4 5 what is the closest 8' a. Using the preceding fifths and eighths number lines to approximate 1- number on the fifths number line for this difference? 7 3 b. Using the preceding eighths and fifths number lines to approximate 1 5' what is the closest 8. number on the eighths number line for this difference?

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Author:Erwin Kreyszig
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Differences of fractions can be approximated on number lines. For example, place the edge of a piece of paper on the fifths line below, and mark off the length \(\frac{3}{5}\). Then place the end of the marked-off length at the \(\frac{7}{8}\) point on the eighths line to approximate the difference \(1\frac{7}{8} - \frac{3}{5}\).

### Number Lines:

1. **Fifths Line:**
   - Markings: 0, \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(\frac{4}{5}\), 1, \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(\frac{4}{5}\), 2, \(\frac{1}{5}\), \(\frac{2}{5}\)

2. **Eighths Line:**
   - Markings: 0, \(\frac{2}{8}\), \(\frac{4}{8}\), \(\frac{6}{8}\), 1, \(\frac{2}{8}\), \(\frac{4}{8}\), \(\frac{6}{8}\), 2, \(\frac{2}{8}\), \(\frac{4}{8}\)

3. **Tenths Line:**
   - Markings: 0, \(\frac{2}{10}\), \(\frac{4}{10}\), \(\frac{6}{10}\), \(\frac{8}{10}\), 1, \(\frac{2}{10}\), \(\frac{4}{10}\), \(\frac{6}{10}\), \(\frac{8}{10}\), 2, \(\frac{2}{10}\), \(\frac{4}{10}\)

### Exercises:

a. Using the preceding fifths and eighths number lines to approximate \(1\frac{4}{5} - \frac{5}{8}\), what is the closest number on the fifths number line for this difference? [____]

b. Using the preceding eighths and fifths number lines to approximate \(1\frac{7}{8} - \frac{3}{5}\
Transcribed Image Text:Differences of fractions can be approximated on number lines. For example, place the edge of a piece of paper on the fifths line below, and mark off the length \(\frac{3}{5}\). Then place the end of the marked-off length at the \(\frac{7}{8}\) point on the eighths line to approximate the difference \(1\frac{7}{8} - \frac{3}{5}\). ### Number Lines: 1. **Fifths Line:** - Markings: 0, \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(\frac{4}{5}\), 1, \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(\frac{4}{5}\), 2, \(\frac{1}{5}\), \(\frac{2}{5}\) 2. **Eighths Line:** - Markings: 0, \(\frac{2}{8}\), \(\frac{4}{8}\), \(\frac{6}{8}\), 1, \(\frac{2}{8}\), \(\frac{4}{8}\), \(\frac{6}{8}\), 2, \(\frac{2}{8}\), \(\frac{4}{8}\) 3. **Tenths Line:** - Markings: 0, \(\frac{2}{10}\), \(\frac{4}{10}\), \(\frac{6}{10}\), \(\frac{8}{10}\), 1, \(\frac{2}{10}\), \(\frac{4}{10}\), \(\frac{6}{10}\), \(\frac{8}{10}\), 2, \(\frac{2}{10}\), \(\frac{4}{10}\) ### Exercises: a. Using the preceding fifths and eighths number lines to approximate \(1\frac{4}{5} - \frac{5}{8}\), what is the closest number on the fifths number line for this difference? [____] b. Using the preceding eighths and fifths number lines to approximate \(1\frac{7}{8} - \frac{3}{5}\
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