Ordering the Expressions from Least Value to Greatest Value

Oct 13, 2025 by recoveryshake.com 48 views

In mathematics, ordering expressions from least value to greatest value is an essential skill that requires a deep understanding of mathematical operations and properties. In this article, we will explore three different expressions and order them from least value to greatest value.

Expression 1: Mixed Numbers and Fractions

The first expression is a combination of mixed numbers and fractions: $ -3 \frac{3}{10} - \left(-\frac{7}{200}\right) + 5 \frac{6}{15} + \left(-2 \frac{4}{5}\right) $. To order this expression from least value to greatest value, we need to follow the order of operations (PEMDAS):

Evaluate the expressions inside the parentheses: $ -3 \frac{3}{10} $ and $ -2 \frac{4}{5} $.
Convert the mixed numbers to improper fractions: $ -3 \frac{3}{10} = \frac{-33}{10} $ and $ -2 \frac{4}{5} = \frac{-14}{5} $.
Simplify the fractions: $ \frac{-33}{10} = -3.3 $ and $ \frac{-14}{5} = -2.8 $.
Evaluate the expression: $ -3.3 - (-0.035) + 5.4 + (-2.8) $.
Simplify the expression: $ -3.3 + 0.035 + 5.4 - 2.8 = -0.655 $.

Expression 2: Multiplication of Negative Numbers

The second expression is a multiplication of negative numbers: $ -4.5 \times -2.3 $. When multiplying two negative numbers, the result is always positive.

Multiply the numbers: $ -4.5 \times -2.3 = 10.35 $.

Expression 3: Division of a Fraction

The third expression is a division of a fraction: $ \frac{5}{-1.6} $. When dividing a fraction by a negative number, the result is always negative.

Divide the fraction: $ \frac{5}{-1.6} = -3.125 $.

Ordering the Expressions from Least Value to Greatest Value

Now that we have evaluated each expression, we can order them from least value to greatest value:

$ -0.655 $
$ -3.125 $
$ 10.35 $

In conclusion, ordering expressions from least value to greatest value requires a deep understanding of mathematical operations and properties. By following the order of operations and simplifying expressions, we can accurately determine the order of the expressions.

Key Takeaways

When ordering expressions from least value to greatest value, follow the order of operations (PEMDAS).
Simplify expressions by evaluating expressions inside parentheses, converting mixed numbers to improper fractions, and simplifying fractions.
When multiplying two negative numbers, the result is always positive.
When dividing a fraction by a negative number, the result is always negative.

Practice Problems

Order the expressions from least value to greatest value: $ 2 \frac{3}{4} - \left(-\frac{1}{2}\right) + 1 \frac{1}{3} + \left(-3 \frac{1}{4}\right) $.
Order the expressions from least value to greatest value: $ -6 \times -2.5 $.
Order the expressions from least value to greatest value: $ \frac{3}{-2.5} $.

Answer Key

$ 2.25 + 0.5 + 1.33 - 3.25 = 0.83 $
$ 15 $
$ -1.2 $