Number & Operations - Fractions

Fractions 

The top part of a fraction is called the numerator and the bottom part is the denominator.  The denominator shows how many equal parts are in the whole amount and the numerator shows how many of them you're talking about.   Example, 3/4  If you cut an apple into four equal pieces  and eat three of them, you've eaten 3 out of 4 pieces.  As a fraction this is 3/4.  The numerator is 3 and the denominator is 4. 

Proper Fractions:  the numerator is smaller than the denominator    Example, 5/6

Improper Fractions:  the numerator is bigger than its denominator   Example,  8/6

Mixed Number:  is made up of a whole number and a fraction    Example,  2 2/3 

Equivalent Fractions:  fractions are worth the same as each other, even though they look different.  Exampler,  1/2 is equivalent to 2/4 and 3/6, and 4/8.  

Changing an improper fraction to a mixed number:   Example,   9/2

9/2 = 9 divide 2 = 4 1/2  (2 goes into 9 four times, with a half left over. 


Fractions on a number line:

Fractions of quantities:

Adding Fractions:

Subtraction Fractions:

Multiplying Fractions:

Dividing Fractions: 

Mixed Numbers:

Improper Fractions: 

Decimals:

A decimal is made up of whole numbers and parts of whole numbers, separated by a dot called a decimal point.  Examples;  0.1  22.3

Decimal Fractions:

Mixed decimals: 

Recurring decimals:

Decimal Places:

Changing decimals to fractions & changing fractions to decimals 

Adding decimals: If you know how to add whole numbers, you also know how to add decimals.  With both decimals and whole nubmers, there are a few important things to remember.  Pay attention to place value, add in each place, and regroup when needed.   You  still need to line up the ones digit.  This means the decimal points line up, too. 

Subtracting decimals:  If you knkow how to subract whole numbers, you also know how to subctract decimals.  With both decimals and whole numbers, there are a few things to remember.  Pay attention to place value, subtract in each place, and regroup when you have to.  Be sure to line up the ones (or the decimal points).

Multiplying decimals:  You multiply decimals the same way you multiply whole numbers.  The only difference is that you must correctly place a decimal point in the product.  Compare these two multiplication problems. 

   37

x 45

______

1665 

   3.7

x 4.5

______

16.65

Dividing decimals: When you divide a decimal by a whole number, you place the decimal point for the quotient directly above the decimal point in the dividend.  Then you divide the same way you divide whole numbers.