Fractions are a different way to write a division problem
Fractions have two parts: a top or numerator, and a bottom or denominator
The numerator tells what part you have and the denominator tells you the total number of pieces
Understanding Fractions II
If the numerator is smaller than the denominator the fractions is less than 1
If the numerator is bigger than the denominator the fractions is worth more than 1
If the top and bottom are the same the fraction is exactly 1
Understanding Fractions III
To make a fraction strip or number line using fractions ?cut the strip or line into the same number of pieces as the denominator. Use the top number to count over that many spaces or sections from the left edge.
Mixed Numbers I
A number that has both a whole part and a fraction part is called a mixed number You can change fractions into mixed numbers and mixed numbers into fractions
Mixed Numbers II
To turn a fraction into a mixed number you simply divide (numerator / denominator) i.e. 22/7= 3r1, so 3 and 1/7 (answer and remainder over divisor. ?Notice that the denominator DOES NOT CHANGE)
Mixed Numbers III
To turn a mixed number into a fraction you multiply bottom times the side plus the top, ?so 3 1/2= 2x3+1 or 7? the denominator DOES NOT CHANGE so the final answer is 7/2
Least Common Multiples I
Least Common Multiples (also called LCM's or LCD's) are used to make the denominators of two or more fractions the same. This is done because you CANNOT add, subtract, compare, or put fractions in order unless the denominators are the same
Least Common Multiples II
To find the least common multiple of two denominators you need to:
Make a sideways t-chart
List your multiples (or math facts) for each number
Find the smallest thing the two numbers have in common
Comparing Fractions
To compare two fractions you need to:
Find the LCM of the denominators
Remember that whatever you do to change the bottom numbers you must also do to the top
REMEMBER: you cannot compare two fractions unless their denominators are the same
Putting Fractions in Order
To put three or more fractions in order you need to:
Find the LCM of the denominators
Whatever you do to the bottom you must also do to the top
Remember: you cannot put fractions in order unless all the denominators are the same
Read and follow directions (big-small or small-big)
UNIT 9 (part 2) Prime, Composite, and Square Numbers; Greatest Common Factors (GCF?s); Equivalent Fractions; Putting Fractions in Simplest or Lowest Terms
Prime Numbers
A PRIME number is only divisible by 1 and itself
?another way to think of it is that it has only 2 factors 1 and itself
?a third way to think of it is one and the number is the only multiplication problem that will give you the number as an answer
?for example 47 can only be made by multiplying 1 and 47?so 47 is PRIME
Composite Numbers
A COMPOSITE number can be made in more than one way. Not only can 1 times the number make the number, but there will be another combination as well. Use your math facts and divisibility rules to help you. For example 32 can be made from 1x32, 2x16, and 4x8?so it is a composite number
Square Numbers
A SQUARE number is a composite number that can be reached by multiply the same numbers together. For example 9 is a square number because I can reach it when I multiply identical numbers together 3x3. 25 is also a square number 5x5, as is 64 (8x8)?square numbers will become much more important in Algebra
Greatest Common Factors I
Greatest Common Factors (or GCF's) are used to reduce a fraction to lowest terms or put it in simplest form. This is a special way of writing the final answer to your fraction problems. All answers will have to be put in lowest terms (or simplest form) in order to be counted right. YOU CAN ALSO YOU PRIME FACTORIZATION AND REPEATED DIVISION TO REDUCE FRACTIONS.
Greatest Common Factors II
After you have finished a fraction problem you will need to put it in simplest form (sometimes called lowest terms). In order to do this you will need to find ALL of the FACTORS for both the numerator and denominator. Factors are the ways to make a number using multiplication?like what we do to find composite numbers (only we have to find ALL of them when we?re searching for the GCF)
Greatest Common Factors III
You can use math facts, divisibility rules, knowledge of prime numbers, etc?to help you find the factors. It helps to search for factors in a sequence or order (for example lowest to highest) REMEMBER: if the numerator is 1 it cannot be reduced; if the top and bottom are one apart it cannot be reduced; if the top and bottom are the same it is 1; and if the top and bottom are even it CAN be reduced.
Greatest Common Factors IV
Example: My answer to a math problem is 12/16?I need to find the factors for 12 and 16?12 can be made by 1x12, 2x6, and 3x4?16 can be made by 1x16, 2x8, and 4x4?the GCF is 4, so I need to divide the top and bottom of the fraction by 4?the answer is � (a fraction is simplest form)
Equivalent Fractions
Equivalent fractions look different but have the same value ?for example 2/4 and 8/16 are equivalent ?they both mean one half
To make an equivalent fraction simply multiply the top and bottom by the same number
To determine if two fractions are equivalent you have three options
?1) can you multiply top and bottom by the same number
2) you can cross multiply, and
3) you can change the fractions to decimals and compare them
Adding and Subtracting Fractions
Step 1: use least common multiple to make the bottom numbers the same
Step 2: add or subtract the top numbers
Step 3: ask 2 questions 1) is it improper? 2) can it be reduced?
Step 4: change to mixed number (if needed) or reduce the fraction using GCF
Adding and Subtracting Mixed Numbers
Stack the numbers Add or subtract the fraction side ?borrowing from the whole number or carrying to the whole number if you need to
Add or subtract the whole number side (change from improper to mixed and reduce the fraction if necessary)
Combine the whole number answer with the fraction answer
Multiplying Fractions
The denominators DO NOT need to be the same in multiplication (only in addition and subtraction) Simply multiply the tops, and multiply the bottoms. Make sure to ask the 2 questions about your answer?1) is it improper?, and 2) can it be reduced ?
Estimating with Fractions
Whether it's adding, subtracting, comparing, ordering, or multiplying fractions the process is the same for estimation Round all fractions in the problem to the nearest half or whole number, then complete the operation with the rounded numbers 4/5 + 1/3 would round to 1 + �, so the answer would be 1 1/2. When you have mixed numbers you can round as above or use front-end estimation like the book shows.