Joke for the Day! “Do you want that cut into six slices or eight slices?” A man orders a cheese pizza. “Six slices. I’m not hungry enough to eat eight.”

Fractions, Mixed Numbers, and Decimals Convert, rewrite, and compare fractions and decimals

Suppose you had a box of red and green marbles and there are twice as many red marbles as green ones. What possibilities are there for the number of marbles in your box? Equivalent fractions are different expressions for the same number.

To create equivalent fractions, you must multiply/divide the numerator and the denominator by the same number. Example 1 Find a fraction equivalent to the given fraction Since the numerator and denominator are prime you should multiply by a number Since the numerator and denominator are not prime you can either multiply or divide by a new number.

Example 2 Determine Whether Fractions are Equivalent Write the fractions with a common denominator. Then determine if they are equivalent. Since the fractions both express the same number, the fractions are equivalent. Since the fractions do not express the same number they are not equivalent.

Thoughts for Review improper fraction Is an improper fraction because its numerator is larger than its denominator. mixed number Is a mixed number because it contains both a whole number and a fraction.

Convert Improper Fractions to Mixed Numbers Divide the numerator by the denominator Use the quotient and the remainder to write the mixed number 2 3 5

Convert Mixed Number to Improper fraction

Fractions Decimals To write a fraction as a decimal, divide the numerator by the denominator

You try it! 1.8 This is called a terminating decimal because it ends This is called a repeating decimal because it repeats the same pattern

Decimals to Fractions To write a decimal as a fraction, use the place value furthest to the right as your denominator. Simplify if necessary = -0.6 = 1.55 = You try it!

Compare and Order Rational Numbers To compare fractions you must first convert them to the same denominator –T–Then compare the numerators To compare decimals, line up the decimal points. To compare a fraction to a decimal, write the fractions as decimals and then compare the decimals.

Compare the fractions. Write. Write both fractions with a common denominator.

Compare the fractions. Write. Write both fractions with a common denominator. Put the negative signs in the numerators

Compare the decimals. Write. Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 7 > 5

Ordering Fractions and Decimals Order the numbers from least to greatest. First convert all fractions to decimals. Put decimals in order from least to greatest. Therefore…