Multiplication of Integers

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Transcript Multiplication of Integers

Grade 7 Mathematics
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5+8=
How could you model this problem using
chips?
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At a desert weather station, the temperature
at sunrise was 10°c. It rose 25°c by noon.
The temperature at noon was 10°c + 25°c =
35°c
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Kim had 9 CDs. She sold 4 CDs at a yard sale.
How many CDs does she have left?
How could you model this problem using
chips?
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Otis earned $5 babysitting. He owes Latoya
$7. He pays her the $5, how much does he
owe her now?
How could you model this problem using
chips?
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The Arroyo family just passed mile 25 on the
highway. They need to get to the exit at mile
80. How many more miles do they have to
drive?
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http://nlvm.usu.edu/en/nav/grade_g_2.html
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Subtracting a Negative
is the same as Adding
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Example:
What is 6 – (-3) ?
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6+3=
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9
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Example:
What is 14 – (-4) ?
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14 + 4 =
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18
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Subtracting a Positive
or Adding a Negative is
Subtraction
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Example
What is 5 + (-7) ?
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5–7=
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2
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Example
What is 6 – (+3) ?
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6–3=
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3
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Rules:
Two like signs become a positive sign.
Two unlike signs become a negative sign.
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Common Sense Explanation:
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A friend is +, an enemy is –
+ + = +, a friend of a friend is my friend
+ - = -, a friend of an enemy is my enemy
- + = -, an enemy of a friend is my enemy
- - = +, an enemy of an enemy is my friend
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You will understand and use the relationship
between addition and subtraction to simplify
computation by changing subtraction
problems to addition or vice versa.
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(+5) + (-3) =
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(+5) – (+3) =
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(+5) + (+3) =
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(+5) – (-3) =
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http://nlvm.usu.edu/en/nav/grade_g_2.html
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You will understand and use the relationship
between addition and subtraction found in
fact families
Fact families are built based on the
relationship between addition and
subtraction
Definition: A fact family is a group of
numbers that are related to each other in that
those numbers can be combined to create a
number of equations.
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3+2=5
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2+3=5
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5–3=2
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5–2=3
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(-7) + (+2) = -5
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(+2) + (-7) = -5
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What is the next fact family?
(-5) – (+2) = -7
What is the next fact family?
(-5) – (-7) = +2
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Develop and use algorithms for multiplying
integers.
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Two positives make a
positive
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Example:
3x2=
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Two negatives make a
positive
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Example:
(-3) x (-2) =
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A negative and a
positive make a
negative
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Example:
(-3) x 2 =
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A positive and a
negative make a
negative
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Example:
3 x (-2) =
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Step 1: Multiply the top numbers (the
numerators)
Step 2: Multiply the bottom numbers ( the
denominators)
Step 3: Simplify the fraction if needed
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Step 1: Convert to Improper Fractions
Step 2: Multiply the fractions
Step 3: Convert the result back to Mixed
Fractions
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Converting a mixed number to improper
fraction
Step 1: Multiply the denominator by the
whole number
Step 2: Then add that to the numerator
Step 3: Then write the result on top of the
denominator
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Converting an improper fraction to a mixed
number
Step 1: Divide the numerator by the
denominator
Step 2: Write down the whole number answer
Step 3: Then write down any remainder above
the denominator
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Division is the opposite of multiplying
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Example:
3 x 5 = 15
Which means 15 / 3 = 5
Also, 15 / 5 = 3
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Dividend ÷ Divisor = Quotient
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Example:
12 ÷ 3 = 4
12 = Dividend
3 = Divisor
4 = Quotient
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Two positives make a
positive
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Example:
8÷2=
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Two negatives make a
positive
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Example:
(-8) ÷ (-2) =
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A negative and a
positive make a
negative
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Example:
(-8) x 2 =
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A positive and a
negative make a
negative
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Example:
8 ÷ (-2) =