What is 2 thirds divided by one half? ... - Brainly.com This Is a Certified Answer × Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest. Its 2/3 divided in half. It's 1/3 Im pretty sure What is one half of two-thirds? | Reference.com What is one half of two-thirds? A: Quick Answer One half of two-thirds is equal to one-third. One finds this answer by multiplying the fraction two-thirds by one-half, which gives 2/6. This fraction simplifies to one-third, or 1/3. Full Answer Another method one can use to arrive at this answer is division. One can divide the dividend, two-thirds, by two, the divisor. However, one needs to use the reciprocal of two, which is one-half when performing a division of fractions. The divisor needs to be changed into its reciprocal number. One can then multiply the two fractions of one-half and two-thirds. Fractions have numerators, the top numbers, and denominators, the bottom numbers.

After performing either a division or multiplication of fractions, one may need to reduce or simplify the fraction into lowest terms. How to find half, or a third, or any part of a number -- A complete course in arithmetic Example 1. How much is a third of 120? Answer. Ignore the 0. Then A third of 12 is 4. A third of 120 is 40. Similarly, A third of 1,200 is 400. A third of 120,000 is 40,000. It is a 4 followed by four 0's. Example 2. How much is a third of $1.20? Solution. Ignore the decimal point. A third of 120 is 40. Now replace the decimal point. A third of $1.20 is $.40. Ignoring decimal points is typical in practically all problems involving decimals. (Compare Lesson 9 .) Example 3. How much is a fifth of $4.50? Solution. Ignore the decimal point. A fifth of 450 is 90.

(A fifth of 45 is 9.) Therefore a fifth of $4.50 is $.90. Example 4. How much is an eighth of 4,000? Answer. If we ignore all the 0's, then we cannot take an eighth of 4. But if we ignore only two 0's, then An eighth of 40 is 5. Therefore, An eighth of 4000 is 500. Decomposing Example 5. How much is half of 112? Solution. Just as we can divide by decomposing, so we can find a part of a number. We can easily decompose 112 into two numbers whose half we know: 112 = 100 + 12. Half of 100 is 50. Half of 12 is 6. Therefore, half of 112 is 56. We see then that to find a part of a sum -- of 100 + 12 -- we may find that part of each term of the sum, and then add.

Half of 112 = Half of 100 + Half of 12. This is also true for adding parts, plural: Three fourths of 108 = 84. Why did we choose 240? Because, since 24 has an exact third, then so does 240. And 240 is close to 252. Example 7. Three people go to lunch and the bill is $32.40. How much does each one pay? Solution. We must find a third of $32.40. Now, a third of $30 is $10. A third of the remainder, $2.40, is $.80. (Compare Example 2 .) Each one will pay $10.80. Example 8. How much is a fifth of $47.50 Solution. What number closest to 47 has an exact fifth? 45. Therefore decompose $47.50 into $45 + $2.50. A fifth of $45 is $9. A fifth of $2.50 is $.50.

Therefore, a fifth of $47.50 is $9.50. According to Lesson 15, we have found that $9.50 is 20% of $47.50. Also in Lesson 15, we saw that to calculate a part of a number, divide . Symmetrically, then, to divide we may take a part. 3. Take the part that corresponds to the name of the divisor. To divide by 2, take half. To divide by 3, take a third. And so on. Example 9. There are 500 envelopes in a box. If you use 2 envelopes every day, how many days until the box will be empty? Solution. How many 2's are there in 500? This is a division problem. The divisor is 2. Therefore take half. Half of 500 is 250. The box will be empty in 250 days. Now, to divide by 2 does not mean to take half. (It means to name the number of 2's.) But by taking half we can know how many 2's.

For, That means that 250 is half of 500. But that implies 250 × 2 = 500. That means there are two hundred fifty 2's in 500. And we could know that by taking half. Compare Lesson 11, Example 5 . Example 10. How many 3's are there in 252?. Solution. This is a division problem: 252 ÷ 3. To answer, take a third of 252. That was Example 6 . 252 ÷ 3 = 84. 4. Example 14. A jacket originally sold for $150. a) It now sells for a third more. What is the present price? Answer. A third of $150 is $50. It now sells for $50 more. It sells for $200. b) It now sells for a third less. What is the present price? Answer. $150 − $50 = $100. Example 15. A photograph measures 8 inches by 12 inches.

