Multiplying Fractions and Mixed Numbers Warm Up 1

Multiplying Fractions and Mixed Numbers Warm Up 1 What is 2 of each of the following? 1. 24 12 3. 30 15 2. 16 4. 28 8 14

Multiplying Fractions and Mixed Numbers Essential Question: How do you multiply fractions and mixed numbers? Standard: MCC 7. NS. 2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Multiplying Fractions and Mixed Numbers To multiply fractions, multiply the numerators to find the product’s numerator. Then multiply the denominators to find the product’s denominator. In other words: Multiply straight across Review Video

Multiplying Fractions and Mixed Numbers Additional Example 1 A: Multiplying Fractions Multiply. Write the answer in simplest form. – 12 · 3 4 3 = – 12 · 3 Write – 12 as a fraction. – 12 · 4 1 4 3 12 · 3 Simplify. =– 1 · 41 = – 9 Multiply numerators. 1 Multiply denominators. Helpful Hint The product of two positive proper fractions is less than either fraction.

Multiplying Fractions and Mixed Numbers Additional Example 1 B: Multiplying Fractions Multiply. Write the answer in simplest form. 1 · 3 3 8 1 · 3 = 1 · 3 3 8 13· 8 = 1 8 1 Simplify. Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Additional Example 1 C: Multiplying Fractions Multiply. Write the answer in simplest form. Integer Rules still apply!!!!! 3 · – 1 5 4 3 · – 1 = – 3 · 1 5· 4 4 5 =– 3 20 The signs are different, so the answer will be negative. Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Check It Out: Example 1 A Multiply. Write the answer in simplest form. – 16 · 1 4 1 = – 16 · 1 Write – 16 as a fraction. – 16 · 4 1 4 4 16 · 1 Simplify. =– 1 · 41 = – 4 Multiply numerators. 1 Multiply denominators.

Multiplying Fractions and Mixed Numbers Check It Out: Example 1 B Multiply. Write the answer in simplest form. 1 · 6 6 9 1 · 6 = 1 · 6 6 9 16· 9 = 1 9 1 Simplify. Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Check It Out: Example 1 C Multiply. Write the answer in simplest form. – 3 · 1 7 8 · 1= – 3 · 1 7 8 7· 8 – 3 =– 3 56 The signs are different, so the answer will be negative. Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Additional Example 2 A: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 · 12 5 3 2 · 12 = 2· 5 5 3 3 5 = 2· 5 5 3 1 =2 3 Write the mixed number as an improper fraction. 1 Simplify. Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Additional Example 2 B: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. · -21 -41 7 5 -41 · -21 = -21· -15 Write the mixed numbers as 5 7 improper fractions. 3 3 21 · 15 Simplify. = 5 7 1 1 or 9 = 9 1 Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Additional Example 2 C: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 63 · 2 -45 6 2 · -42 = 20 · -22 3 5 4 = 20 · -22 3 51 = -88 or -291 3 3 Write the mixed numbers as improper fractions. Simplify. Multiply numerators. Multiply denominators.

Multiplying Fractions and Mixed Numbers Check It Out: Example 2 A Multiply. Write the answer in simplest form. 3 · 21 5 3 3 · 21 = 3· 7 5 3 3 5 Write the mixed number as an improper fraction. 13 7 = · Simplify. 5 31 = 7 or 12 Multiply numerators. 5 5 Multiply denominators.

Multiplying Fractions and Mixed Numbers Additional Example 3: Transportation Application In 2001, the car toll on the George Washington Bridge was $6. 00. In 1995 the toll was 2 of that 3 toll. What was the toll in 1995? 6 · 2 = 2+ 2 + 2 + 2 3 3 3 3 = 12 3 1 1 3 3 + 1 1 3 3 + 1 1 3 3 1 1 1 3 3 3 4 = 1 Simplify. = $4. 00 Divide 4 by 1 to write the fraction as a decimal. 1 1 The George Washington Bridge toll for a car was $4. 00 in 1995.

Multiplying Fractions and Mixed Numbers Check It Out: Example 3 In 2002, the fee to park in a parking garage was 3 $4. In 2000 the fee was 4 of the fee in 2002. What was the fee in 2000? 4· 3 =3 + 3 +3 4 4 4 = 12 4 111 444 + 111 444 111111 444444 3 = 1 Simplify. = $3. 00 Divide 3 by 1 to write the fraction as a decimal. 1 1 1 The fee to park in the parking garage was $3. 00 in 2000.

Multiplying Fractions and Mixed Numbers Lesson Quiz: Part I Multiply. Write each answer in simplest form. 1. 1 · -5 8 6 -5 48 2. -55 · -1 6 2 35 or 2 11 12 12 3. 5 1 · 1 2 10 3 17 or 8 1 2 2 4. -3 · 4 2 16 3 -7 8

Multiplying Fractions and Mixed Numbers Pg. 73 Do odd only