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Understanding the Relationship Between Fractions and Decimals in Mathematics

This educational text explores the connection between fractions and decimals, providing clarity on how to convert between the two. It covers fundamental concepts such as identifying what fraction or decimal part of a figure is highlighted, writing decimals as fractions, and simplifying those fractions. The document also delves into the process of dividing to express fractions as decimals, distinguishing between terminating and repeating decimals, and emphasizes the importance of division in this context. Engage with practical examples and homework exercises to reinforce your understanding!

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Understanding the Relationship Between Fractions and Decimals in Mathematics

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  1. The relationship between fractions and decimals Decimals

  2. Two Questions 2 ponder

  3. What fraction of the rectangle is green? They sound alike!!! What decimal part of the rectangle is green? .6

  4. To write a decimal as a fraction, write the fraction as you would say the decimal Hundredths Ten-thousandths tenths 0.12345 Hundred-thousandths Thousandths

  5. .5 .65 .22 .2 .225 Say the decimal….Write it as a fraction Notice….when you change a decimal to a fraction the denominator is always 10, 100, 1000 (powers of ten!)

  6. Is that all there is? Of Course Not You have to simplify the fraction if possible

  7. Can be simplified to: .6 = .6 = Write .6 as a fraction BUT SO

  8. What about fractions to decimals? You can write a fraction as a decimal by dividing the numerator by the denominator…..the fraction symbol means division!

  9. To make a decimal…do the division! .75 .00 28 20 20 0

  10. One more thing……… When you divide, REMEMBER, add zeros to finish your division. AND 2 THINGS CAN HAPPEN

  11. The division problem ends A Terminating decimal The division problem goes on forever….Repeating decimal

  12. Repeating Decimals A single digit might repeat…. .3333…. Or a group of digits might repeat… .275275275….

  13. Show repeating decimals by placing a line over the digit or group of digits that repeats .33333…. Becomes .3 And .275275….becomes .275

  14. Will be 1.4 1.2 will be Simplified to: Remember Whole numbers stay the same!

  15. Homework Page 212 in your textbook…. Problems 14-38 Start now!

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