[tex]\left(-1 \frac{2}{7}\right) \times 1 \frac{5}{9}[/tex]
Answer (2)
Convert the mixed fractions to improper fractions: − 1 7 2 = − 7 9 and 1 9 5 = 9 14 .
Multiply the improper fractions: ( − 7 9 ) × 9 14 = − 7 × 9 9 × 14 .
Simplify the fraction by canceling common factors: − 7 × 9 9 × 14 = − 2 .
The final answer is − 2 .
Explanation
Understanding the Problem We are given the expression ( − 1 7 2 ) × 1 9 5 . Our goal is to evaluate this expression and simplify the result.
Converting to Improper Fractions First, we convert the mixed fractions to improper fractions. − 1 7 2 = − 7 1 × 7 + 2 = − 7 9 1 9 5 = 9 1 × 9 + 5 = 9 14
Multiplying the Fractions Now, we multiply the improper fractions: ( − 7 9 ) × 9 14 = − 7 × 9 9 × 14
Simplifying the Result We can simplify the fraction by canceling common factors. Both the numerator and denominator have a factor of 9. Also, 14 and 7 have a common factor of 7. So we have: − 7 × 9 9 × 14 = − 7 × 9 9 × ( 2 × 7 ) = − 2
Final Answer Therefore, the result of the expression is -2.
Examples
Mixed fractions are commonly used in everyday situations, such as cooking and baking. For example, if a recipe calls for 1 2 1 cups of flour and you want to double the recipe, you would need to multiply 1 2 1 by 2. This involves converting the mixed fraction to an improper fraction, multiplying, and then converting back to a mixed fraction if necessary. Understanding how to perform these operations is essential for accurate measurements and successful cooking.
To evaluate ( − 1 7 2 ) × ( 1 9 5 ) , first convert the mixed numbers to improper fractions, resulting in − 7 9 and \frac{14}{9}. Multiply the fractions to get − 7 14 , which simplifies to − 2 . Thus, the final answer is − 2 .
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