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to practice showing work, which is required on Tests. Show steps of solving, e example videos. Work must be shown for full credit. \[ \text { 2. }-\frac{1}{3} \div\left(-\frac{5}{6}\right) \]

Ask by Collins Mejia. in the United States
Feb 13,2025

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\[ -\frac{1}{3} \div \left(-\frac{5}{6}\right) = \frac{2}{5} \]

Solución

We are given:   –1/3 ÷ (–5/6) Step 1. Write the Division as Multiplication by the Reciprocal  A division by a fraction is the same as multiplying by its reciprocal.   –1/3 ÷ (–5/6) = –1/3 × (reciprocal of –5/6) Step 2. Determine the Reciprocal  The reciprocal of –5/6 is –6/5 (flip numerator and denominator, keeping the same sign). Step 3. Multiply the Two Fractions  Now multiply:   –1/3 × –6/5  Multiply numerators and denominators:   Numerator: (–1) × (–6)   Denominator: 3 × 5 Step 4. Calculate the Products   (–1) × (–6) = 6       (Since a negative times a negative is positive)   3 × 5 = 15  Thus, the product is 6/15. Step 5. Simplify the Fraction  Both 6 and 15 are divisible by 3:   6 ÷ 3 = 2   15 ÷ 3 = 5  So, 6/15 simplifies to 2/5. Final Answer: 2/5 This step-by-step solution shows the work needed to arrive at the answer.

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To solve \(-\frac{1}{3} \div \left(-\frac{5}{6}\right)\), start by flipping the second fraction and changing the division to multiplication: \[ -\frac{1}{3} \times \left(-\frac{6}{5}\right) = \frac{1}{3} \times \frac{6}{5} \] Next, multiply the numerators and the denominators: \[ \frac{1 \times 6}{3 \times 5} = \frac{6}{15} \] Finally, simplify \(\frac{6}{15}\) by dividing both the numerator and the denominator by their greatest common divisor (3): \[ \frac{6 \div 3}{15 \div 3} = \frac{2}{5} \] Another helpful practice is to familiarize yourself with the process of changing signs when dealing with negative numbers. It can be tricky since you have to keep track of the negatives while simplifying fractions. A fun way to practice might include creating flashcards that depict different fraction problems with varying signs, helping you get a visual understanding of how they interact! Additionally, if you're interested in further exploring fractions, consider resources like educational YouTube channels, which often create engaging content illustrating complex mathematical concepts. For example, channels like "Khan Academy" or "Math Antics" provide step-by-step guidance in an easy-to-understand format, perfect for both beginners and those looking to sharpen their skills!

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