multiplication, and division.
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