Download 7th grade Math

7th grade Math
Chapter 4 Number Patterns and Fractions
Notes
FACTORING
A prime number is a whole number greater than 1 whose only whole number factors are 1
and itself. Examples: 2, 11, 23
A composite number is a whole number greater than 1 that has whole number factors
other than 1 and itself. Examples: 6, 15, 49
To factor a whole number as a product of
prime numbers is called prime factorization.
We can use a diagram called a factor tree to
make this easier. We would write the factors
of 108 as: 22 · 33
GREATEST COMMON FACTOR
The greatest common factor (often written GCF) is the greatest factor that is common to
two or more nonzero whole numbers. There are at least three strategies we can use to
find GCF.
Method 1 – List all the factors of each number, circle the common ones and find the
greatest of these.
Method 2 – Write the prime factorization of each number, find the common factors and
multiply.
Method 3 –Place the numbers in a box, then write a common factor to the left; under each
number write the answer if you divide the number by the factor. Continue until the
numbers are relatively prime. The GCF is the product of the factors in the left column.
2 [ 42 12
3 [ 21 6
7
2
the GCF is 2·3 = 6
Numbers are relatively prime if their greatest common factor is 1.
FRACTIONS
A fraction is a number of the form a/b, where a is called the numerator and b is called the
denominator. Equivalent fractions are fractions that are equal. A fraction is in simplest
form if the numerator and denominator are relatively prime.
LEAST COMMON MULTIPLE
A multiple of a number is a product of the number and any nonzero number. The least
common multiple (LCM) of two or more numbers is the least of all the shared multiples.
There are at least three strategies we can use to find LCM.
Method 1 – List all the multiples of each number, circle the common ones and find the
least of these.
Method 2 – Write the prime factorization of each number, find the common factors and
multiply, then multiply by each of the non-common factors
Method 3 –Place the numbers in a box, then write a common factor to the left; under each
number write the answer if you divide the number by the factor. Continue until the
numbers are relatively prime. The LCM is the product of the factors in the left column
multiplied by the numbers left across the bottom.
2 [ 42 12
3 [ 21 6
7
2
the LCM is 2·3·7·2 = 84
COMPARING AND ORDERING FRACTIONS
You can compare fractions by using the LCM of the denominators, this is called the least
common denominator (LCD).
A mixed number has a whole number part and a fraction part. A proper fraction is a
fraction where the numerator is less than the denominator. An improper fraction is a
fraction where the numerator is more than the denominator.
W n/d = (W·d +n)/d
FRACTIONS AND DECIMALS
When a division problem results in a remainder of 0, the quotient is a terminating
decimal. If one or more of the digits repeat without end, this is called a repeating
decimal.
To change a fraction to a decimal, divide the numerator by the denominator.
To change a decimal to a fraction, follow the “three R’s”: Read it, Rite it, Reduce it.