today we use the distributive property in equations and expressions with variables. distributive=to...
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distributive=to give out
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When you see a number next to another number in parentheses, this means to multiply. For
example: 8(8)= 64What are other ways to arrange
problems that lets you know that you have to multiply?
8(8 x y)
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states that the product of a number and a sum is equal to the sum of the
individual products of the addends and the number
An example is:5(3 + t) = 5 × 3 + 5 × t
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5(3 t) =
5(3 + t) = 5 × 3 5 × t
+
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8(k 2) =
8(k - 2) = 8 × k 8× 2
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5(3 + t) = 5 × 3 + 5 × t
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5(3 + t) =
5(3 + t) = 5 × 3
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5(3 + t) =
5(3 + t) = 5 × 3 + 5 × t
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states that the product of a number and a sum is equal to the sum of the individual
products of the addends and the number An example is:
(5 x 6) + (5 x t)=5(6 + t)
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(5 x 6) + (5 x t)=
5(
1. What is the common factor in the above equation?2. You factor it out3. What remains in the 1st term?4. What remains in the 2nd term?5. What operation is being done?
6 t )
+
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(8 x r) - (8 x 6)=
8(
1. What is the common factor in the above equation?2. You factor it out3. What remains in the 1st term?4. What remains in the 2nd term?5. Once the numbers and variables are in the
parentheses, what do you do to the new term?
r 6)
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Why else is it important to use the distributive property in equations and
expressions with variables
It is important to use the distributive property to be able to solve complex problems
It will also prepare you for algebra which you have to pass in order to graduate high school
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We are going to use the distributive property in equations and expressions with variables
When they look like this:
6( 5 + y)= You distribute (multiply) the
factor (6) with the first number in the term and place them in a parentheses
( 6 x 5) You distribute (multiply) the
factor (6) with the second number in the term and place them in a parentheses
( 6 x y) You place both terms together
and include the operation sign found inside the original term
(6 x 5) + (6 + y)
When they look like this:
(5 + 6) + ( 5 + y)• You look at both terms and
find the common factor in both terms
5• You place the number that you
factored, outside of the parentheses
5( )• You look at what remains in
the first term and you place it in the parentheses
5(6 )• You look at what remains in
the second term and you place it in the parentheses
5(6 Y)• Look at the operation sign between both terms and place
that in your new term5(6 + y)
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.
(8 + 6) + ( 8 + h)• You look at both terms and find the common factor in both terms
• You place the number that you factored, outside of the parentheses
• You look at what remains in the first term and you place it in the parentheses
• You look at what remains in the second term and you place it in the parentheses
• Look at the operation sign between both terms and place that in your new term
8
8( )
8(6 h)
8(6 + h)
8(6 )
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.
7( 6 + g)• You distribute (multiply) the factor (7) with the first number in the term and
place it in parentheses
• You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses
• You place both terms together and include the operation sign found inside the original
(7 x 6)
(7 x g)
(7 x 6) + (7 x g)
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.
(8 + 6) + ( 8 + h)• You look at both terms and find the common factor in both terms
• You place the number that you factored, outside of the parentheses
• You look at what remains in the first term and you place it in the parentheses
• You look at what remains in the second term and you place it in the parentheses
• Look at the operation sign between both terms and place that in your new term
8
8( )
8(6 h)
8(6 + h)
8(6 )
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.
7( 6 + g)• You distribute (multiply) the factor (7) with the first number in the term and
place it in parentheses
• You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses
• You place both terms together and include the operation sign found inside the original
(7 x 6)
(7 x g)
(7 x 6) + (7 x g)
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.
(8 + 6) + ( 8 + h)• You look at both terms and find the common factor in both terms
• You place the number that you factored, outside of the parentheses
• You look at what remains in the first term and you place it in the parentheses
• You look at what remains in the second term and you place it in the parentheses
• Look at the operation sign between both terms and place that in your new term
8
8( )
8(6 h)
8(6 + h)
8(6 )
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.
7( 6 + g)• You distribute (multiply) the factor (7) with the first number in the term and
place it in parentheses
• You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses
• You place both terms together and include the operation sign found inside the original
(7 x 6)
(7 x g)
(7 x 6) + (7 x g)
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Let’s review what we learned:What is distributive?Why is a term?What do you think is the most important reason to know how use the distributive property in equations and expressions with variables?
Do one last problem!(3 + 5) – (3 + s)=