In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14

Verified step by step guidance

1. Convert the fractions on the left side of the inequality to have a common denominator.
2. Calculate the left side: $\frac{30}{40}-\frac{3}{4}$.
3. Simplify the left side by finding a common denominator and performing the subtraction.
4. Calculate the right side: $\frac{14}{15}\cdot \frac{15}{14}$.
5. Simplify the right side by multiplying the fractions and reducing the result.

Key Concepts

Fractions and Operations

Understanding fractions is crucial for this problem, as it involves comparing two expressions that are both in fractional form. Operations with fractions, such as addition, subtraction, multiplication, and division, must be performed correctly to evaluate the expressions accurately.

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value. Recognizing and simplifying fractions to their lowest terms can help in comparing them more easily, which is essential for determining the correct inequality symbol (<, >, or =).

Order of Operations

The order of operations (PEMDAS/BODMAS) dictates the sequence in which mathematical operations should be performed. This concept is important when evaluating expressions to ensure that calculations are done correctly, especially when dealing with multiple operations within the fractions.