Fractions, Mixed Numbers, and Rational Expressions 5.1 Fractions, Mixed Numbers, and Rational Expressions

Fraction: A number that describes a part of a whole.  Numerator  Denominator Numerator: The number written in the top position of a fraction Denominator: The number written in the bottom position of a fraction.

Rational Number: A number that can be expressed as a ratio of integers.

Name the Fraction Represented by a Shaded Region Answer: Explanation: There are 10 equal-sized divisions in the whole region and 3 are shaded.

Word Question In a group of 35 people at a conference, 17 are wearing glasses. What fraction of the people at the conference are wearing glasses? What fraction are not wearing glasses?

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Graph fractions on a Number Line Divide the distance between 0 and 1 into X equal spaces, where X is the number in the denominator position. Ex.

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Simplify Fractions Simplify: The process of writing an equivalent expression with fewer symbols or smaller numbers Simplest form: An equivalent expression written with the fewest symbols and the smallest numbers possible

Rules to Keep in Mind

Write Equivalent Fractions An equivalent fractions are fractions that name the same number Ex. Rule of thumb, You can multiply or divide a fraction by any non- zero number as long as you do it to both the numerator and the denominator.

Examples

Use <, >, or = to Write a True Statement We can easily compare fractions that have the same denominator by looking at their numerator. What if they do not have the same denominator?

To Compare Two Fractions: Write equivalent fractions that have a common denominator Compare the numerators of the equivalent fractions

Example a. Write equivalent fractions that have a common denominator, then compare numerators. A common multiple for 8 and 7 is 56, so our common denominator is 56. Answer:

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Write Improper Fractions as Mixed Numbers Improper Fraction: A fraction in which the absolute value of the numerator is greater than or equal to the absolute value of the denominator. ie. If the number on top is bigger than or equal to the number on the bottom. Mixed Number: An Integer combined with a fraction.

To write an improper fraction as a mixed number: Divide the denominator into the numerator. Write the result in the following form.

Write the improper fraction as a mixed number. Solution: Divide 20 by 3. quotient original denominator remainder

Example

Write Mixed Numbers as Improper Fractions The same but opposite Multiply the integer by the denominator. Add the resulting product to the numerator to find the numerator of the improper fraction. Keep the same denominator.

Write the mixed number as an improper fraction. Solution: We multiplied 8 by 5 to get 40 , then added 7 to get 47 for the numerator of the improper fraction. We kept the denominator the same.

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