Bell Work: Find a number which decreased by 18 equals 5 times its opposite.

Answer: N – 18 = 5(-N) N – 18 = -5N +18 +18 N = -5N + 18 +5N +5N 6N = 18 N = 3

Lesson 33: Products of Prime Factors, Statements About Unequal Quantities

The number 6 can be composed by multiplying the two counting numbers 3 and 2. 3 x 2 = 6 6 is a composite number.

Composite Number*: the product of two counting numbers that are both greater than 1.

The number 35 is also a composite number because it can be composed as the product of the counting numbers 5 and 7. 5 x 7 = 35

The number 1 must be one of the factors if we wish to compose 17 by multiplying. 17 x 1 = 17 The number 1 must also be a factor if we wish to compose either 3, 11 or 23. 1 x 3 = 3 1 x 11 = 11 1 x 23 = 23

Since these numbers can be composed only if 1 is one of the factors, we do not call these numbers composite numbers. We call them prime numbers.

Prime Number*: a counting number greater than 1 whose only counting number factors are 1 and the number itself.

The number 12 can be written as a product of integral factors in four different ways. 12 x 1 4 x 3 2 x 6 2 x 2 x 3

In 12 x 1, 4 x 3, and 2 x 6, one of the factors is not a prime number, but in 2 x 2 x 3 all three of the factors are prime numbers. A prime factor is a factor that is a prime number. To find the prime factors of a counting number, we divide by prime numbers.

Example: Express 80 as a product of prime factors Example: Express 80 as a product of prime factors. Start by dividing by prime numbers. 80 = 40 40 = 20 20 = 10 10 = 5 2 2 2 2 Using the five factors we have found, we can express 80 as a product of prime factors as 2 x 2 x 2 x 2 x 5

Practice: Express 147 as a product of prime factors.

Answer: 147 = 49 49 = 7 3 7 3 x 7 x 7

Statements about unequal quantities: Often a word problem makes a statement about quantities that differ by a specified amount. Thus, the statement tells us that the quantities are not equals, and our task is to write an equation about quantities that are equal. To perform this task, we must add as required so that both sides of the equation represent equal quantities.

Example: Twice a number is 42 less than -102. Find the number.

Answer: The problem said that 2N was 42 less than -102, so we must add 42 to 2N or we must add -42 to -102. 2N + 42 = -102 0r 2N = -102 – 42 -42 -42 2N = -144 2N = -144 N = -72 N = -72

Check answer: 2(-72) + 42 = -102 -144 + 42 = -102 -102 = -102 Correct

Practice: Five times a number is 72 greater than the opposite of the number. Find the number.

Answer: 5N – 72 = -N or 5N = -N + 72 +N +72 +N +72 +N +N 6N = 72 6N = 72 N = 12 N = 12

Check answer: 5(12) – 72 = -12 60 – 72 = -12 -12 = -12 Correct

Practice: If the sum of twice a number and -14 is multiplied by 2, the result is 12 greater than the opposite of the number. Find the number.

Answer: 2(2N – 14) – 12 = -N or 2(2N – 14) = -N + 12 N = 8 N = 8 Check 2(2 x 8 – 14) – 12 = -8 2(2) – 12 = -8 -8 = -8

Practice: Five times a number is 21 less than twice the opposite of the number. What is the number?

Answer: 5N + 21 = 2(-N) N = -3 Check: 5(-3) + 21 = 2(3) -15 + 21 = 6 6 = 6

HW: Lesson 33 #1-30 Due Tomorrow