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Preview Warm Up California Standards Lesson Presentation

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Warm Up In Spiral Add or subtract. 1. 2. 3. 4. . 7 8 1 3 7 12 1 5

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NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Also covered: NS2.4 California Standards

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**Additional Example 1A: Adding Mixed Numbers**

Add. Write the answer in simplest form. 2 3 2 3 9 + 12 9 2 3 + 12 = 21 + 4 3 Add the integers, and then add the fractions. Rewrite the improper fraction as a mixed number. = 1 3 = 22 1 3 Add.

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**Additional Example 1B: Adding Mixed Numbers**

Add. Write the answer in simplest form. 1 8 5 6 5 + 3 5 1 8 + 3 6 = 20 24 3 Find a common denominator. = 8 + 23 24 Add the integers, and then add the fractions. = 8 23 24 Add.

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Check It Out! Example 1A Add. Write the answer in simplest form. 4 5 2 5 7 + 10 Add the integers, and then add the fractions. 7 4 5 + 10 2 = 17 + 6 5 Rewrite the improper fraction as a mixed number. = 1 5 = 18 1 5 Add.

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Check It Out! Example 1B Add. Write the answer in simplest form. 1 4 3 8 4 + 4 4 1 + 4 3 8 = 3 8 2 Find a common denominator. = 8 + 5 8 Add the integers, and then add the fractions. = 8 5 8 Add.

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**REGROUPING MIXED NUMBERS**

Sometimes when you subtract mixed numbers, the fraction portion of the first number is less than the fraction portion of the second number. In these cases, you must regroup before subtracting. REGROUPING MIXED NUMBERS WORDS NUMBERS Regroup. 1 8 7 = Rewrite 1 as a fraction with a common denominator. 8 = 6 + + 1 = 6 9 8 Add.

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Remember! Any fraction in which the numerator and denominator are the same nonzero number is equal to 1.

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**Additional Example 2A: Subtracting Mixed Numbers**

Subtract. Write the answer in simplest form. 2 3 1 3 4 – 2 4 2 3 – 1 = 2 1 3 Subtract the integers, and then subtract the fractions. Caution! Must check to see if you will need to borrow to subtract the fractions. If not, okay to go ahead and subtract.

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**Additional Example 2B: Subtracting Mixed Numbers**

Subtract. Write the answer in simplest form. 8 9 2 3 12 – 8 12 8 9 – 2 3 = 12 8 9 – 6 Find a common denominator. = 4 2 9 Subtract the integers, and then subtract the fractions. Caution: Borrow? No, so go ahead.

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**Additional Example 2C: Subtracting Mixed Numbers**

Subtract. Write the answer in simplest form. 1 8 3 8 CAUTION: Borrow? Yes, so look to re-group before subtracting. 17 – 12 17 1 8 – 12 = 3 16 9 – 12 Regroup 17 1 8 = 16+ + . = 4 6 8 = 4 3 Subtract the integers, and then subtract the fractions. Simplify.

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**Additional Example 2C: Subtracting Mixed Numbers**

Subtract. Write the answer in simplest form. 1 8 3 8 CAUTION: Borrow? Yes, so look to re-group before subtracting. 17 – 12 Other option: Convert mixed numbers to improper fractions, then subtract numerators. Downside? May have a lot of multiplying of big numbers and then dividing, so can lead to mistakes. 17*8+1 = 137 12 * 8 +3 = 99 137 – 99 = 38 = 4 ¾

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**Subtract the integers, and then subtract the fractions.**

Check It Out! Example 2A Subtract. Write the answer in simplest form. 4 5 1 5 3 – 2 3 4 5 – 2 1 = 1 3 5 Subtract the integers, and then subtract the fractions.

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**Find a common denominator.**

Check It Out! Example 2B Subtract. Write the answer in simplest form. 7 8 3 4 10 – 4 10 7 8 – 4 3 = 10 7 8 – 4 6 Find a common denominator. Subtract the integers, and then subtract the fractions. = 6 1 8

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Check It Out! Example 2C Subtract. Write the answer in simplest form. 1 4 3 4 14 – 10 14 1 4 – 10 = 3 13 5 – 10 Regroup 14 1 4 = 13+ + . = 3 2 4 = 3 1 Subtract the integers, and then subtract the fractions. Simplify.

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**Additional Example 3: Measurement Application**

Kevin is inches tall. His brother Keith is 5 3 8 5 inches taller. How tall is Keith? Add the integers, and then add the fractions. 3 8 5 8 8 48 + 5 = 53 + 8 = 53 + 1 Rewrite as 1. Keith is 54 inches tall. 48 1 2 + 5 = 54 Round 3 8 to and to . 1 2 5 Estimate 54 equals 54, so the answer is reasonable.

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**Add the integers, and then add the fractions. 72 + 15 87 +**

Check It Out! Example 3 Alvin weighs 72 lbs. His baby brother weighs lbs. How much do they weigh together? 2 3 1 3 2 3 1 3 3 Add the integers, and then add the fractions. 72 + 15 = 87 + 3 Rewrite as 1. = 87 + 1 Together they weigh 88 pounds. Estimate 2 3 Round 72 to 73 and 15 to 15. 1 = 88 88 equals 88, so the answer is reasonable.

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**Add or subtract. Write each answer in simplest form. 1. 5 2. 9 3. 7 **

Lesson Quiz Add or subtract. Write each answer in simplest form. 1. 5 2. 9 3. 7 4. 10 10 5 12 1 4 1 6 + 5 2 3 7 12 20 1 4 + 10 7 8 3 4 5 1 8 – 2 2 9 5 6 5 7 18 – 4 1 2 5. A single roll of wallpaper unrolls to 15 yards. 7 8 You hang 13 yards from the roll. How much wallpaper remains? 1 yards 5 8

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