Exploring Operations with Rational Numbers

This video tutorial covers lesson 4-6, focusing on applying rational number operations using the order of operations, PMZ (parentheses, exponents, multiplication, division, addition, subtraction). It includes two examples demonstrating how to evaluate expressions by substituting values and simplifying using common factors and least common multiples. The video emphasizes understanding the order of operations and provides detailed steps for solving expressions with rational numbers.

What does PMZ stand for in the order of operations?

• Parentheses, Multiplication, Zero

• Parentheses, Exponents, Multiplication, Division, Subtraction, Addition

• Parentheses, Exponents, Multiplication, Zero

• Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

What is the first step in the order of operations?

• Evaluate exponents

• Perform multiplication and division

• Evaluate expressions inside parentheses

• Perform addition and subtraction

In the expression a * b + c - d, if a = 56, b = -4/5, c = 75/100, and d = 1/3, what is the first operation to perform?

• Division

• Multiplication

• Subtraction

• Addition

When multiplying fractions, what should you do first?

• Add the numerators

• Multiply straight across

• Divide by common factors

• Subtract the denominators

After multiplying fractions, what is the next step in the order of operations?

• Perform division

• Evaluate expressions inside parentheses

• Perform addition and subtraction

• Evaluate exponents

In the expression 2/5 * x + y + z, if x = 7/8, y = -1/4, and z = -2/3, what is the first step?

• Evaluate expressions inside parentheses

• Add y and z

• Multiply 2/5 by x

• Subtract y from z

What is the least common multiple (LCM) of 4 and 8?

• 4

• 8

• 16

• 12

When adding fractions with different denominators, what should you do first?

• Multiply the fractions

• Subtract the denominators

• Find a common denominator

• Add the numerators

What is the result of adding 1/4 and -2/3 with a common denominator of 12?

• 5/12

• 1/12

• -5/12

• -1/12

What should you do if you have fractions with different signs?

• Add the absolute values

• Subtract the absolute values and keep the sign of the larger absolute value

• Multiply the fractions

• Divide the fractions