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Fraction Concepts Fraction Concepts • A fraction is a piece of something. • For example, a fraction can be: – A piece of cake – A piece of pie – A slice of pizza – A portion of an apple Fraction Concepts • A fraction is shown as a number over another number with a line separating them (X/W) Fraction Concepts • The top number is the numerator. • The numerator represents how much you have to split up. For example: 2 pizzas, 3 sandwiches, 5 pies Fraction Concepts • The denominator is the bottom number. • The number represents how things are being split up or divided. Fraction Concepts • In a regular fraction, the denominator is a higher number than the numerator. Fraction Concepts Fraction and Division Are Related • Fractions and division are related. • The numerator in a fraction is the same as the dividend in a division equation • The denominator is the same as the divisor in a division equation Fraction Concepts Equivalent Fractions • Equivalent fractions are two or more different fractions that represent the same amount. • For example: ½ = 2/4 = 3/6 = 4/8 = 5/10 Fraction Concepts Determining an Equivalent Fraction • To determine an equivalent fraction, multiply the numerator and the denominator by the same amount. • You get a different fraction, but it is the same amount. • For example: 2/4 x 2/2 = 4/8 Fraction Concepts Determining an Equivalent Fraction: Another Way • You can also divide the numerator and the denominator by the same amount to get an equivalent fraction. • For example: 4/8 ÷ 2/2 = 2/4 Fraction Concepts Why Do I Need Equivalent Fractions • Equivalent fractions are needed to add and subtract fractions with different denominators. • For example: 1/4 + 1/3 • Step 1: Find a common multiple for 4 and 3 which is 12. • Step 2: Convert 1/4 and 1/3 to equivalent fractions with a denominator of 12 (3/12 and 4/12). • Step 3: Add the numerators of the equivalent fractions to solve the equation (7/12). Fraction Concepts • To convert a fraction to an equivalent fraction in a simplest form, divide the numerator and denominator by the same common factor. • If the resulting fraction is even, ends in 5, or is divisible by 3, continue simplifying. • For example: 4/12 ÷ 4/4 = 1/3 Fraction Concepts Mixed Numbers and Improper Fractions • A mixed number is a combination of a whole number and a fraction. For example: 4 ½ • An improper fraction is a fraction when the numerator is greater than the denominator. For example: 12/5 Fraction Concepts Converting a Mixed Number to an Improper Fraction • To convert a mixed number to an improper fraction ( 4 3/5): – Convert the whole number to a fraction: 4 = 4/1 – Convert the fraction to an equivalent fraction with the same denominator as the fraction piece: 4/1 x 5/5 = 20/5 – Add the equivalent whole number fraction to the fraction piece: 20/5 + 3/5 = 23/5. Fraction Concepts Converting an Improper Fraction to a Mixed Number • To convert an improper fraction to a mixed number: – Rewrite the fraction as a division equation: 23/5 = 23 ÷ 5 – Solve the division equation. 23÷5= 4 r 3 • The quotient is the whole number of the mixed number • The remainder is the numerator of the fraction piece • The denominator is the original denominator – For example: 23/5 = 4 3/5 Fraction Concepts Adding Fractions with Same Denominators • To add fractions with the same denominator, add the numerators only. • Do not add the denominators. They are the noun of the fractions representing the size of the piece. • Example: 3/8 + 4/8 = 7/8 Fraction Concepts Subtracting Fractions with Same Denominator • To subtract fractions with same denominator, subtract the numerators. • Do not subtract the denominators. • For example: 4/5 – 2/5 = 2/5 Fraction Concepts Adding Mixed Numbers with Same Denominator • Step 1: Rewrite the equation in vertical format • Step 2: Add the fraction pieces of the mixed number – If the result is a regular fraction, continue to step 2 – If the result is an improper fraction, convert the improper fraction to a mixed number – Add the whole number to the first whole number – Leave the fraction alone. • Step 3: Add the whole number pieces of the equation. Fraction Concepts Adding Mixed Numbers with Same Denominator • Example 1 – 3 2/5 + 2 1/5 = 5 3/5 • Example 2 – 3 4/5 + 4 2/5 • • • • Step 1: 4/5 + 2/5 = 6/5 Convert to a mixed number: 6÷5 = 1 r 1 = 1 1/5 Step 2: 1+3+4 = 8 Solution 8 1/5 Fraction Concepts Subtracting Mixed Numbers with Same Denominators • Step 1: Rewrite the equation in vertical format • Step 2: Subtract the fraction pieces – If the top fraction is greater than the bottom fraction, subtract the numerators – If the top fraction is less than the bottom fraction, • Regroup one of the ones from the whole number as a fraction with the same denominator as the fraction • Add the regrouped fraction to the original fraction • Subtract the lower fraction from the upper fraction. • Step 3: Subtract the whole numbers Fraction Concepts Subtracting Mixed Numbers with Same Denominators • Example 1: 5 ¾ - 2 ¼ = 3 2/4 = 3 ½ • Example 2: 5 ¼ - 2 ¾ – Step 1: Convert the 5 to 4 and take the 1 and convert it to a fraction with 4 as the denominator (4/4) – Step 2: Add 4/4 to ¼ to get 5/4 – Step 3 Subtract ¾ from 5/4 to get 2/4 or ½ – Step 4: Subtract 2 from 4 to get 2. – Solution: 2 2/4 or 2 ½ Fraction Concepts Applying Your Knowledge • To add or subtract fractions with uncommon denominators, convert the two fractions to equivalent fractions with the same denominator. • For example: 1/3 + ¼ – – – – 3 and 4 share 12 as a common multiple Convert 1/3 to 4/12 (1/3 x 4/4 = 4/12) Convert ¼ to 3/12 ( ¼ x 3/3 = 3/12) Add the numerators of the two equivalent fractions • 4/12 + 3/12 = 7/12 Fraction Concepts Applying Your Knowledge • When you are multiplying a fraction, you are taking a fraction of the first fraction. You multiply the numerators and then multiply denominators. • For example ¾ x ½ means you are taking ½ of ¾. • To solve: ¾ x ½ =3/8 Fraction Concepts Applying Your Knowledge • Dividing two numbers is the same as multiplying the dividend by the reciprocal of the divisor. • For example: 6 ÷ 2 = 6 x ½ • A reciprocal is flipping the numerator and the denominator. For example 2 = 2/1. the reciprocal of 2 is ½.