a) Each side will be increased by one quarter. What are the new dimensions? Answer. A quarter of 8 is 2. A quarter of 12 is 3. The new dimensions are: (8 + 2) inches by (12 + 3) inches = 10 inches by 15 inches. b) Each side will be reduced by one quarter. What are the new dimensions? Answer. (8 − 2) inches by (12 − 3) inches = 6 inches by 9 inches. 6. Euclid, VII, 5 . Let the number A be a part of number C, and let number B be the same part of number D. Then the sum of A and B will be that same part of the sum of C and D. For, since A is the same part of C that B is of D, there are as many numbers in C equal to A as there are in D equal to B. Therefore divide C into the numbers equal to A, namely G, H, I, and divide D into the numbers equal to B, namely J, K, L; thus C and D have been divided into the same number of parts.

Then since G is equal to A, and J equal to B, the sum of G and J is equal to the sum of A and B . For the same reason, the sum of H and K, and the sum of I and L, are also equal to the sum of A and B. Therefore, as many numbers as there are in C equal to A, so many are there in the sum of C and D equal to the sum of A and B. Therefore, whatever multiple C is of A, the sum of C and D is the same multiple of the sum of A and B. Therefore, whatever part A is of C, the sum of A and B is the same part of the sum of C and D. Which is what we wanted to prove. * That property of numbers is also true for parts, plural. For example: Three fifths of 100 + Three fifths of 10 = Three fifths of (100 + 10). Here is the theorem: Euclid, VII, 6 . Let the number A be the same parts of number C that number B is of number D. Then the sum of A and B will be the same parts of the sum of C and D.

For, since A is the same parts of C that B is of D, there are as many numbers in A equal to a part of C as there are in B equal a part of D. Divide A into those numbers equal to a part of C, namely G, H, I. And divide B into those numbers equal to a part of D, namely J, K, L; thus A and B have been divided into the same number of parts. Then since G is the same part of C that J is of D, the sum of G and J is that same part of the sum of C and D. ( Theorem 1 .) For the same reason, the sum of H and K, and the sum of I and L, are also that same part of the sum of C and D. Therefore, whatever parts A is of C, the sum of A and B is the same parts of the sum of C and D. Which is what we wanted to prove. Since these are true theorems of arithmetic, the factoring axiom of algebra, ab + ac = a(b + c), can be applied to arithmetic -- when multiplication by a fraction a is defined as in Lesson 27.

At this point, please "turn" the page and do some Problems . or Parts of natural numbers, Section 2 -- A complete course in arithmetic It means that the larger number is not a multiple of the smaller. 100 is not a multiple of 75. Therefore we say that 75 is parts of 100. It is three fourth parts, or simply three fourths. If the entire figure represents 15, then 5 is the third part of 15, and 10 is two third parts of 15. If the entire figure represents 18, then 6 is the third part of 18, and 12 is two third parts of 18. If the entire figure represents 21, then 7 is the third part of 21, and 14 is two third parts of 21. And so on. Two thirds of a number are twice as much as one third. Example 1. Fifths. Here is 10 divided into fifths, that is, into five equal parts: Each 2 is a Fifth. Let us count them. 2 is is the fifth part of 10.

4 is two fifth parts of 10. 6 is three fifth parts of 10. 8 is four fifth parts of 10. And 10 is all five of its fifth parts. Example 2. How much is two thirds of 12? Answer. To name two thirds of 12, we must first name one third. But to name one third, we can simply divide by 3 . "12 divided by 3 is 4." Two thirds will then be two times 4: 8. We see, then, that to take two thirds of a number, divide it by 3, then multiply times 2. Example 3. How much is two thirds of 27? Answer. "3 goes into 27 nine times. Nine times 2 is 18." (One third of 27 is 9. Two thirds are 18.) Example 4. How much is three fourths of 28? Answer. "4 goes into 28 seven times. Seven times 3 is 21." We can illustrate this with any number that has a fourth part, namely any multiple of 4.

For example, 12, 40, 100: One fourth of 12 is 3. Three fourths are 9. One fourth of 40 is 10. Three fourths are 30 One fourth of 100 is 25. Three fourths are 75. 6. Example 5. How much is four fifths of 15? Answer. "5 goes into 15 three times.. Three times 4 is 12." Each 3 is a fifth part of 15. 6 is two fifth parts of 15. 9 is three fifth parts of 15. 12 is four fifth parts, or simply four fifths, of 15. Example 6. In a class of 32 students, five eighths are girls. How many boys are there? Answer. The whole class is eight eighths. Therefore, if five eighths are girls, then the remaining three eighths are boys. Now, one eighth of 32 -- 32 ÷ 8 -- is 4. Therefore three eighths will be three times 4: 12.

