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Learn how to compare and order rational numbers using inequality symbols. Convert fractions to decimals and vice versa using calculators. Use number lines to place and compare rational numbers effectively. Practice ordering rational numbers with examples.

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  1. Activator • Compare: Which is more of a dollar? 5 dimes and 3 pennies to 17/34

  2. How do you compare rational numbers using inequality symbols?

  3. Name the inequality symbol < Less Than > Greater Than

  4. Comparing Rational Numbers • Make sure all numbers are in the same form My suggestion would be to turn all numbers into decimals. It is easier to compare decimals than fractions with different denominators.

  5. Using the Calculators • On the next two slides you will see ways to change fractions to decimals and decimals to fractions. • If you already know how to do this then you do not need to copy, but if you don’t you will want to copy the notes. • I do want you to try both methods on each slide with a calculator.

  6. Using the Calculator • Turning a fraction to a decimal (2 ways) • One way to turn a fraction into a decimal is simply divide the numerator by the denominator. • The other way is to use the F to D button. To use type in the fraction as follows. Numerator, A b/c button, denominator, 2nd key, PRB button (above it will have in yellow, F < >D.

  7. Using the Calculator • Turning a decimal to a fraction (2 ways) • One way to turn a decimal into a fraction is to write the decimal number (minus the decimal), A b/c button, place value of the last digit. Push equal and it should simplify if it can. Example: 0.325 = 325/1000 = 13/40 2. The other way is to use the F to D button. Type in the decimal, 2nd key, PRB (in yellow above it is F<>D), equal button.

  8. Placing and Comparing Using Number Lines • The key with number lines is to know how the number line is divided. • To determine how the number line is divided you simply count the number of marks between two marked numbers. • If it is broken into sets of ten then you can use a decimal number. • If it is broken into any other set of numbers then you are using a fraction. Some fractions can easily be changed to decimals if needed. Example ¼ can be turned into .25

  9. Ordering Rational Numbers • Order -1, -1.6, 2/5, 1 ¼, and -3/8 from least to greatest.

  10. Ordering Rational Numbers • Order -1, -1.6, 2/5, 1 ¼, and -3/8 from least to greatest. • How do I order these? • All numbers MUST be in the same form! Option 1 • Find the rational numbers of each value. • Find an LCD and create equivalent fractions. • Order from least to greatest. • Place values back into original form. • Option 2 • Convert all numbers to decimals. • Order from least to greatest. • Place Numbers back into original form.

  11. On Your Own Order from least to greatest using rational numbers: a) 2.5, -1, -5/8, -0.8 b) 4 1/5, -3.6, -3 8/9, 0

  12. Comparing and Ordering Decimals

  13. Tenths Number Line

  14. Hundredths Number line

  15. Thousandths Number line

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