Presentation on theme: "Adding, Subtracting, Multiplying, and Dividing Fractions 3-5, 3-6, 3-7"— Presentation transcript:
1 Adding, Subtracting, Multiplying, and Dividing Fractions 3-5, 3-6, 3-7 Notes 8Adding, Subtracting, Multiplying, and Dividing Fractions3-5, 3-6, 3-7
2 VocabularyReciprocal: A fraction’s opposite (or flipped upside down). The two numbers should equal 1.Multiplicative Inverse: Same as reciprocal: A fraction’s opposite (or flipped upside down). The two numbers should equal 1.
3 Adding & Subtracting Fractions Additional Example 1A: Adding or Subtracting Fractions with Like DenominatorsAdd. Write the answer in simplest form.5818+58185 + 1Add the numerators and keepthe denominator.+=86834==Simplify.
4 Subtract. Write the answer in simplest form. Additional Example 1B: Adding or Subtracting Fractions with Like DenominatorsSubtract. Write the answer in simplest form.911411–Subtract the numerators andkeep the denominator.9114119 – 4–=11=511The answer is in the simplestform.
5 Two Ways to Find a Common Denominator To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator.Two Ways to Find a Common DenominatorFind the LCM (least common multiple)of the denominators.Multiply the denominators.The LCM of two denominators is the lowest common denominator (LCD) of the fractions.Helpful Hint
6 Additional Example 2A: Adding and Subtracting Fractions with Unlike Denominators Add. Write the answer in simplest form.5678+56785 · 46 · 47 · 38 · 3+=+The LCM of the denominator is 24.2024212441241724Write equivalent fractions. Add=+==1is a reasonable answer.11724Estimate = 2
7 Additional Example 2B: Adding and Subtracting Fractions with Unlike Denominators Subtract. Write the answer in simplest form.2334–23342 · 43 · 3–=–Multiply the denominators.3 · 44 · 3=812–9= –112Write equivalent fractions. Subtract.is a reasonable answer.-112Estimate 1 – 1 = 0
8 Add. Write the answer in simplest form. Additional Example 2C: Adding and Subtracting Fractions with Unlike DenominatorsAdd. Write the answer in simplest form.2713–+27+13=–2 · 37 · 3+1 · 73 · 7–Multiply the denominators.=+–7216121=Write equivalent fractions. AddEstimate = 012is a reasonable answer.121
9 Multiplying Fractions To multiply fractions, multiply thenumerators to find the product’snumerator. Then multiply thedenominators to find the product’sdenominator.
10 Additional Example 1A: Multiplying Fractions Multiply. Write the answer in simplest form.3–12 ·43123–12 ·= –Write –12 as a fraction.414312 · 3=–Simplify.1 · 419Multiply numerators.Multiply denominators.= –= –91The product of two positive proper fractions is less than either fraction.Helpful Hint
11 Additional Example 1C: Multiplying Fractions Multiply. Write the answer in simplest form.31–543514–The signs are different, so the answer will be negative.3514–==320–Multiply numerators.Multiply denominators.
12 Additional Example 2A: Multiplying Mixed Numbers Multiply. Write the answer in simplest form.221532225Write the mixed number as animproper fraction.1=3535125=Simplify.5312Multiply numerators.Multiply denominators.=3
13 Dividing FractionsReciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. The reciprocal of is 3 because1313· 3=1.Dividing by a number is the same as multiplying by its reciprocal.2 ÷13= 2 · 3 = 6
14 Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form.3725÷A.3725375225÷=Multiply by the reciprocal of .375=21514141=or 138B.÷1238138Multiply by the reciprocal of 12.÷12=121381Simplify.=1241=32
15 Additional Example 2: Dividing Mixed Numbers Divide. Write each answer in simplest form.2314A.5÷1Write mixed numbers as improperfractions.2317354514÷1=÷1734554=Multiply by the reciprocal of.6815=or 48153412B.÷2Write 2 as an improper fraction.1234123452÷2=÷523425=Multiply by the reciprocal of .132Simplify.=452310=