上一片，🧮 小算盘机器人带你逛了 0 左边的负数世界。这一片它只问一个问题：不管在 0 的左边还是右边，只看“离 0 有多远”，会怎样？Last leaf, 🧮 the tiny abacus robot toured the negative world left of zero. This leaf it asks just one question: forget left or right — what if we only care how far a number sits from 0?
第 1 步：距离不问方向Step 1: Distance ignores direction
先看跑步机：它从不问你面朝哪边。Start with a treadmill: it never asks which way you face.
小机器人在跑步机上跑，屏幕只显示“4 公里”——不管你朝前跑还是朝后跑，跑过的路程都是 4 公里。距离就是这样：它只问“多远”，从不问“哪个方向”。The robot runs on a treadmill and the screen shows “4 km” — whether you run facing forward or backward, you've covered 4 km. That's what distance is like: it asks “how far”, never “which way”.
那把“距离”搬到数轴上，会得到什么？Now put that idea of distance onto the number line — what do we get?
第 2 步：-4 和 4 一样远Step 2: -4 and 4 are equally far
数轴上，-4 在 0 左边 4 格，4 在 0 右边 4 格。方向相反，可离 0 的距离一样，都是 4。离 0 的距离有个专门的名字：绝对值，写作两条竖线 | |。所以 |-4| = 4，|4| = 4。On the number line, -4 sits 4 steps left of 0 and 4 sits 4 steps right of 0. Opposite directions — same distance from 0. That distance has a name: absolute value, written with two vertical bars | |. So |-4| = 4 and |4| = 4.
生活里还有哪些“不问方向的距离”？Where else do we meet direction-free distances?
第 3 步：地图上的距离Step 3: Distance on a map
从学校走到广场是 3 公里，从广场走回学校也是 3 公里——地图上的距离不分方向。绝对值就是数轴上的“距离牌”：|x| 念作“x 的绝对值”，表示 x 到 0 的距离，永远不会是负的。School to the square is 3 km, and the square back to school is also 3 km — map distance has no direction. Absolute value is the number line's distance sign: |x| means “the distance from x to 0”, and it is never negative.
🎮 你来把两点归位（30 秒）🎮 Your turn: put both dots in place (30 seconds)
题目给出 |x|，拖动两个滑块，把两个答案都拖到位——4 组全对，就撒花。Each task gives |x|. Drag the two sliders to place both answers — finish all 4 pairs and confetti falls.
一句话记住它：绝对值 = 离 0 有多远，不问方向；|x| = a 有两个答案——a 和 -a。Remember it in one line: absolute value is how far from 0, no direction; |x| = a has two answers — a and -a.
绝对值就是到 0 的距离，永远不为负Absolute value is the distance to 0, never negative|-4| = |4| = 4：左右两点，离 0 一样远|-4| = |4| = 4: two points, one distance|x| = a（a > 0）有两个解：x = a 和 x = -a|x| = a (a > 0) has two solutions: x = a and x = -a
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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