3.1 Dividing a Whole into Fractional Parts. 3.1 Dividing a Set into Fractional Parts. 3.2 Identifying Parts of Wholes.

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1 . Dividing a Whole into Fractional Parts Fraction: represents a part of a whole object or unit Numerator: (top number) represents number of parts of the whole Denominator: (bottom number) represents how many parts make up the whole (total) The flag design shown is made up of square units. Three square units are purple, so / of the flag design is purple. Dividing a Set into Fractional Parts A fraction can also represent a part of a set There are students in your class. Ten of the students are boys. If 0 of the students are boys, there must be girls. So / of the students in your class are girls.. Identifying Parts of Wholes To determine the value of a fractional part of any whole, set, unit, or group, identify the number of parts in the whole, and then determine the value of the fractional part of the whole. Information: Each triangle shown is / of the hexagon

2 . Plotting Fractions on a Number Line A unit fraction is a fraction that has a numerator of and a denominator that is a positive integer. Two fractions are equivalent when they each represent the same part-to-whole relationship. A fraction can be represented on a number line by plotting a point. Plot 0 0. Estimating Fractions Using Benchmark Fractions Benchmark fractions, such as 0, /, and, are common fractions that can be used to estimate the value of other fractions. A fraction is close to 0 when the numerator is very small compared to the denominator. A fraction is close to / when the numerator is about half of the denominator. A fraction is close to when the numerator is very close to the denominator. / is less than but close to / / is close to 0 / is less than but close to. Comparing and Ordering Fractions Using Benchmark Fractions Benchmark fractions can be helpful when comparing and ordering fractions To order the fractions from least to greatest, follow the steps shown: 0 Greater than / Less than / So, the fractions in order from least to greatest are

3 . Writing Equivalent Fractions Equivalent fractions are fractions that represent the same part-to-whole relationship. To write an equivalent fraction, multiply or divide the numerator and the denominator by the same number, which is a form of. When the numerator and the denominator of a fraction do not share any common factors, you can say that the fraction is in simplest form. To write in simplest form, divide the fraction by a form of. The GCF (greatest common factor) of and is. So, divide the numerator and denominator by. Adding & Subtracting Fractions ( Like and Unlike Denominators) To add or subtract fractions, first write the fractions with a common denominator. Then add or subtract the numerators while keeping the denominators the same. The least common denominator (LCD) is 0. Writing Improper Fractions as Mixed Numbers To write an improper fraction as a mixed number: ) Divide the numerator (top #) by the denominator (bottom #) ) The quotient (answer) is the whole number ) The remainder becomes the numerator and the denominator stays the same Write as a mixed number

4 . Writing Mixed Numbers as Improper Fractions To write a mixed number as an improper fraction: ) Multiply the denominator by the whole number ) Add the numerator of the fraction to the total of step number. This answer is the numerator of the improper fraction. ) Keep the denominator the same Write as an improper fraction. (x+) = () =. Adding & Subtracting Mixed Numbers To add or subtract mixed numbers: ) Find a common denominator and then make equivalent fractions using that denominator ) Add or subtract the numerators and keep the denominator the same ) Add or subtract the whole number ) Simplify the fraction if necessary Using an Area Model to Represent a Part of a Part Multiplying two fractions is the same as determining a part of a part. ) Divide the square into the first fraction (fifths-vertical) and then again by the second fraction (thirds-horizontal) ) Shade in the fractions ( purple = /, green is /, and red is overlapping) ) Overlapping region represents the product of the fraction The area model shown represents The product is Total number of overlapping sections is the numerator Total number of squares is the denominator / / / / / / / /

5 . Multiplying Fractions To calculate the product of two fractions: ) Convert any mixed numbers into improper fractions ) Cross simplify ) Multiply numerators ) Multiply denominators ) Convert improper fractions into mixed numbers and/or simplify fractions. Dividing Fractions Reciprocal or (Multiplicative inverse) of a number a/b is b/a, where a and b are nonzero numbers. The product of any nonzero number and its multiplicative inverse is. To calculate the quotient of two fractions, multiply the dividend by the reciprocal of the divisor. To divide fractions: ) Leave first fraction alone ) Change the problem to multiplication ) Change the second fraction to the reciprocal ) Now solve like a multiplication problem ) Simplify the fraction if necessary 0.0 Dividing Mixed Numbers Dividing two mixed numbers: ) Convert mixed numbers into improper fractions ) Leave first fraction alone ) Change the problem to multiplication ) Change the second fraction to the reciprocal ) Now solve like a multiplication problem ) Simplify the fraction if necessary

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