Chapter 2 - Rational Numbers
Rational Numbers: a ratio of two integers; a number that can be written as a fraction. -0.5 -1/4 7.53 6.204 -5/12 -11/19 Even this scuba diver is using rational numbers. . . . He is going 21.997 meters, or 72.168 feet below sea level. Oxygen can last about 1.23 hrs for each diver. Temperature of the water is 12.79 degrees Celsius, 55 degrees F. |
2.0 Fractions to Decimals2.0 Decimals to Fractions |
2.1 Rational Numbers7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then −(p/q ) = (−p )/q = p/(−q ). Interpret quotients of rational numbers by describing real-world contexts.
7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. |
2.2 Adding Rational Numbers7.NS.1a Describe situations in which opposite quantities combine to make 0.
7.NS.1b Understand p + q as the number located a distance ∣ q ∣ from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. |
2.3 Subtracting Rational Numbers7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p − q = p + (−q ). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. |
2.4 Multiply/Divide Rational Numbers7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (−1)(−1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers.
7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then −(p/q ) = (−p )/q = p /(−q ). Interpret quotients of rational numbers. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. |