There are 12 boys in the class. Percent: Parts of 100% We have seen that a percent is another way of naming a part. Since 100% is the whole ( Lesson 4, Question 5 ), and since 50% is half of 100%, then 50% means half. 50% of 40 -- half of 40 -- is 20. Since 25% is a quarter of 100%, then 25% is another way of saying a quarter. A quarter of 40 -- 25% of 40 -- is 10. Since 75% is three quarters of 100%, then 75% means three quarters. 30 is 75% of 40. Whichever part or parts the percent is of 100%, the percent means that part or those parts. Fifths Let the circle represent 100%, and let us divide it into fifths, that is, into five equal parts -- into 20's. Each 20% is a fifth of the circle.

Two fifths of the circle -- of 100% -- is 40% Three fifths is 60%. Four fifths is 80%. That is what those percents mean: 20% means one fifth. 100% is the whole; it is all five fifths. Example 7. How much is 60% of 45? Answer. 60% means three fifths. "5 goes into 45 nine times. Nine times 3 is 27. 60% of 45 is 27. Example 8. A scarf that sells for $35 is on sale at 40% off. How much do you pay? Answer. "40% off" means that two fifths of the price will be subtracted. One fifth of 35 is 7. Therefore, two fifths are 14. You will pay $14 less: $35 − $14 = $21. You will pay $21. More simply, since 40% of the price will be subtracted, then you will pay 60%.

60% -- or three fifths of $35 -- is three times $7, which is $21. For more on percent, see Lesson 17 . Finally, we will state this theorem: Each number is either a part of a larger number or parts of it. (Euclid, VII.4.) We will illustrate that with each number less than 9. We will see that each number less than 9 is either a part of 9 or parts of 9. Now, 9 units can be divided either into Ninths or Thirds: (If 9 is divided into Ninths, then it is divided into 1's. If 9 is divided into Thirds, then it is divided into 3's: 3, 6, 9.) Let us now see how each number is related to 9. 1 is the ninth part -- or one ninth -- of 9. 2 is two ninth parts of 9. (The point again is that each 1 is a ninth part of 9.) 3 is three ninths of 9 -- and also the third part of 9. 4 is four ninths of 9. Count them! 5 is five ninths of 9.

6 is six ninths -- and also two thirds -- of 9. 3 + 3. 7 is seven ninths of 9. 8 is eight ninths of 9. Notice again how each number says its name: 1 is one ninth of 9. 2 is two ninths of 9. 3 is three ninths of 9. The first number says its cardinal name. 9 says its ordinal name. Each number less than 9, then, is either a part of 9 or parts of it. We can therefore express in words how each number is related to 9. We can say that 5, for example, is "five ninths" of 9. Example 9. What relationship has 9 to 10? Answer. If we divide 10 into 1's, then each 1 is a tenth part of 10. 1 is one tenth of 10. 2 is two tenths of 10. 3 is three tenths of 10. And so on, until we come to 9: 9 is nine tenths of 10. Again, the numbers 9 and 10 say their names.

9 says its cardinal name "nine." 10 says its ordinal name "tenth." Please "turn" the page and do some Problems . or Fractions Fractions Unit 14 > Lesson 1 of 11 A circle is a geometric shape that we have seen in other lessons. The circle to the left can be used to represent one whole. We can divide this circle into equal parts as shown below. This circle has been divided into 2 equal parts. This circle has been divided into 3 equal parts. This circle has been divided into 4 equal parts. We can shade a portion of a circle to name a specific part of the whole as shown below. Definition: A fraction names part of a region or part of a group. The top number of a fraction is called its numerator and the bottom part is its denominator. So a fraction is the number of shaded parts divided by the number of equal parts as shown below: number of shaded parts denominator Looking at the numbers above, we have: There are two equal parts, giving a denominator of 2. One of the parts is shaded, giving a numerator of 1. There are three equal parts, giving a denominator of 3.

