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Title: Rational Numbers (Addition and Multiplication)
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Series: Start Learning Numbers
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Parent Series: Start Learning Mathematics
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Chapter: Numbers
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YouTube-Title: Start Learning Numbers 10 | Rational Numbers (Addition and Multiplication)
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: sln10_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Use the definition of the multiplication in $\mathbb{Q}$ to calculate the following product. Which is correct?
A1: $[(4,2)] \cdot [(6,3)] = [(24,6)]$
A2: $[(4,2)] \cdot [(6,3)] = [(6,6)]$
A3: $[(4,2)] \cdot [(6,3)] = [(10,8)]$
A4: $[(4,2)] \cdot [(6,3)] = [(12,12)]$
A5: $[(4,2)] \cdot [(6,3)] = [(4,2)]$
Q2: Use the definition of the addition in $\mathbb{Q}$ to calculate the following product. Which is correct?
A1: $[(4,2)] + [(1,3)] = [(14,6)]$
A2: $[(4,2)] + [(1,3)] = [(10,5)]$
A3: $[(4,2)] + [(1,3)] = [(5,5)]$
A4: $[(4,2)] + [(1,3)] = [(8,3)]$
A5: $[(4,2)] + [(1,3)] = [(0,1)]$
Q3: What is not correct?
A1: $(\mathbb{Q}, \cdot)$ is an abelian group.
A2: $(\mathbb{Q}, +)$ is an abelian group.
A3: $\mathbb{Q}$ together with the addition and multiplication is a field.
A4: $\mathbb{Q}$ together with the addition and multiplication satisfies the common distributive laws.
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Last update: 2025-07
