7Th Grade Math Chapter 4 Number Patterns and Fractions Notes

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.