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Representing Multiplying Fractions. 7.2E Simplify numerical expressions involving order of operations and exponents. Mr. Brewer’s 7 th Grade Math October 26-30, 2009. 7.2A Represent multiplication and division situations involving fractions with models, pictures, words, and numbers.
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Representing Multiplying Fractions 7.2E Simplify numerical expressions involving order of operations and exponents. Mr. Brewer’s 7th Grade Math October 26-30, 2009 7.2A Represent multiplication and division situations involving fractions with models, pictures, words, and numbers. Order of Operations
Use a rectangle to graphically multiply two fractions. 1 1 2 First, shade in of the rows. 3 X 3 5
Use a rectangle to graphically multiply two fractions. 2 1 2 Next, shade in of the columns. 5 X 3 5 Now find the intersection.
Use a rectangle to graphically multiply two fractions. Now, write the fraction for the intersecting squares. 1 2 X 3 5 2 15
Use a rectangle to graphically multiply two fractions. 1 First, shade in of the rows. 1 1 4 X 4 2
Use a rectangle to graphically multiply two fractions. 1 Next, shade in of the columns. 1 1 2 X 4 2 Now find the intersection.
Use a rectangle to graphically multiply two fractions. Now, write the fraction for the intersecting squares. 1 1 X 4 2 2 1 = 16 8
1 ÷ 4 Which model best represents this expression: 3
1 1 Which model best represents this expression: X 5 3
Order of Operations A standard way to simplify mathematical expressions and equations. For example: 8 + 3 X 4 = 11 X 4 = 44 …or does it equal 8 + 3 X 4 = 8 X 12 = 20
Order of Operations • Simplify within Grouping Symbols ( ), { }, [ ], | |, Fraction Bars • Simplify Exponents • Complete Multiplication and Division from Left to Right • Complete Addition and Subtraction from Left to Right
Representing Squares & Square Roots 7.2E Simplify numerical expressions involving order of operations and exponents. Mr. Brewer’s 7th Grade Math October 26-30, 2009 7.1C Represent squares and square roots using geometric models. Order of Operations
Squares and Square Roots The square of a number is the product of a number and itself. Ex. The square of 4 is 16, because 4 X 4 = 16. The square of 4 can be written as 4 = 16. This expression is read “Four squared equals 16. 2 The square root of a number is the is the number that you can square to get the original number. Ex. A square root of 36 is 6, because 6 X 6 = 36. The symbol for square root is . The square root of 36 is written as 36 and is read “the square root of 36.”
You can use grids to model the square and square root of a number. This grid represents 5 = 25 2
Look for the square! Which group of objects represents a square?
Which square root is represented by one side of the model below?
Order of Operations • Simplify within Grouping Symbols ( ), { }, [ ], | |, Fraction Bars • Simplify Exponents • Complete Multiplication and Division from Left to Right • Complete Addition and Subtraction from Left to Right
What is are Grouping Symbols? • Grouping symbols are symbols that separate parts of an equation from other parts of an equation. 5(3 – 3 x 3) x 4 5 + 3 – 3 x {3 x 4} 5 + [3 – 3 x 3] x 4
What is an Exponent? • An exponent is a little number high and to the right of a regular or base number. Exponent 3 4 Base
What an Exponent Represents • An exponent tells how many times a number is multiplied by itself. 4 = 3 x 3 x 3 x 3 3
Reading Exponents • This exponent is read three to the 3rd power or three cubed. Exponent 3 3 Base
Read These Exponents 3 2 6 5 2 7 3 4
What is the Exponent? 2 x 2 x 2 = 2
What is the Exponent? 5 x 5 x 5 x 5 = 5
Multiplying Exponents Out 4 3 = 3 x 3 x 3 x 3 9 27 81
2 8 x (5 - 3)
2 4(6-3)
2 8 x (3 + 5)
2 5(3 – 3 x 3) x 4