MATH 110 Lecture 7: Signed Numbers

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silvercicada472

10 Jul 2018

School

University of Alabama

Department

MATH

Course

MATH 110

Professor

davidneal

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Document Summary

The term signed numbers refers to positive and negative numbers. If no sign is shown, the number automatically is considered positive. On a number line, numbers to the right of 0 are positive. Numbers to the left of 0 are negative, as shown in figure 1. Given any two numbers on a number line, the one on the right is always larger, regardless of its sign (positive or negative). Note that fractions may also be placed on a number line as shown in figure 2. When adding two numbers with the same sign(either both positive or both negative), add the absolute values (the number without a sign attached) and keep the same sign. Addition problems can be presented in either a vertical form (up and down) or in a horizontal form (across). When adding two numbers with different signs (one positive and one negative), subtract the absolute values and keep the sign of the one with the larger absolute value.

Related Questions

How can the multiplication table be used to solve divisionâ problems?

Find the column for the firstâ factor, if possible. Then find the row corresponding to the second factor. The quotient is the entry diagonally up and to the right of the corresponding entry.

Find the row for theâ quotient, if possible. Within thisâ row, find the entry corresponding to either factor. The other factor is the number of the corresponding column.

Find the column for eitherâ factor, if possible. Within thisâ column, move down nâ rows, where n is the other factor. The resulting entry is the quotient.

Find the row for eitherâ factor, if possible. Within thisâ row, find the entry corresponding to the other factor. The quotient is the number of the corresponding column.

2. Consider the odd number 35 shown in the multiplication table. Consider all the numbers that surround it. Note that they are all even. Does this happen for all odd numbers in theâ table? Explain why or why not.

No. A product of two numbers is odd if at least one factor is odd.â Therefore, the surroundingâ row(s) andâ column(s) will contain products of odd and evenâ numbers, which are odd and even.

No. An odd number has the form

2kplus+â1,

where k is a whole number.â Therefore, the entry to the right will equal

2kplus+1plus+âb,

where b is the number of the correspondingâ row, and

1plus+b

can be even or odd.

Yes. The only way for a product of two numbers to be odd is if both factors are odd.â Therefore, the surroundingâ row(s) andâ column(s) will contain products of evenâ numbers, which are even.

Yes. An odd number has the form

2kplus+â1,

where k is a whole number.â Therefore, the entry to the right will equal

2kplus+1plus+âb,

where b is the number of the correspondingâ column, and

1plus+b

must always be an even number.

General Math Terms A product B. digit C. numeral D. compass E. equation F. formula G. negative H. sum I. mean J. statistics K. positive L. percent M. straight-edge N. squareroot O. quotient P. prime numbers Q. difference R. addend S. minuend T. divisor Greater than zero: plus. A number being added to another number. A mathematical sequence whose verb is equal (=). The result of addition. The number doing the dividing in a division problem. An instrument used to construct straight lines. A mathematical expression of a natural law. The result of multiplication. The number from which another number is being subtracted. Any non-negative numeral less than ten. Less than zero: minus. An instrument used to construct circles and arcs of circles. A number that produces another number (it's square) when multiplied by itself. The result of subtraction. A symbol or name of a number. The average: the sum of the elements divided by the number of elements. The result of division. Parts per hundred: hundredths. Natural numbers greater than one that have no other factors except one and themselves. Set of numerical data. Geometry A. chord B. diameter C. radius D. perimeter E. cylinder F. surface area G. right angle H. square I. Hypotenuse J. obtuse angle K. vertex L point M. ray N. bisect O arc P. hexagon Q. pentagon R. polygon S. perpendicular T. rectangle U. rhombus V. triangle W. circumference X cube Y pyramid Z. sphere A six-sided polygon. The common end point of the sides of an angle. An angle measuring more than 90 degree. A long, round object with flat, circular ends. An angle of 90 degree. The side of a right triangle opposite the right angle. The total area of all the surfaces of an object. To multiply a number by itself. A location, the place where two lines cross or intersect. A closed geometric figure made up of three or more line segments. The perimeter of a circle: the distance around a circle. A shape having the same dimensions of length, height, and width. A half-line with a designated end point which extends in only one direction without stopping. A figure having a polygon base and triangular sides which meet in a point at the top. Divide an angle into two equal angles. A part of a circle

MATH 110 Lecture 7: Signed Numbers

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