Fractions Fractions: A numerical quantity that is not a whole number (e.g. 1/2). A small or tiny part, amount, or proportion of something. Key Vocabulary/ Concepts: Numerator, Denominator, Mixed Number, Improper fractions, Equivalent Fractions, Lowest Common Multiple (LCM), Greatest Common Factor (GCF) Numerator: The top number of a fraction. The numerator indicates the parts being counted or considered. Denominator: The bottom number of a fraction. The denominator indicates how many equal parts the item is divided into. ퟏ ퟐ 0 ퟑ ퟑ 1 Visual Model Number Line Model Unit Fraction: A fraction with a numerator of one Examples Benchmark Fraction: Common fractions that are often used to judge against, when measuring, comparing or ordering other fractions. Examples SC STANDARDS: 5.NSF.1 Fractions Fractions: A numerical quantity that is not a whole number (e.g. 1/2). A small or tiny part, amount, or proportion of something. Equivalent fraction: Two or more fractions with the same value but with different Numerators and denominators. OR Improper fraction: A Mixed number: A whole fraction where the numerator number and fraction together. is larger than the denominator. Example: Simplest Form: When a fractions numerator and denominator have no common factors other than 1. 18 To write in simplest form: 21 . 1st find the Greatest Common Factor (GCF) of both the numerator and denominator. ÷ – 1, 2, 3, 6, 9, 18 – 1, 3, 7, 21 ÷ . 2nd Divide both numerator and Denominator by the GCF. SC STANDARDS: 5.NSF.1 Adding & Subtracting Fractions with Unlike Denominators Common Denominator Method Step 1: Change the fractions to equivalent fractions with like denominators. To do this you must first find the Least Common Multiple (LCM). + Multiples of 3 – 3, 6, 9, 12, 15, 18 + + Multiples of 5 – 5, 10, 15, 20 Step 2: Write your equivalent fractions, with your LCM as the denominator and add or subtract. Step 3: Always simplify if possible! Butterfly Method Step 1: Cross Multiply Step 2: Cross Multiply the digits in the orange the digits in the Purple ellipse. ellipse. + Step 3: Multiply the denominators to find a common denominator. Step 4: Complete the operation and simplify. SC STANDARDS: 5.NSF.1 Adding & Subtracting Fractions with Unlike Denominators Common Denominator Method + Step 1: Change the fractions to equivalent fractions with like denominators. To do this you must first find the Least Common Multiple (LCM). Multiples of 3 – 3, 6, 9, 12, 15, 18 Multiples of 5 – 5, 10, 15, 20 Step 2: Write your equivalent fractions, with your LCM as the denominator and add or subtract. + + Step 3: Always simplify if possible! SC STANDARDS: 5.NSF.1 Adding & Subtracting Fractions with Unlike Denominators Butterfly Method + Step 1: Cross Step 2: Cross Multiply the digits in Multiply the digits in the orange ellipse. the Purple ellipse. + Step 3: Multiply the denominators to find a common denominator. + Step 4: Complete the operation and simplify if possible. SC STANDARDS: 5.NSF.1 Multiplying Fractions Fraction by a Fraction Step 1: Multiply the numerators, then multiply the denominators. x Step 2: Simplify Fraction by a Whole Number Step 1: Change the whole number to a fraction x Step 2: Multiply the numerators, then multiply the denominators. x Step 3: Simplify Fraction by a Mixed Number Step 1: Change the mixed x number to a fraction Step 2: Multiply the numerators, then multiply x the denominators. Step 3: Simplify SC STANDARDS: 5.NSF.4 Dividing Fractions Fraction Divided by a Fraction Step 1: Find the reciprocal of the divisor ÷ (the number you are dividing by) ÷ Step 2: Multiply the numerators, then multiply the denominators. X Step 3: Simplify Fraction Divided by a Mixed Number Step 1: Change the mixed number into an ÷ improper fraction. Step 2: Find the reciprocal of the divisor ÷ (the number you are dividing by) X Step 3: Multiply the numerators, then multiply the denominators. Step 4: Simplify SC STANDARDS: 5.NSF.7 Dividing Fractions Whole Number Divided by a Fraction Step 1: Change the whole number to a fraction. ÷ Step 2: Find the reciprocal of the divisor (the number you are dividing by) ÷ Step 3: Multiply the numerators, then multiply X the denominators. Step 4: Simplify Fraction Divided by a Whole Number Step 1: Change the whole number to a fraction. ÷ Step 2: Find the reciprocal of the divisor (the number you are dividing by) ÷ Step 3: Multiply the numerators, then multiply the denominators. X Step 4: Simplify SC STANDARDS: 5.NSF.7 .