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# Integers

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#### Transcript of Integers

By: Sher Yao

8A Integers TRANSLATION: One way to easily add integers

is using a number line. How do you subtract integers? SUBTRACTING INTEGERS GRAPHING TRANSLATION & REFLECTION ADDING INTEGERS When you are adding a POSITIVE integers, on the number line you have move towards the RIGHT.

When you are adding a NEGATIVE integers, on the number line you have to move towards the LEFT. Question: George owes Mandy $10. On Monday he worked and gained $4. How much money does George owe Mandy now? To answer this question, you can use a number line. Answer: Here George owed Mandy $10, so I placed a lign obove -10 and when he earned $4 i moved 4 spaces towards the right. Now George owes Mandy $6. Information: Always subtract integers by adding it's opposite: For example: (+10) - (+3) = ?

First you must use opposite operations so:

(+10) - (+3) = (+10) + (-3)

= (+7) This is how it looks on a NUMBER LINE: So to subtract a POSITIVE INTEGER, on a number line you must move to the LEFT.

To subtract a NEGATIVE INTEGER, on a number line you must move to the RIGHT. QUESTION:

(+9) - (-5) = ?

= (+9) + (+5)

= (+14) MULTIPLYING INTEGERS You multiply judgging by the signs on the integers. If the two integers have the SAME SIGNS; their product would be POSITIVE.

(+12) x (+3) = (+12)(+3) or (-2) x (-6) = (-2)(-6)

= (+36) = (+12) If the two integers have DIFFERANT SIGNS; their product would be NEGATIVE.

(+3) x (-10) = (+3)(-10) and (+9) x (-4) = (+9)(-4)

= (-30) = (-36) DIVIDING INTEGERS To divide integers it also depends on the SIGNS of the integers. It has the same rule as MULTIPLYING two INTEGERS When two integers have SAME signs, the quotients are always POSITIVE.

When two integers have DIFFERANT integers, the quotients are always NEGATIVE. POSITIVE DIVIDING TWO INTEGERS WITH THE SAME SIGNS, the quotient will be positive.

(+10) /(+2) = (+5) and/or (-10) / (-2) = (+5) DIVIDING INTEGERS WITH DIFFERANT SIGNS. The quotient will be negative

(-12) / (+3) = (-4) and/or (+20) / (-10) = (-2) ORDER OF OPERATIONS WITH INTEGERS The order of operation applies to WHOLE NUMBERS and INTEGERS. Order of Operations:

BRACKETS- First do the operations in brackets

EXPONENTS- Evaluate if there are any exponents in the equation.

DIVISION & MULTIPLICATION- Division and Multiplication always come before Addition and Subtraction. Always go in order from LEFT to RIGHT.

ADDITION & SUBTRACTION: Addition and Subtraction always occur in order from LEFT to RIGHT. To subtract integers you may also use a NUMBER LINE. One easy way to remember: BEDMAS Question: (-2) * (-100) / 5 * 5 + 2 = ? Answer: (-2) * (-100) / 5 * 5 + 2=

DIVISION & MULTIPLIATION:

(-2) * (-100) = (+200)

5 * 5 = 25

+200 / +25 = +8

ADDITION & SUBTRACTION:

(+8) + 2 = (+10) GRAPHING IN A COORDINATE GRID What is it? A coordinate grid is formed by 2 axis that meet at the ORIGIN. Horizontal axis: X-Axis and the Vertical axis: Y-AXIS. The coordinate grid is divided into 4 Quadrants: 1, 2, 3 and 4 The numbers on a grid are used to locate points. Each point is shown by an ORDERED PAIR.

Ordered pair is shown by 2 numbers, the first number is located on the x-axis which is called a x-coordinate. The second number is located on the y-axis which is called a y-coordinate. Ordered pairs are shown in parentheses (x-coordinate, y-coordinate). Ex. (+2,-10) The ORIGIN (0.0) A translation is a funtion that moves every point of the figure a constant distance and in a specific direction on a coordinate grid. The figure and it's image have the same SIZE and SHAPE and they both FACE the same directions. The FIGURE The IMAGE When translated a figure, to describe the movements: up, down left and right the amount of units! In the following grid, you will see that the triangle 1 (The FIGURE). Point A is in (-4, 2), point B (-2, 2) and pont C (-2, 4) A B C A' B' C' When translated: point A' (1,0), point B' (3,0) and point C (3,2). So in the end, the Figure translated 5 units to the RIGHT and 2 units DOWN. ROTATIONS Center of Rotation A B C A' B' C' The Figure The Image the triangle ABC was also rotated 1/4 clockwise at the origin The triangle ABC was rotated 3/4 counter-clockwise at the origin. And/or GRAPHING REFLECTIONS A reflection creates the MIRROR image of a figure. The mirror line is a line of SYMMETRY for the figure and it's image. The triangle A'B'C' is the image of triangle ABC after a reflection on the Y-AXIS Try to figure out the REFLECTIONS of each dot!!! Extra Help: view the video below ADDING INTEGERS!!

