Unit 2

Add, subtract, multiply and divide decimals and fractions; comparing and ordering rational numbers; graphing on coordinate grids including rational numbers

Decimal Numbers from Ms Garcia on Vimeo.

Add/Subtract decimals. (1) Align your decimal point and
place value.
(2) Write place keepers if needed
(3) Add or subtract
(4) Keep your decimal point.

   
Adding/Subtracting Fractions.  
  (1) Find the common denominator by finding the LCM of the denominators.
  (2) Find your new fractions with the new denominator by using cross
multiplication.
  (3) Add or subtract only the numerators. The denominators stay the 
same.
  (4) Simplify if necessary or change to a mixed number.
Simplify (reducing).   
(1) Do the factor tree for both numbers.
(2) Find what they have in common and divide the numerator (top) and denominator (bottom) by that number, therefore renaming it to an equivalent fraction in lower terms.
                                                           6 =  * 3                                        
                                                           8 =  * 4        
                                                          the GCF of (6,8) is 
Multiplication of Fractions. 
(1) Multiply the numerators (tops) and multiply the denominators 
(bottoms), 
(2) then reduce the answer to lowest terms.
Division of Fractions. 
(1) Change division to multiplication by the reciprocal
(2) Multiply,

Mixed Number. Whole numbers followed by fractions

Improper Fractions. Are fractions that have a  numerator (top larger than the denominator  (bottom)
Conversions:     
Mixed Number to Improper Fractions.  

(1) Multiply the denominator with the whole number. 
(2) Add the numerator to the product             1*3+2 = 5
 (3) The sum is the new numerator
(4) The denominator stays the same.
Improper Fractions to Mixed Number.
(1) Divide. The numerator goes inside the radical and the denominator goes outside.
(2) The quotient is the whole number. 
(3) The remainder is the numerator.
(4) The denominator stays the same.
(5) Simplify if necessary.  If there is no remainder, there is no  fraction.

Comparing and Ordering decimals. 

Align decimal points and place values,  write a place keeper if needed.    (Pretend it’s money)

Percents.  Means “per 100”.  Percents can be written as fractions by placing the number over 100 and simplifying.

 

Percents.   Percents can be written as decimals (1) moving the 
decimal point 2 places to the left, and (2) deleting the percent sign.

 

 

Percent formula








Example: 4% of 50 is____ 






or      50 x 4% = 50 X 0.04 = 2

Example:         10% of X is 15,   find X

X*10%=15
X=15/10% = 15/0.10=150
Percent change



Percentage change between two numbers A & B can be calculated as:
(B-A)/A * 100

For example, if a game price increases in value from $10 to $12 
the percentage increase is: 

(12-10)/10 * 100 = 2/10 *100 = 0.2*100 = 20 percent 

Alternatively, if a game price decreases in value from $10 to $9 the
percentage decrease is: 

(10-9)/10 * 100 = 0.1*100 = 10 percent


Convert Fractions, Decimals, Percents

Move the decimal point twice to the right
Move the decimal point twice to the left, 
delete the percent sign
Write down the decimal divided by 1
Multiply its numerator and denominator
by the same  number (10, 100, 1000, ..)
Simplify if necessary



To convert a decimal to a percent, multiply the decimal by 100, 
                                  then add on the % symbol.


  Conversion. Use the math chart. Do a proportion to solve. 

Ex. How many centimeters are in 2.5 meters?
Now cross multiply            1 * X = 100 * 2.5 = 2500
There are 2500 centimeters in 2.5 meters

Essential Questions:

How do I explain the meaning of a fraction and its numerator and denominator, and use my understanding to represent and compare fractions?

What strategies can be used to solve estimation problems with common and decimal fractions

 

Learning Targets:

Apply and extend previous understandings of multiplication and division to divide fractions by fractions

Solve word problems involving division of fractions by fractions.

Represent the context of a fraction word problem using a variety of models

 

Vocabulary:

decimal

place value

round

percentage

numerator

denominator

fraction

common fraction

proper fraction

improper fraction

mixed numeral

unit fraction

lowest common multiple

equivalent

 

“I can” Statements

I can add, subtract, multiply and divide rational numbers (including fractions and mixed numbers, with like denominators o with unlike denominators, with/without regrouping).

I can change freely between improper fractions and mixed numbers.

I can recognize if my answer is reasonable using estimation.

I can apply the commutative, associative, and distributive properties appropriately in multiplying and dividing rational numbers.

I can represent addition and subtraction on horizontal and vertical number lines.

I can subtract a rational number by adding its opposite (additive inverse).

I can use the absolute values of numbers on a number line to illustrate both addition and subtraction.

I can apply the properties of operations (commutative, associative, and distributive) to add and subtract rational numbers.

I can convert a fraction to a decimal using long division.

I can explain the difference between a rational and an irrational number.

I can add and subtract rational numbers in real-world situations.

I can use the four operations to solve problems involving rational numbers.

I can convert between whole numbers, fractions, and decimals.

I can estimate and compute in my head to determine whether an answer makes sense.