Unit 7 Study Guide Fraction and Decimal Number Sense 5.2 – Simplifying fractions – Write, identify, and represent fractions in their simplest form. 5.2A – Equivalent forms – Recognize and name fractions in their equivalent decimal form and vice versa. 5.2B – Comparing fractions – Compare fractions and decimals to determine which value is greater. 5.2B – Ordering fractions – Order fractions and decimals in a given set from least to greatest and greatest to least. *All fractions will be limited to denominators less than or equal to 12. Unit Vocabulary denominator mixed fraction divisor numerator decimal equivalent factor and GCF percent product proper fraction whole number remainder improper fraction least/greatest compare/order percent fraction decimal Simplifying Fractions There are two ways to simplify a fraction: Method 1 Divide the numerator and the denominator (top and bottom) by the same factor until you can't go any further (try dividing by 2,3,5,7,... etc). A factor goes evenly into the number without a remainder. Remember, if both numbers are even, then 2 is always a common factor. Method 2 Divide both the numerator and the denominator of the fraction by the greatest common factor. First, list all of the numbers that go into both numbers without a remainder and then choose the greatest number from the list to use as the divisor. (Example, 12 – 1, 2, 3, 4, 6, 12 and 8 – 1, 2, 4, 8, so the GCF is 4) Method 1 Example 18 24 ÷ 2 = ÷ 3 9 3 12 = ÷ 2 4 ÷ 3 ÷ 6 2 = 9 ÷ 3 Method 2 Example ÷ 3 18 24 = 3 4 ÷ 6 Equivalent Forms Three Types of Fractions Proper Fractions: The numerator is less than the denominator Examples: 1/3, 3/4, 2/7 Improper Fractions: The numerator is greater than (or equal to) the denominator Examples: 4/3, 11/4, 7/7 Mixed Fractions: A whole number and proper fraction together Examples: 1 1/3, 2 1/4, 16 2/5 Get M.A.D.! Multiply & Add or Divide Converting Mixed Fractions to Improper Fractions To convert mixed fractions to improper fractions: • Multiply the denominator and the whole number • Add the product to the numerator • Put the answer as the numerator • Use the denominator of the mixed fraction as the denominator of the improper fraction. Converting Improper Fractions to Mixed Fractions To convert an improper fraction to a mixed fraction, follow these steps: • Divide the numerator by the denominator. • Write down the whole number answer • Then write down any remainder as the numerator. • Use the denominator of the improper fraction as the denominator of the mixed fraction. Memorize these equivalents! “Easy Fractions” List for Ordering Fraction 3/4 2/3 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12 *Approximate Decimal 0.75 0.66 0.5 0.33 0.25 0.2 0.16 0.14 0.125 0.11 0.1 0.09 0.08 Ordering Fractions and Decimals 1) Sort fractions and decimals into those greater than ½ and less than ½. less than ½ greater than ½ 1/3 , .21 .875 ¾ 2) Change fractions to decimals(see fraction, decimal, percent chart) 1/3= .33 1/6 = .16 ¾ = 75% 3/8 = .375 3) Cross Multiply 45 5
8
48 6
8 x 6 = 48 and 9 x 5 = 45 9
48 is bigger than 45 so 5/8 is bigger than 6/9