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## Converting Terminating Decimals to Fractions.

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**Converting Terminating Decimals to Fractions.**This will take you to the previous slide. This will advance to your next slide.**Teachers Page**Learners: This will be taught in a seventh grade math class with basic knowledge of their math operations. Environment: Can be done at home for study purposes OR The teacher could take students to a computer lab and supervise the students as they work independently at their own pace.**Teachers Page Cont.**Objectives: Given ten terminating decimals, students will be able to convert them to fractions with 100% accuracy. Given ten fractions, students will be able to reduce them to simplest form with 90% accuracy. Given ten combinations of two different fractions, students will be able to add them together with 80% accuracy. Given ten combinations of two different fractions, students will be able to subtract them with 80% accuracy. Given ten combinations of two different fractions, students will be able to multiply them with 80% accuracy. Given ten combinations of two different fractions, students will be able to divide them with 80% accuracy.**Menu**Motivation Decimals Reducing Fractions Multiplying and Dividing Fractions Adding and Subtracting Fractions Review Quiz**Menu**Mr. Hopkins needs your help Mr. Hopkins needs us to help him learn how to convert decimals to fractions so he can make his fortune back.**Menu**Decimals Before we go into Fractions we need to make sure we know our decimal places. .1 = one tenth, 10 = ten .01 = one hundredth, 100 = one hundred .001 = one thousandth, 1000 = one thousand And it continues to increase just like regular numbers would as shown in the figure.**Menu**Decimals You can see how the name of the decimal place corresponds with the number in the denominator.**Menu**Examples You can see in the examples that the number in the numerator (the top number) is the same as the numbers in the decimal. But wait… That last example is different. In the last example we have an improper fraction. The numbers in the decimal are still on top but the denominator still only goes as far as the last decimal.**Menu**Practice Problems Convert the following decimal into a fraction: 0.0001 A. #1 B. C. D.**Menu**Incorrect Which decimal place was the number in? RETRY**Menu**CORRECT The one was in the ten thousandth place so the denominator is 10000. Next Problem**Menu**Convert the following decimal into a fraction: 0.536 A. #2 B. C. D.**Menu**Incorrect The numerator consists of all the numbers in the decimal AND Don’t forget what decimal place you’re in Retry**Menu**CORRECT The last decimal place was in the thousandths place so 1000 ends up in the denominator and since the numbers in the decimal are 536, these end up in the numerator. Next Problem**Menu**Convert the following decimal into a fraction: 2.53 A. #3 B. C. D.**Menu**Remember that the denominator is based on the last decimal place. Retry**Menu**CORRECT The last decimal point is in the hundredths place so 100 goes in the denominator and then the number in the decimal, 253, will go in the numerator, which in this case will create an improper fraction.**Menu**What would you like to do? Decimals Continue to Reducing Fractions**Menu**Reducing Fractions Now that we know how to create fractions from decimals we will learn how to simplify those fractions. Simple Example: ÷ 5 → At this point you can no longer divide both numbers by a common integer so you are at its simplest form.**Menu**Reducing Fractions To reduce a fraction, there is a series of steps that must be taken. 1.) List all the Factors of both the numerator and denominator. 2.) Find the Greatest Common Factor (GCF). 3.) Then Divide both numerator and denominator by the GCF. 4.) Then repeat the previous three steps to make sure you really are in the simplest form.**Menu**Reducing Fractions EXAMPLE: Reduce to its simplest form. 1.) 120 200 2.) The GCF here is 40. 120200 60100 3.) Divide both by GCF. 40 50 30 40 2425 20 20 15 10 12 8 4.) 3 5 Only matching factor is 1 so we are in the 10 6 35 simplest form. 8 5 1 1 6 4 5 2 4 1 3 2 1**Menu**Practice Problems Reduce the Fraction to its simplest form: A. #4 B. C. D.