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Bars showing where PDF bytes usually sit, with embedded images dominant, then fonts, duplicated resources and metadata, beside two columns splitting lossless steps that change nothing visible, such as compressing streams, subsetting fonts and deduplicating resources, from lossy steps that trade quality for size, such as downsampling images and lowering JPEG quality, plus the arithmetic that a Letter page at 300 dpi is about 8.4 million pixels and about 2.1 million at 150 dpi.
Web ToolsUpdated 4 Sept 20268 min

How PDF Compression Works

PDF compression reduces file size by compressing images, fonts, and streams. Learn how lossy and lossless compression apply, and how to shrink PDFs without ruining them.

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Three panels run across the width. The first, labelled ratio, shows three dots above two dots with the value 3 to 2 and the caption three cups of flour to two cups of water. An arrow labelled times 3 leads to the second panel, labelled equivalent ratio, showing nine dots above six dots with the value 9 to 6 and the caption that every term is multiplied by the same number. A second arrow leads to the third panel, labelled proportion, reading 3 over 2 equals 9 over 6 and described as an equation, so it can be checked and solved for a missing term. A check band explains that cross products must match: 3 times 6 is 18 and 2 times 9 is 18, so 9 to 6 is equivalent, and that dividing every term of 9 to 6 by 3 returns 3 to 2. A solving band shows 3 over 2 equals x over 10 giving 3 times 10 equals 2 times x, so x is 15, meaning 10 cups of water needs 15 cups of flour. A closing band warns that part-to-part is not part-to-whole: a 3 to 2 ratio is 5 parts, so the shares are 3 fifths and 2 fifths, which is 60 percent and 40 percent, not 30 percent and 20 percent.
MathUpdated 31 Aug 202610 min

Ratios and Proportions Explained

A ratio compares quantities. A proportion states that two ratios are equal. Learn the notation, how to simplify and scale, how to solve proportions two ways, unit rates, and when proportional reasoning breaks down.

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