How Zero Affects Positive and Negative Numbers
It isn’t too tricky to perform operations using positive and negative numbers with zero. You follow normal addition and subtraction rules, and what zero does to the final sign depends on where the zero is. When you multiply or divide using zero, that zero just wipes out the numbers and leaves you with zero.
Here are some general guidelines about zero:
Adding with zero: 0 + a is just a. Zero doesn’t change the value of a. (This is also true for a + 0.)
Subtracting with zero: 0 – a = –a. Use the rule for subtracting signed numbers: Change the operation from subtraction to addition and change the sign of the second number. Likewise, a – 0 = a. It doesn’t change the value of a to subtract zero from it.
Multiplying by zero: a × 0 = 0. If you’re in a club with a bunch of friends and none of you has anything, multiplying what each of you has yields nothing: Likewise, 0 × a = 0.
Multiplying any number by zero always yields zero.
Dividing zero by a number: 0 ÷ a = 0. Take you and your friends: If none of you has anything, then dividing that nothing into shares just means that each share has nothing. And you can’t use zero as the divisor because if you have a things, you can’t divide them into zero parts.
Algebra GlossaryAn operation that tells you how far a number is from zero.
Algebra GlossaryThe number with the same numerical part but the opposite sign (plus or minus) of a given number. If zero is the sum of two numbers, then these two numbers are additive inverses of one another.
Algebra GlossaryA characteristic of addition and multiplication that allows the grouping of terms to change without affecting the result.
Algebra GlossaryA value multiplied repeatedly in an exponential expression.
Algebra GlossaryA process requiring two values to produce a third value.
Algebra GlossaryTwo terms separated by addition or subtraction.
Algebra GlossaryA grouping symbol that looks like this: { }.
Algebra GlossaryA grouping symbol that looks like this: [ ].
Algebra GlossaryA number multiplied by a variable. The coefficient precedes the variable.
Algebra GlossaryA method of counting that tells how many ways a designated number of objects can be selected from a given set.
Algebra GlossaryThe same value on the bottom of more than one fraction.
Algebra GlossaryA characteristic of addition and multiplication that allows the order of the values in an operation to be changed without affecting the result.
Algebra GlossaryA whole number larger than 1 that isn’t prime.
Algebra GlossaryA variable or number that never changes in value in an expression.
Algebra GlossaryThe third power of a number; the result of multiplying a number by itself three times.
Algebra GlossaryA number that you can multiply by itself three times to get a given number. For example, the cube root of 8 is 2, because 2 times 2 times 2 equals 8.
Algebra GlossaryAn adjective that describes an expression in which the highest power is three.
Algebra GlossaryA fraction with an unwritten denominator of 10 indicated by the decimal point.
Algebra GlossaryThe highest power occurring in an expression.
Algebra GlossaryThe bottom number in a fraction.
Algebra GlossaryThe result of subtraction.
Algebra GlossaryNumerals from zero through nine, so called because they were originally counted on the fingers.
Algebra GlossaryA characteristic of multiplication and addition that allows for the multiplication of each individual term in a grouped series by a term outside of the grouping without changing the value of the expression.
Algebra GlossaryA number to be divided by another number.
Algebra GlossaryA number that can be divided by another number with no remainder.
Algebra GlossaryA solution that appears twice when solving an equation because the related factor appears twice in the factored form. For example, in (y – 2)(y – 2) = 0, y = 2 is a double root or solution. In (y – 2)(y – 2)(x + 3) = 0, y = 2 is still a double root or solution.
Algebra GlossaryA mathematical statement with an equal sign showing that two values are equal.
Algebra GlossaryFractions equal to one another, even though they may have different denominators.
Algebra GlossaryA number that can be divided by 2.
Algebra GlossaryA value in smaller type found above and to the right of the base that indicates the number of times the base is multiplied by itself.
Algebra GlossaryAny combination of values (variables, numbers, and/or constants) and operations that can be used to show how things belong together and compare to one another.
Algebra Glossary1. (noun) Any of the values involved in a multiplication problem that when multiplied together produces a result. 2. (verb) To rewrite an algebraic expression as a product.
Algebra GlossaryAn operation that multiplies a whole number by every counting number smaller than the whole number.
Algebra Glossary1. An acronym for first, outer, inner, and last — which indicates the order in which two terms (one from each of two binomials) are multiplied together. 2. The process of multiplying two binomials.
Algebra GlossaryA rule or method that is accepted as true and used over and over in common applications.
Algebra GlossaryAny quantity expressed as a numerator (the value above the fraction line) and a denominator (the value below the fraction line).
Algebra GlossaryA line separating the numerator from the denominator in a fraction.
Algebra GlossaryThe largest possible value that evenly divides each term of an expression containing two or more terms.
Algebra GlossaryParentheses, brackets, and braces that can affect the order of operations. Terms and operations within the grouping symbol take precedence.
Algebra GlossaryTerms and operations within grouping symbols.
Algebra GlossaryA fraction whose numerator is larger than the denominator.
Algebra GlossaryA relationship between two unequal values.
Algebra GlossaryWithout end; uncountable, as in a repeating decimal.
Algebra GlossaryA positive or negative whole number or zero; numbers starting with zero and going up or down in increments of one.
