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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblema 107
Capitolo 1, Problema 107

Insert either <, >, or = in the shaded area to make a true statement. 3040−34 □ 1415⋅1514\(\frac{30}{40}\) - \(\frac{3}{4}\) \ \(\square\) \ \(\frac{14}{15}\) \(\cdot\) \(\frac{15}{14}\)

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First, simplify the left side of the inequality: calculate \(\frac{30}{40} - \frac{3}{4}\). Start by simplifying \(\frac{30}{40}\) to its lowest terms.
Next, convert both fractions on the left side to have a common denominator so you can subtract them easily.
Then, simplify the right side of the inequality: calculate \(\frac{14}{15} \cdot \frac{15}{14}\). Notice that multiplication of these fractions might simplify directly.
After simplifying both sides, compare the resulting values to determine whether the left side is less than, greater than, or equal to the right side.
Finally, insert the correct inequality symbol ($<$, $>$, or $=$) in the shaded area based on your comparison.

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Concetti chiave

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Comparing Fractions

To compare fractions, they must be expressed with a common denominator or converted to decimal form. This allows for a direct comparison of their sizes to determine which is greater, smaller, or if they are equal.
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Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Correct application ensures accurate evaluation of expressions.
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Simplifying Fractions and Products

Simplifying fractions involves reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor. Multiplying fractions requires multiplying numerators and denominators directly, followed by simplification to compare or evaluate expressions.
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