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To change the mixed number there are two whole numbers at 3 pieces each plus the 2 you already had. To multiply fractions any whole numbers must be converted to fractions by placing them over one. All mixed numbers must change to improper. 4 4 1 • • 3 8 8 3 • • 2 x + 8 3 2 3 = = Since multiplication is commutative, we can now simplify any numerator with any denominator. Now multiply across the top. Put the answer on top. Multiply across the bottom. Put the answer on bottom. Make sure the answer is simplified.
1 4 1 4 • • 3 8 1 1 1 1 ÷ 3 ÷ 8 • • 1 1 1 8 3 1 ÷ 3 ÷ 8 = or 4 = New Problem. To multiply fractions any whole numbers must be converted to fractions by placing them over one. All mixed numbers must change to improper. To change the mixed number there is one whole number at 3 pieces plus the 2 you already had. 1 6 6 • • 1 x + 5 3 2 3 = = Since this problem is commutative, simplify any top with any bottom. Multiply across numerators. Record on top. Multiply across the denominators. Record on bottom. Make sure it is simplified. 1 2 6 1 ÷3 • • 5 1 5 3 = or 10 ÷3 = 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. Repeat if there are others (one on top and one on bottom) that can simplify. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Make sure it is simplified. (If you did step 3 right, this will automatically happen.)6 6 1 ÷3 • • 3 + x 10 3 1 3 ÷3 = = 20 1 or 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. Repeat if there are others (one on top and one on bottom) that can simplify. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Make sure it is simplified. (If you did step 3 right, this will automatically happen.)4 4 1 ÷2 • • 1 2 3 1 2 ÷2 = = 6 1 or 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Simplified? Before it is simplified. After it is simplified. 6 6 1 1 ÷2 • • • 2 11 + x 11 3 4 ÷2 = = 33 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Simplified? Before it is simplified. After it is simplified. 2 1 1 ÷2 • • • 2 5 5 1 2 ÷2 = = 5 or 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Simplified? Before it is simplified. After it is simplified. 6 6 1 1 ÷3 • • • 1 2 3 ÷3 = = or 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Simplified? Before it is simplified. After it is simplified. 3 1 ÷3 • • • 1 5 6 ÷3 = = Before it is simplified. After it is simplified. 6 + x 1 4 ÷5 ÷2 • • • 1 + x 1 5 ÷2 ÷5 = Before it is simplified. After it is simplified. 2 + x 1 4 ÷3 ÷4 • • • 1 + x 1 3 ÷4 ÷3 = Before it is simplified. After it is simplified. 2 3 4 ÷2 • • • 1 + x 1 5 ÷2 = Remember we only simplify if we can. Some do not simplify. The tops and the bottoms have no common factors other than one. 11 is relatively prime to 3 and 4 as is 5 to 4 and 3. This one does not simplify. 2 4 3 • • 1 2 3 = = Before it is simplified. After it is simplified. 5 + x 1 4 • • • 1 1 7 = Before it is simplified. After it is simplified. 5 + x 1 4 • • • 6 7 = 1) Whole numbers to fractions. Mixed to improper. 2) Simplify any one top with any one bottom. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Simplified? Before it is simplified. After it is simplified. 3 ÷3 • • • 1 1 6 ÷3 = = Before it is simplified. After it is simplified. 3 3 4 • • • 1 3 5 = Before it is simplified. After it is simplified. 5 1 4 • • • 1 3 7 = Before it is simplified. After it is simplified. 1 4 • • • 1 3 7 = REMEMBER: 1) Whole numbers to fractions. Mixed to improper. 2) Simplify if you can. 3) Multiply across the top. Record on top. 4) Multiply across the bottom. Record on bottom. 5) Double check for simplest form. 5 • • 1 3 7 = = Before it is simplified. After it is simplified. 6 • • • 2 3 4 = 4 1 • 7 3 = 3 2 • 7 3 = Before it is simplified. After it is simplified. 3 • • • 2 1 6 = Before it is simplified. After it is simplified. 4 4 5 • • • 4 1 6 = Before it is simplified. After it is simplified. 4 1 5 • • • 4 1 6 = After it is simplified. Simplify any one top with any one bottom. Before it is simplified. 1 1 3 • • • 1 1 4 • • • 10 9 = After it is simplified. Simplify any one top with any one bottom. Before it is simplified. 1 1 3 • • • 2 1 4 • • • 1 2 5 = After it is simplified. Simplify any one top with any one bottom. Before it is simplified. 3 1 3 • • • 1 1 4 • • • 10 9 = |