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Simplify by reducing the index of the radical.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 109
In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 8/13÷8/13 □ |−1|
Guida verificata passo dopo passo1
Step 1: Simplify the left-hand side of the inequality. The expression is \( \frac{8}{13} \div \frac{8}{13} \). Recall that dividing fractions involves multiplying by the reciprocal of the second fraction. This means \( \frac{8}{13} \div \frac{8}{13} = \frac{8}{13} \times \frac{13}{8} \).
Step 2: Multiply the numerators and denominators of the fractions. \( \frac{8}{13} \times \frac{13}{8} = \frac{8 \cdot 13}{13 \cdot 8} \). Simplify the fraction by canceling out the common terms in the numerator and denominator, which results in \( 1 \).
Step 3: Simplify the right-hand side of the inequality. The expression is \( | -1 | \), which represents the absolute value of \( -1 \). Recall that the absolute value of a number is its distance from zero on the number line, so \( | -1 | = 1 \).
Step 4: Compare the simplified left-hand side and right-hand side. The left-hand side is \( 1 \), and the right-hand side is also \( 1 \).
Step 5: Insert the appropriate symbol (\( = \)) in the shaded area to make the statement true. The final inequality is \( \frac{8}{13} \div \frac{8}{13} = | -1 | \).
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Division of Fractions
To divide fractions, you multiply the first fraction by the reciprocal of the second. In this case, 8/13 ÷ 8/13 simplifies to 8/13 × 13/8, which equals 1. Understanding this operation is crucial for evaluating the expression correctly.
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05:45
Radical Expressions with Fractions
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, |−1| equals 1. Recognizing how absolute values work is essential for comparing the results of the division with the absolute value in the expression.
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7:12Parabolas as Conic Sections Example 1
Inequality Symbols
Inequality symbols (<, >, =) are used to compare two values. Understanding how to interpret these symbols is vital for determining the correct relationship between the results of the division and the absolute value, allowing you to fill in the shaded area accurately.
Video consigliato:
06:07Linear Inequalities
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