Rational Numbers. Because you can divide any integer by any nonzero integer, you can use long division to write fractions and mixed numbers as decimals.

Rational Numbers

A rational number is a number that can be written as where a and b are integers and b ≠ 0.

Because you can divide any integer by any nonzero integer, you can use long division to write fractions and mixed numbers as decimals. These decimals are also rational numbers and will either terminate or repeat.

A terminating decimal is a decimal that ends.For example: 1.5, −0.25, 10.625A repeating decimal is a decimal that has a pattern that repeats.For example: −1.333 . . . = −1. 3 0.151515 . . . = 0. 15

Modeling

Write -2 as a decimal.

Write as a decimal.

Practice

1.

Modeling

Write −0.26 as a fraction in simplest form.

Practice

Write the decimal as a fraction or a mixed number in simplest form.5. −0.7 6. 0.125 7. −3.1 8. −10.25

Modeling

A box turtle hibernates in sand at feet. A spotted turtle hibernates at feet. Which turtle is deeper?

Practice

You lose one quarter, two dimes, and two nickels.a. Write the amount as a decimal.b. Write the amount as a fraction in simplest form.

Lesson Beginning

Copy and complete the statement.a. -0.85 ___

Commutative Property of Addition

Words: In a sum, you can add terms in any order.Numbers: 5 + (-6) -6 + 5Algebra: a + b b + a

Commutative Property of Multiplication

Words: In a product, you can multiply factors in any order.Numbers: 4(-7) -7(4)Algebra: ab ba

Associative Property of Addition

Words: Changing the grouping of terms will not change the sum.Numbers:(9 + 8) + 6 9 + (8 +6)Algebra:(a + b) + c a +(b + c)

Associative Property of Multiplication

Words: Changing the grouping of factors will not change the product.Numbers:(2 x 3) x 4 2 x (3 x 4)Algebra:(ab)c a(bc)

Inverse Property of Addition

Words:The sum of a number and its additive inverse, or opposite, is 0.Numbers:5 + (-5) 0Algebra:a + (-a) 0

Inverse Property of Multiplication

Words: The product of a non zero number and its multiplicative inverse ,or reciprocal, is 1.Numbers: x Algebra:For nonzero integers a and b,

Identity Property of Addition

Words: The sum of a number and the additive identity, 0, is the number.Numbers: -7 + 0 = -7Algebra: a + 0 = a

Identity Property of Multiplication

Words: The product of a number and the multiplicative identity , 1, is the number.Numbers: 9 x 1 = 9Algebra: a(1) = a

Modeling

Identify the properties.

a. -3.5 + 3.5 = 0b. -4 + 8 = 8 + (-4)c. (-7.9)(1) = -7.9

Practice

Tell which property is being illustrated.a. -3 + 0 = -3b. 15 x 8 = 8 x 15c. (5 + 4) + 6 = 5 + (4 + 6)

Modeling

Evaluate the expression. Justify each step.-10.6 + 3 + (-4.4)

Modeling

Evaluate the expression. Justify each step you take.

PracticeEvaluate the expression. Justify each step you take.a. -25 (7) (-4)

Homework

Pg 304 # 1, 2, 3 – 37 odd