(6th grade - 2021)
♡Algebra♡
•in "5^3" the 5 is called the base, the 3 is called the power, and the entire problem is called a exponent
•when reading the problem "6^3", you can read this as, "six to the third power" or "six cubed"
•when reading the problem "6^2", you can read this as, "six to the second power" or "six squared"
•if you know that (2/3)^2 = 4/9, then you can find out that the value of (2/3)^3 would equal 8/27
•"what is the value of 0.3^2?" 0.09
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2^5 = 5x5
5^3 = 5x5x5
6^0 = 1
10^3 = 10x10x10
4 • 4 • 4 • 4 = 4^2 • 4^2
4 • 4 • 4 • 4 = 4^2 • 4 • 4
4 • 4 • 4 • 4 = 4 • 4^3
4 • 4 • 4 • 4 = 2• 2 • 2 • 2 • 2 • 2• 2 • 2
4 • 4 • 4 • 4 # 4^2+4^2
4 • 4 • 4 • 4 # 4+4+4+4
4 • 4 • 4 • 4 = 16 • 4^2
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•5x,15, 3x are called terms
•5 and 3 are the coefficients
•15 is the constant
• x is the variables
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An expression is a mathematical sentence without an equals sign
•n times 7 is the same as; 7n
•4 minus y is the same as; 4-y
•13 added to x is the same as; x+13
•11x is the same as; 11 multiplied by x
•8-y is the same as; 8 minus y
"x divided by 12" is an expression for x/12
"10 multiplied by y" is an expression for "10y"
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•x divided by 16 is (the same as;) x/16
•x multiplied by 16 is 16x
•x plus 16 is x+16
•90 times a is 90a
•x take away 16 is x-16
•a less than 90 is a-90
•the quotient of 90 and a is 90/a
•a added to 90 is 90+a
•the sum of m and 15 is m+15
•the difference of m and 15 is m-15
•c less than 2 is c-2
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•5-k is k less than 5
•5k is 5 times k
•k/5 is k divided by 5
•k+5 is 5 added to k
•12/h is the quotient of 12 and h
•12h is the product of 12 and h
•12+h is the sum of 12 and h
•12-h is the difference of 12 and h
•2+c is c more than 2
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♡PEMDAS + Algebra♡
P ( )
E ^2
M × D /
A + S -
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•"1. Solve any operations inside of parentheses"
•"2. Solve exponents"
•"3. Multiplication and division moving from left to right" [?]
•"4. Addition and Subtraction moving from left to right" [?]
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•(21-3) ÷ 3^2 = 2
[how to solve:]
•17+15 ÷ 3 - 24 = 6
[how to solve:]
•7×6+4×3 = 54
[how to solve:]
•(8+6^2)/11+ 7 • 2 =
[how to solve:]
•12 + 9^2/3 =
[how to solve:]
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"4(x-4); x=7
1. Find the value of the variable.
2. _________ the problem substituting the value of the variable.
3. _________ using the order of operations."
4(x - 4); x = 7
4(7 - 4)
4(3)
12
When x = 7, 4(x - 4) = 12
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"If x is 6, what is:
a. x+4
b. 7-x
c. x^2
d. 1/3x"
A. 10, B.1, C. 36, D. 39
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a = 3, b = 4, c = 6
bc+5a 4(6) + 5(3)
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"The expression 1.8c+32 gives the temperature in degrees Fahrenheit for a given temperature in degrees Celsius, C. Find the temperature in degrees Fahrenheit that is equivalent 19 30°c."
1.8(30) + 32
54+32
1.8 86°F
x 3 0
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0 0 54[.]Ø
5 4 0
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"The expression 6x^2 gives the surface area of a cube, and the expression x^3 gives the volume of a cube, where x is the length of one side of the cube. Find the area and the volume"
x = 2
6×2^2 or 6(2^2)
2^2 = 4
x^3 = 2
2^3 = 8