Algebra GlossaryA number with no fractional equivalent whose decimal never repeats or terminates.
Algebra GlossaryAn adjective describing an expression or equation in which the highest power of any variable is one. Constants can be higher powers.
Algebra GlossaryThe status of a fraction whose numerator and denominator cannot be divided evenly by the same number.
Algebra GlossaryAn improper fraction written as a whole number alongside a fraction.
Algebra GlossaryAn expression with only one term.
Algebra GlossaryA number evenly divisible by a specific factor.
Algebra GlossaryA rule stating if the product of two numbers is zero, then one of the numbers must be zero.
Algebra GlossaryAlso known as a reciprocal, one of two numbers whose product is one. The reciprocal of a number is that particular number in the denominator of a fraction with a value of one in the numerator.
Algebra GlossaryAn integer multiplied with both the numerator and denominator of a fraction.
Algebra GlossaryValues starting with one and increasing by one.
Algebra GlossaryAny quantity that is less than zero; it is usually preceded by a minus sign.
Algebra GlossaryTwo numbers, one positive and one negative, whose product is –1.
Algebra GlossaryA condition where two or more grouping symbols are inside one another.
Algebra GlossaryA set of numbers.
Algebra GlossaryThe top number in a fraction.
Algebra GlossaryA whole number that is not evenly divided by 2.
Algebra GlossaryA mathematical process, such as addition, subtraction, multiplication, and division, performed on one or more quantities.
Algebra GlossaryFractions with a denominator of 100. The percentage is the numerator of the fraction, indicating the number of parts out of 100.
Algebra GlossaryA counting method that determines the number of ordered arrangements there are when a certain number of objects are selected from a given set.
Algebra GlossaryAn expression with one or more terms.
Algebra GlossaryAny quantity greater than zero.
Algebra GlossaryA value of an exponent indicating the number of times the base is multiplied by itself.
Algebra GlossaryA rule of exponents, where any number raised to the power of zero equals one as long as the base number isn’t zero.
Algebra GlossaryThe process of finding the prime numbers that, when multiplied together, produce a given composite number.
Algebra GlossaryA whole number larger than one that can be divided evenly only by itself and one.
Algebra GlossaryA positive number that when multiplied by itself produces a given positive number.
Algebra GlossaryThe result of multiplication.
Algebra GlossaryA fraction whose value is less than one; thus, the numerator is always smaller than the denominator.
Algebra GlossaryAn equation showing that two ratios are equal to one another.
Algebra GlossaryAlso known as second degree, an expression or equation in which the highest power is 2.
Algebra GlossaryThe result of division.
Algebra GlossaryThe symbol for the operation to find a square root.
Algebra GlossaryMultiplying a base number the number of times indicated by the exponent.
Algebra GlossaryA quantity, positive or negative, that can be written as a fraction; its decimal equivalent terminates or repeats.
Algebra GlossaryAny rational or irrational number.
Algebra Glossary1. Two numbers whose product is always one. 2. Either one of the two numbers in a reciprocal.
Algebra GlossaryTo divide out a common factor of the numerator and denominator of a fraction, leaving an equivalent fraction.
Algebra GlossaryThe condition of two numbers that have no factors in common other than the number one.
Algebra GlossaryA value that is left over when one number is divided by another.
Algebra GlossaryA decimal in which, beyond a certain point, a digit or set of digits repeats indefinitely.
Algebra GlossaryA value that, multiplied by itself a number of times, results in the value or number wanted.
Algebra GlossaryApproximating a value to the nearest digit or decimal place.
Algebra GlossaryA standard way of writing very large and very small numbers as the product of two values — a number between 1 and 9 and a power of 10. Scientific notation follows the form N × 10a where N is a number from 1 up to 10, but not 10 itself, and a is an integer (positive or negative number).
Algebra GlossaryA symbol indicating whether a value is positive (+) or negative (−).
Algebra GlossaryA fraction in which both the numerator and the denominator are whole numbers.
Algebra GlossaryTo combine all that can be combined in an expression or equation, and put it in its most easily understandable form.
Algebra GlossaryValue(s) of a variable that make an equation a true statement.
Algebra GlossaryFind the answer or the number that a variable stands for.
Algebra Glossary1. The product of another number times itself. 2. A value with an exponent of 2.
Algebra GlossaryA value resulting when a given value is multiplied by itself.
Algebra GlossaryA method of replacing a value with its equivalent.
Algebra GlossaryThe result of addition.
Algebra GlossaryA characteristic of equations that allows for the exchange of the value(s) on one side of the equal sign with the value(s) on the other side (quantities on the right go to the left; quantities on the left go to the right) without changing the truth of the equation: If x = y, then y = x.
Algebra GlossaryA short-cut division process in which only the coefficients of the terms in an expression are used. The answer is obtained by multiplying and adding.
Algebra GlossaryA group of number(s) and/or variable(s) connected to one another by multiplication or division and separated from other terms by addition or subtraction.
Algebra GlossaryAn expression with three terms. Each term is separated from the others by addition or subtraction.
Algebra GlossaryTo factor a trinomial into two binomials.
Algebra GlossaryA numeric equivalent or worth of an expression or variable.
Algebra GlossaryA letter representing an unknown number or what you’re solving for in an algebra problem.
Algebra GlossaryAll natural numbers plus zero.
