Presentation on theme: "NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number."— Presentation transcript:
1 NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) and justify the process used.CaliforniaStandards
2 Two numbers whose product is 1 are multiplicative inverses, or reciprocals.
3 A division problem can always be rewritten as a multiplication problem by using the reciprocal of the divisor.
4 Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form.5 111 2÷5 11÷1 25 11•2 1=Multiply by the reciprocal.5 11•2 1=No common factors.10 11=Simplest form
5 Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form.3 82÷23 8÷2=19 82 1÷Write as an improper fraction.=19 81 2Multiply by the reciprocal.19 • 18 • 2=No common factors19 16=3 16=1
6 ÷ 28 45 Divide. Write the answer in simplest form. 7 15 3 4 7 15 ÷ 3 4 Check It Out! Example1ADivide. Write the answer in simplest form.7 153 4÷7 15÷3 47 15•4 3=Multiply by the reciprocal.7 • 415 • 3=No common factors28 45=Simplest form
7 4 ÷ 3 ÷ ÷ 3 4 1 Divide. Write the answer in simplest form. Check It Out! Example1BDivide. Write the answer in simplest form.2 54÷3=22 53 1÷Write as an improper fraction.2 5÷ 34=22 51 3Multiply by the reciprocal.22 • 15 • 3=No common factors7 15= or122 15
8 When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10.1.320.41.320.41013.24==1 decimal place1 zero
9 Additional Example 2: Dividing Decimals Find ÷ Estimate the reasonableness of your answer.0.24 )0.3840.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer.1.624 )38.4Then divide as a whole number.- 240.384 ÷ 0.24 = 1.6Estimate: 40 ÷ 20 = 2144– 144The answer is reasonable.
10 Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer. Check It Out! Example 2Find 0.65 ÷ Estimate the reasonableness of your answer.0.25 )0.650.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer.2.625 )65.0Then divide as a whole number.- 5015– n 0The answer is reasonable.0.65 ÷ 0.25 = 2.6Estimate: 60 ÷ 20 = 3
11 Additional Example 3: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable.5.25for n = 0.15n5.25n0.15=Substitute 0.15 for n.0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.0.15 )5.253515 )525When n = 0.15, = 35.5.25n- 525
12 3.60 for n = 0.12 n 3.60 = Substitute 0.12 for n. n 0.12 Check It Out! Example 3Evaluate the expression for the given value of the variable.3.60for n = 0.12n3.60n0.12=Substitute 0.12 for n.0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.0.12 )3.603012 )360When n = 0.12, = 30.3.60n- 360
13 Understand the Problem Additional Example 4: Problem Solving Application1 2A muffin recipe calls for cup of oats.You have cup of oats. How many batches of muffins can you bake using all of the oats you have?3 41Understand the ProblemThe number of batches of muffins you can bake is the number of batches using the oats that you have. List the important information:The amount of oats is cup.One batch of muffins calls for cup of oats.1234
14 Additional Example 4 Continued 2Make a PlanSet up an equation.
15 Additional Example 4 Continued Solve3Let n = number of batches.1234= n÷3421= n•64, or 1 = n12You can bake 1 batches of the muffins.12
16 Additional Example 4 Continued Look Back4One cup of oats would make two batches so 1 is a reasonable answer.12