Two of the parts are shaded, giving a numerator of 2. There are four equal parts, giving a denominator of 4. One of the parts is shaded, giving a numerator of 1. Note that the fraction bar means to divide the numerator by the denominator. Let's look at some more examples of fractions. In examples 1 through 4 below, we have identified the numerator and the denominator for each shaded circle. We have also written each fraction as a number and using words. Example 1 four-fifths Why is the number written as three-fourths? We use a hyphen to distinguish a fraction from a ratio. For example, "The ratio of girls to boys in a class is 3 to 4." This ratio is written a 3 to 4, or 3:4. We do not know how many students are in the whole class. However, the fraction is written as three-fourths (with a hyphen) because 3 is 3/4 of one whole. Thus a ratio names a relationship, whereas, a fraction names a number that represents the part of a whole. When writing a fraction, a hyphen is always used.

It is important to note that other shapes besides a circle can be divided in equal parts. For example, we can let a rectangle represent one whole, and then divide it into equal parts as shown below. two equal parts four equal parts five equal parts Remember that a fraction is the number of shaded parts divided by the number of equal parts. In the example below, rectangles have been shaded to represent different fractions. Example 5 one-fourth one-fifth The fractions above all have the same numerator. Each of these fractions is called a unit fraction. Definition: A unit fraction is a fraction whose numerator is one. Each unit fraction is part of one whole (the number 1). The denominator names that part. Every fraction is a multiple of a unit fraction. In examples 6 through 8, we will identify the fraction represented by the shaded portion of each shape. Example 6 a In example 6, there are four equal parts in each rectangle. Three sections have been shaded in each rectangle, but not the same three. This was done intentionally to demonstrate that any 3 of the 4 equal parts can be shaded to represent the fraction three-fourths. b a b In example 7, each circle is shaded in different sections.

However, both circles represent the fraction two-thirds. The value of a fraction is not changed by which sections are shaded. Example 8 a In example 8, each rectangle is shaded in different sections. However, both rectangles represent the fraction two-fifths. Once again, the value of a fraction is not changed by which sections are shaded. b In the examples above, we demonstrated that the value of a fraction is not changed by which sections are shaded. This is because a fraction is the number of shaded parts divided by the number of equal parts. Let's look at some more examples. Example 9 answer 4 Summary: A fraction names part of a region or part of a group. A fraction is the number of shaded parts divided by the number of equal parts. The numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. Exercises In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the fraction two-thirds, enter 2/3 into the form. 1.

How to Calculate Two Thirds of a Number | Sciencing How to Calculate Two Thirds of a Number By Sky Smith calculette noire image by Tadzio from <a href=' Fractions generally represent a portion of something. For instance, if 75 percent of 1,000 students passed a math course, then you could say that 75 out of 100, or three-fourths, of every student passed the course. By applying this fraction, three-fourths, to the whole number, 1,000, you can find exactly how many students passed the course. In this case, three-fourths (3/4) equals 0.75, which when multiplied to 1,000 yields 750. Needless to say, converting fractions to decimals is just one of many ways to handle fractions and other numbers. By Calculator Step 1 Type in two divided by three and press the equals sign on your calculator. You should receive a decimal similar to 0.666... repeating. Step 2 Press the multiplication sign and type in the number of interest.

For example, if you are finding two-thirds of 100, after you press multiplication sign type in "100." Then press the equals sign. Step 3 Interpret your result. If you have 66.666... repeating, then you may wish to round this to the tenths place of 66.7. Thus, two-thirds of 100 is approximately 66.7. By Hand Step 1 Divide the number of interest by 3. If you are finding two-thirds of 60, then first divide 60 by 3. You will get the number 20 as your result. Step 2 Round your result to the tenths place. In some cases, you may get a repeating decimal and it may be easier to use a smaller approximation. For instance, if you divide 250 by 3 you get 83.333... repeating. You may want to use 83.3 as your result instead of the entire decimal. Step 3 Multiply the result by 2. If you have 20 as your result, then 20 times two is 40.

Therefore, two-thirds of 60 is 40. References Math is Fun: Multiplying Fractions About the Author Sky Smith has been writing on psychology, electronics, health and fitness since 2002 for various online publications. He graduated from the University of Florida with honors in 2005, earning a Bachelor of Science in psychology and statistics with a minor in math. Dividing into thirds Dividing into Thirds Many folds offer the challenge of dividing the sides of a square into thirds. Students can be offered this challenge and then asked to compare methods. Images were made using Paint. Dividing into thirds by estimation What some origami folders call 'making an S' or simple trial-and-error consists of estimating a third from one side and then dividing the other side, that is, dividing the estimated two-thirds portion, and making a mark. You then fold again from the original side. The new mark generally will be different from the original and represents an improved estimate. One iteration is often sufficient, or you can keep going. The question is why does this work? That is, why do the estimates get better and better?

