Estimating Products (pages )
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1 A Estimating Products (pages 8) You can use compatible numbers to estimate products when multiplying fractions. Compatible numbers are easy to divide mentally. A Estimate. means of.? For, the nearest multiple of is. and are compatible numbers because., so the product of about. and is Estimate. For, the nearest multiple of is of 8 is. Since of 8 is, it follows that of 8 is or. So, is about. You can also estimate products by rounding fractions to 0,, or, and by rounding mixed numbers to the nearest whole numbers. Estimate each product. HINT: For 9, what is the nearest multiple of? HINT: For, what is the nearest multiple of?. Estimate.. Estimate. Estimate each product Standardized Test Practice Ann receives an allowance of $0 a week. She spends about of her allowance on school lunches and about on entertainment. About how much does she have left? A $ $0 C $8 D $ Answers: Sample answers are given A Mathematics: Applications and Concepts, Course
2 A Multiplying Fractions (pages ) Use the following rules to multiply fractions. Multiplying Fractions Simplify efore You Multiply To multiply fractions, multiply the numerators and multiply the denominators. Simplify if necessary. You can simplify before you multiply fractions if the numerator of one fraction and the denominator of another fraction have a common factor. Multiply. A To multiply fractions, multiply the numerators and the denominators You cannot simplify. Estimate: 8 The GCF of and 8 is. Divide both the numerator and denominator by and then multiply. Multiply. 8 HINT: Multiply the numerators and the denominators... HINT: Simplify before you multiply. Multiply. Write in simplest form Standardized Test Practice There are a dozen eggs in a carton. You use for an omelet. Your sister uses of the leftover eggs for a cake. How many eggs are left? A 0 C 8 D 9 Answers: C 8 Mathematics: Applications and Concepts, Course
3 A Use the following rules to multiply mixed numbers. Multiplying Express mixed numbers as improper fractions. Mixed Numbers Multiply the numerators and multiply the denominators. Simplify efore You Multiply Multiplying Mixed Numbers (pages ) After you express mixed numbers as improper fractions, check to see if the numerator of one fraction and the denominator of another fraction have a common factor. If they do, simplify before you multiply. Multiply. Estimate: Express as an improper fraction. Multiply and then compare with your estimate. A 8 8 or Estimate and then rewrite the mixed numbers as improper fractions. The GCF of 8 and is. Divide both the numerator and denominator by and then multiply. Rewrite as a mixed number and compare with your estimate. Multiply. Write in simplest form. HINT: Rewrite the mixed number as an improper fraction and multiply... 8 HINT: Simplify before you multiply. Multiply. Write in simplest form Standardized Test Practice It takes Julie minutes to run once around a track. How long will it take her to run 8 laps? A 9 minutes 9 minutes C 8 minutes D 8 minutes Answers: A 9 Mathematics: Applications and Concepts, Course
4 A Dividing Fractions (pages ) Any two numbers whose product is are called reciprocals. For example, and are reciprocals because. You use reciprocals when you divide by fractions. Dividing Fractions To divide by a fraction, multiply by its reciprocal. A Find the reciprocal of. Find. Since, the Multiply by the reciprocal of. reciprocal of is. or Multiply the numerators and denominators. Rewrite the improper fraction as a mixed number. 8 HINT: What times equals? HINT: Multiply by the reciprocal. Simplify before you multiply.. Find the reciprocal of.. Find. Find the reciprocal of each number Divide. Write in simplest form Standardized Test Practice After the initial fee of $.00, a taxi ride costs $0. per mile. How much would a mile cab ride cost, including the initial fee? A $.00 $.00 C $0.00 D $ Answers: D 0 Mathematics: Applications and Concepts, Course
5 A Dividing Mixed Numbers (pages 9) When you divide mixed numbers, first rewrite the mixed numbers as improper fractions. Then divide as you would with a fraction by multiplying by the reciprocal. 8 Rewrite as an improper fraction. Rewrite mixed numbers as improper fractions. 8 Since, the reciprocal of Multiply by the reciprocal. is. A Find the reciprocal of. Find. HINT: Rewrite the mixed number as an improper fraction.. Find the reciprocal of.. Find. HINT: Rewrite the mixed numbers as improper fractions. Multiply by the reciprocal. Write each mixed number as an improper fraction. Then write its reciprocal Divide. Write in simplest form Standardized Test Practice A sand mosaic requires cup of sand per project. If there are cups of sand available, how many mosaics can be completed? A 9 C D Answers:...,.,.,.,.,.,., 0., C Mathematics: Applications and Concepts, Course
6 A Sequences (pages 8 8) A sequence is a list of numbers in a specific order. For example, the numbers,, 9,, are a sequence. In this sequence, notice that is added to each number. The next number in the sequence is, or There are also sequences in which you find the numbers by multiplying by the same number. Describe each pattern. Then find the next number in each sequence. A, 8,, 8,, 0, 0, 0, In this sequence, is added to each number. Each number in this sequence is multiplied by. The next number is 8, or. The next number is 0, or 80. Describe each pattern. Then find the next number in each sequence.., 9,,,.,,, 0, HINT: What number is subtracted from each number in the sequence? HINT: What number is added to each number in the sequence? Describe each pattern. Then find the next two numbers in each sequence..,, 8,.,,,.,, 9,.,, 8,.,,,,,, Find the missing number in each sequence. 9.,?,, ,?, 0,.,,?, 0.,,?,., 0,,?.?, 90,,..... Standardized Test Practice Team A is playing Team in a baseball game. y the end of the fifth inning, how many total outs has each team gotten? (There are outs per inning per team.) A 8 C D Answers:. subtract ;. add ;. multiply by ;,. multiply by ;,. add ; 8,. multiply by 8;,0, 8,9. multiply by ;, 0. add ; 0, C Mathematics: Applications and Concepts, Course
7 Chapter Review Chef s Secret Chefs often have to change the amounts of ingredients that they use in their recipes when they change the size of the recipes. Help Chef Ramirez change the amounts shown in the measuring cups below. Shade in the new amounts in the empty measuring cups. cup. cup cup cup cup cup cup cup cup cup cup cup cup. cup cup cup cup cup cup cup cup cup cup cup cup cup. cup cup cup cup cup cup cup cup cup cup cup cup cup cup cup cup Answers are located on p. 0. Mathematics: Applications and Concepts, Course
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