Textbook Question
Determine whether each statement is true or false. {x | x is a natural number less than 3}= {1, 2}
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0. Review of Algebra
Exponents
2:42 minutesProblem 49
Textbook Question
Multiply or divide as indicated. Write answers in lowest terms as needed.
Verified step by step guidance1
First, convert the mixed numbers to improper fractions. For 2(1/2), multiply the whole number 2 by the denominator 2 and add the numerator 1: \(2 \times 2 + 1 = 5\), so \(2(1/2) = \frac{5}{2}\). For 1(5/7), multiply the whole number 1 by the denominator 7 and add the numerator 5: \(1 \times 7 + 5 = 12\), so \(1(5/7) = \frac{12}{7}\).
Rewrite the original expression using the improper fractions: \(\frac{5}{2} \div \frac{12}{7}\).
Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the division as multiplication by flipping the second fraction: \(\frac{5}{2} \times \frac{7}{12}\).
Multiply the numerators together and the denominators together: numerator \(5 \times 7 = 35\), denominator \(2 \times 12 = 24\), so the product is \(\frac{35}{24}\).
Simplify the fraction \(\frac{35}{24}\) if possible by finding the greatest common divisor (GCD) of 35 and 24 and dividing numerator and denominator by it. If no common factors other than 1 exist, the fraction is already in lowest terms.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mixed Numbers and Improper Fractions
Mixed numbers combine a whole number and a fraction, such as 2(1/2). To perform operations, convert mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator. This simplifies calculations like multiplication and division.
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Dividing Complex Numbers
Division of Fractions
Dividing fractions involves multiplying by the reciprocal of the divisor. For example, to divide by 1(5/7), first convert it to an improper fraction, then flip it and multiply. This method transforms division problems into multiplication ones, making them easier to solve.
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Simplifying Fractions
After performing multiplication or division, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). Simplifying ensures the answer is in lowest terms, making it clearer and easier to interpret.
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