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Changing Improper Fractions to Mixed number Example : Simplify 21 4 = 21 ÷ 4 = 5 remainder 1. The quotient, 5, becomes the whole number portion of the mixed number. 21 4 1 = 5 4 The remainder, 1, becomes the top number of the fraction. The bottom number of the fraction always remains the same. Changing Mixed number to Improper Fractions 3 Example : Change 4 4 to an improper fraction/ Step 1: Multiply the whole number (4) by the bottom number of the fraction (5) Step 2: Add the top number to the product from Step 1 : 20 + 3 = 23 Step 3: Put the answer from step 2 over the bottom number (5) 3 45= 23 5 Multiplying Fractions 1 3 2 4 Example 1: Multiply : × Step 1: Multiply the top number 1 × 3 = 3. The top of the fraction is 3 Step 2: Multiply the bottom number 2 × 4 = 8. The bottom of the fraction is 8 1 2 2 3 3 4 3 3 4 8 × = Example 2: Multiply : × Step 1 : In this problem, the 3’s are both divisible by 3, so they cancel. 3 ÷ 3 = 1 2 3 3 2 1 4 1 4 × = × Step 2: 2 and the 4 are both divisible by 2, so they cancel. 2 ÷ 4 = 2 2 1 2 1 ×4=1×4 1 Step 3: Multiply. × = 1 1 1 1 2 2 Multiplying Mixed Numbers 1 2 Example: Multiply : 3 4 × 3 Step 1: Change 3 4 to an improper fraction 1 1 34 = Step 2: (3×4+1) 4 = 13 4 When multiplying fractions, you can cancel and simplify terms that have a common factor. The 4 in the first fraction will cancel with the 2 in the second 13 2 fraction. × 4 3 The terms 4 and 2 are both divisible by 2, so divide the 4 and 2 by 2. 4 simplifies to 2, and 2 simplifies to 1. Step 3: Multiply the simplified fractions. Step 4: Change 13 6 13 2 13 2 × 1 3 1 ×3= 13 6 1 back to a mixed number. 2 6 Reciprocals 3 Example: Find the reciprocal of 8 Step 1: Invert the fraction, so the numerator is now the denominator, and the denominator is now the numerator. 3 8 𝑏𝑒𝑐𝑜𝑚𝑒𝑠 3 8 Answer: The reciprocal of 3 𝑖𝑠 8 8 3 Dividing Fractions and Mixed Numbers 3 1 Example: Divide: 3 4 ÷ 2 3 Step 1: Change the mixed numbers in the problem to improper fractions. 3 34 = (4×3)+3 4 = 15 4 1 and 2 3 = The problem is now 15 4 (3×2)+1 3 7 =3 7 ÷3 Step 2: Change the sign from division to multiplication , and then change the second 15 7 number to its reciprocal. 4 × 3 Step 3 : Cancel is possible (not needed in this problem) and multiply. Step 4: Simplify to 1 28 17 15 4 3 45 × 7 = 28