**Menu**What are the factors? 8: 8 4 2 1 20: 20 10 5 4 2 1 Retry**Menu**CORRECT 1.) Find the factors: 8: 8 4 2 1 20: 20105 4 2 1 2.) The GCF is 4. 4.) Check for anymore GCFs. 2: 2 1 5: 5 1 3.) Divide both sides by 4. Next Problem**Menu**Reduce the fraction to its simplest form: A. #5 B. C. D.**Menu**What are the factors? 126: 126 63 42 21 18 14 9 7 6 3 2 1 328: 328 164 82 41 8 4 2 1 Retry**Menu**CORRECT 1.) Find the factors: 126: 12663422118149763 2 1 328: 328164824184 2 1 2.) The GCF is 2. 3.) Divide both by 2. 4.) Check for anymore GCFs. 63: 6321973 1 164: 164824142 1 Next Problem**Menu**Reduce the fraction to its simplest form: A. #6 B. C. D.**Menu**What are the factors? 55: 55 11 5 1 40: 40 20 10 8 5 4 2 1 Retry**Menu**CORRECT 1.) Find the factors. 55: 5511 5 1 40: 4020108 5 42 1 2.) The GCF is 5. 3.) Divide both by 5. 4.) Check for anymore GCFs: 11: 11 1 8: 842 1**Menu**What would you like to do? Decimals Reducing Fractions Continue to Multiplying and Dividing Fractions**Menu**Multiplying and Dividing Fractions When it comes to fractions, multiplication and division are much simpler than addition and subtraction so we will be learning these functions first. Example: ❶ There are three simple steps to multiplying a fraction. ❷ ❸**Menu**Multiplying and Dividing Fractions Dividing fractions is slightly more complicated than multiplying them. Example: You can see that dividing fractions is actually just multiplying by the reciprocal of the divisor.**Menu**Practice Problems Solve the following problem and simplify: #7 A. B. C. D.**Menu**Hint: Remember to simplify. Retry**Menu**CORRECT Next Problem**Menu**Solve the following problem and simplify: A. #8 B. C. D.**Menu**Hint: Remember to simplify. Retry**Menu**CORRECT**Menu**What would you like to do? Decimals Reducing Fractions Multiplying and Dividing Fractions Continue to Adding and Subtracting Fractions**Menu**Adding and Subtracting Fractions When adding or subtracting fractions you must first find a Least Common Denominator (LCD). Once the LCD is found you can then add or subtract the numerators and leave the denominator as the LCD. Example: First check if the larger denominator is divisible by the smaller. In this case, we can multiply by 3 to get a common denominator. Once we have a common denominator we add the numerator. Then, as always, we simplify.**Menu**Adding and Subtracting Fractions The next example shows how if the denominators are not divisible by each other we then need to list multiples of the two denominators. Example: We can see that the denominators are not multiples of each other so we will have to list other multiples of these numbers until a LCD is found. 5: 5 10 15 3: 3 6 9 12 15 The smallest multiple that both have is 15 so that is the LCD. When multiplying the denominator, you must also multiply the numerator by the same thing. Like multiplying by one. After creating our LCD we then can subtract the numerator. This is already in its simplest form.**Menu**Practice Problems Solve the following problem and simplify: #9 A. B. 1 C. D.**Menu**You must find an LCD before subtracting. Remember to simplify. Retry**Menu**CORRECT 4: 4 8 12 6: 6 12 This is equivalent to multiplying by one to get a common denominator. Denominator will stay the same as you subtract the numerator. It’s in simplest form so this is our answer. Next Problem**Menu**Solve the following problem and then simplify: A. #10 B. C. D.**Menu**You must find an LCD before adding. Remember to simplify. Retry**Menu**CORRECT 2: 2 4 6 8 10 12 14 16 18 9: 9 18 This is the same as multiplying by one so we can get the LCD. You add the numerator but leave the denominator the same. This is in its simplest form so it is the answer.**Menu**What would you like to do? Decimals Reducing Fractions Multiplying and Dividing Fractions Adding and Subtracting Fractions Continue to Review**Review**Menu Decimals • Need to know which decimal place the number is in. • (.1 = , .01 = , .001 = , etc.) • Know which numbers go in numerator. • .02 = • .21 = Reducing Fractions • First list all factors of numerator and denominator. • Find the Greatest Common Factor. • Then divide both numbers by GCF.