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This lesson dives into rational numbers — what they are, how to recognize them, and how to work with them confidently. From college graduation rates expressed as hard-to-compare fractions, to the hidden math behind stacked retail discounts and unit conversions, Section 3.4 of Contemporary Mathematics shows why understanding fractions is a genuinely practical life skill. Along the way, the lesson also explores the remarkable density property: the idea that between any two rational numbers, you can always find another one. In this video: • Defining rational numbers as ratios of integers, illustrated with pizza slices and groups of hat-wearing people • Identifying terminating decimals (like 1.34) and repeating decimals (like 4.3636…) as rational, and square roots of non-perfect squares (like √10) as irrational • Testing fraction equivalence using cross-multiplication, and why the rule matters beyond a calculator when variables replace numbers • Why adding fractions requires a common denominator (counting identical units) while multiplying does not (scaling a fraction of a fraction) • Dividing fractions by flipping to find the reciprocal — explained through how many halves fit into 10 wholes • The repeated-discount trap: how a 50% + 25% sale actually yields 62.5% off, not 75%, because each discount applies to a new, smaller whole • Unit conversion as fraction multiplication — using liters-to-gallons as an example where units cancel like variables #OpenStax #RationalNumbers #ContemporaryMath #Fractions #Mathematics OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
Answer each question based only on what was presented in the video lesson. No outside knowledge is required — every answer can be found in the video.
Apply the concepts from the video to solve problems involving rational numbers, equivalent fractions, fraction operations, percentages, and unit conversions. Show all work; problems increase in difficulty.
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