SUBTRACTING INTEGERS MULTIPLYING AND DIVIDING INTEGERS ROTATION/REFLECTION AND TRANSLATION

Full transcript8A Integers TRANSLATION: One way to easily add integers

is using a number line. How do you subtract integers? SUBTRACTING INTEGERS GRAPHING TRANSLATION & REFLECTION ADDING INTEGERS When you are adding a POSITIVE integers, on the number line you have move towards the RIGHT.

When you are adding a NEGATIVE integers, on the number line you have to move towards the LEFT. Question: George owes Mandy $10. On Monday he worked and gained $4. How much money does George owe Mandy now? To answer this question, you can use a number line. Answer: Here George owed Mandy $10, so I placed a lign obove -10 and when he earned $4 i moved 4 spaces towards the right. Now George owes Mandy $6. Information: Always subtract integers by adding it's opposite: For example: (+10) - (+3) = ?

First you must use opposite operations so:

(+10) - (+3) = (+10) + (-3)

= (+7) This is how it looks on a NUMBER LINE: So to subtract a POSITIVE INTEGER, on a number line you must move to the LEFT.

To subtract a NEGATIVE INTEGER, on a number line you must move to the RIGHT. QUESTION:

(+9) - (-5) = ?

= (+9) + (+5)

= (+14) MULTIPLYING INTEGERS You multiply judgging by the signs on the integers. If the two integers have the SAME SIGNS; their product would be POSITIVE.

(+12) x (+3) = (+12)(+3) or (-2) x (-6) = (-2)(-6)

= (+36) = (+12) If the two integers have DIFFERANT SIGNS; their product would be NEGATIVE.

(+3) x (-10) = (+3)(-10) and (+9) x (-4) = (+9)(-4)

= (-30) = (-36) DIVIDING INTEGERS To divide integers it also depends on the SIGNS of the integers. It has the same rule as MULTIPLYING two INTEGERS When two integers have SAME signs, the quotients are always POSITIVE.

When two integers have DIFFERANT integers, the quotients are always NEGATIVE. POSITIVE DIVIDING TWO INTEGERS WITH THE SAME SIGNS, the quotient will be positive.

(+10) /(+2) = (+5) and/or (-10) / (-2) = (+5) DIVIDING INTEGERS WITH DIFFERANT SIGNS. The quotient will be negative

(-12) / (+3) = (-4) and/or (+20) / (-10) = (-2) ORDER OF OPERATIONS WITH INTEGERS The order of operation applies to WHOLE NUMBERS and INTEGERS. Order of Operations:

BRACKETS- First do the operations in brackets

EXPONENTS- Evaluate if there are any exponents in the equation.

DIVISION & MULTIPLICATION- Division and Multiplication always come before Addition and Subtraction. Always go in order from LEFT to RIGHT.

ADDITION & SUBTRACTION: Addition and Subtraction always occur in order from LEFT to RIGHT. To subtract integers you may also use a NUMBER LINE. One easy way to remember: BEDMAS Question: (-2) * (-100) / 5 * 5 + 2 = ? Answer: (-2) * (-100) / 5 * 5 + 2=

DIVISION & MULTIPLIATION:

(-2) * (-100) = (+200)

5 * 5 = 25

+200 / +25 = +8

ADDITION & SUBTRACTION:

(+8) + 2 = (+10) GRAPHING IN A COORDINATE GRID What is it? A coordinate grid is formed by 2 axis that meet at the ORIGIN. Horizontal axis: X-Axis and the Vertical axis: Y-AXIS. The coordinate grid is divided into 4 Quadrants: 1, 2, 3 and 4 The numbers on a grid are used to locate points. Each point is shown by an ORDERED PAIR.

Ordered pair is shown by 2 numbers, the first number is located on the x-axis which is called a x-coordinate. The second number is located on the y-axis which is called a y-coordinate. Ordered pairs are shown in parentheses (x-coordinate, y-coordinate). Ex. (+2,-10) The ORIGIN (0.0) A translation is a funtion that moves every point of the figure a constant distance and in a specific direction on a coordinate grid. The figure and it's image have the same SIZE and SHAPE and they both FACE the same directions. The FIGURE The IMAGE When translated a figure, to describe the movements: up, down left and right the amount of units! In the following grid, you will see that the triangle 1 (The FIGURE). Point A is in (-4, 2), point B (-2, 2) and pont C (-2, 4) A B C A' B' C' When translated: point A' (1,0), point B' (3,0) and point C (3,2). So in the end, the Figure translated 5 units to the RIGHT and 2 units DOWN. ROTATIONS Center of Rotation A B C A' B' C' The Figure The Image the triangle ABC was also rotated 1/4 clockwise at the origin The triangle ABC was rotated 3/4 counter-clockwise at the origin. And/or GRAPHING REFLECTIONS A reflection creates the MIRROR image of a figure. The mirror line is a line of SYMMETRY for the figure and it's image. The triangle A'B'C' is the image of triangle ABC after a reflection on the Y-AXIS Try to figure out the REFLECTIONS of each dot!!! Extra Help: view the video below ADDING INTEGERS!!

SUBTRACTING INTEGERS MULTIPLYING AND DIVIDING INTEGERS ROTATION/REFLECTION AND TRANSLATION