This should be in the reach of students familiar with limits, though I frankly doubt that students who have just studied book procedures can transfer their knowledge to this domain. Instead, I think this exercise can and should be done to provide a basis for future work in limits. This is what educators call scaffolding. Take a very long strip of paper, perhaps from a roll of wax paper or aluminum foil. Estimate one third of this length and mark the paper (call it A). Now fold from the other side, that is, divide the 'two-thirds' side in half. Make a mark (call it B). Fold from the original end to the new mark (call it A1). If you repeat this procedure, the marks A, A1, A2, etc. should get closer together and approach the real one-third mark. You can measure the edge, either before or after, to ascertain this. What is happening is that if the original error, the deviation from the one-third point, was E, each fold halves the error. To explain this algebraically, if, starting from one end, the estimated (guessed) one-third point was L/3 + E, then the distance from the other end is L*2/3 -E.

(I use the asterisk, *, for times.) Folding the long portion up to the guess is equivalent to dividing that length by 2: (L*2/3-E) * 1/2 is L/3-E/2. That is, this mark is E/2 from the correct position. As you continue doing this, back and forth, each fold improves the estimate by reducing the error by one-half. Another way of demonstrating this is to take a very long strip of paper, measure the one-third point, and purposely choose a point distinctly different. (Perform the procedure and measure the differences.) It takes two folds, each one halving the error, for each iteration. So if A is E away from the actual point, B will be E/2 off from the desired (2/3) point, A1 will be E/4 away, A2 E/16 away, and so on. It is easy to see that the casual "making an S" method can quickly get to a satisfactory estimate. point A side point for this is that my naming scheme of A and B and A1, A2, etc. is arbitrary.

It does have some appealing aspects to it, but your students may devise schemes that appeal to them more. In any case, it is important to point out what is arbitrary and what is not. The symbolic or algebraic approach complements the experimental exploration. These different approaches to verifying that the iterative approach works provide different entry points to the topic for the students. Dividing into thirds by geometry A totally different way of determining a one third mark is to use similar triangles as shown below. Make a diagonal fold (A to F) for the whole square. Fold the square in half, a book fold (B to E). Make a diagonal fold for the half-square. This is fold EC. The point marked G is one-third of the way from C to A since the edge XG is twice CG, because of the similar triangles EBC and XGC. However, XG is equal to AG because of the similar triangles ACF and AGX. An exercise for the reader (and for your students) is to notice and justify an easy way to mark the other sides of the square once one set of sides has been divided into thirds. Other methods of dividing line segments into specific equal parts exist and are worth studying.

The Dollar Bill Rosette features dividing the long sides of a dollar bill into 11ths.

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Level G Lesson 9 Divide Fractions The objective for lesson 9 is the student will work with division of fractions.

We will have three essential questions that will be guiding our lesson. Question 1, why is it important to know how to build a model for division of fractions? Question 2, what does a division sentence mean? Question 3, what are the steps for dividing a fraction by a fraction? The SOLVE problem for this lesson is, Ms. Sherrill has three fourths of a yard of red material. She needs to cut the material into pieces that are one eighth of a yard in length. How many pieces of material will she have? We�re going to S the problem and we�re going to start by underlining the question. How many pieces of material will she have? The second part of S is to complete the sentence this problem is asking me to find, the number of pieces of material. The first problem we are going to look at is 2 divided by one half. The meaning of this problem is, how many groups of one half are in 2 whole units? We�re going to model this problem using our fraction strips a manipulative model and I�m going to start by representing the first fraction. I have two whole units. In a division problem the first number is called a dividend.

The second number is called the divisor. The divisor tells us what section we�re going to divide the dividend into. So this time our divisor is one half. So we�re going to divide our whole units into groups of one-half. There�s my first whole unit divided into one half and my second whole unit divided into groups of one half. When I add those 1, 2, 3, 4, I have 4 groups of one half in 2 whole units. I�m going to go up here and now I�m going to model it pictorially. I have 1 group, 2 whole groups and I�m going to divide it into groups of One half unit. I have 1, 2, 3, 4, 2 divided by one half is equal to 4. The second problem we�re going to model is 2 divided by one third. The meaning of this problem is, how many groups of one third are in 2 whole units? We�re going to model this problem by following our fraction strip by starting with our dividend which is two whole units. We have one unit and then we have a second unit.

We�re going to divide our whole units into groups of one third. By one third, I take my green fraction strip, I have 3 units in 1 whole unit and I have 3 one third units in the second unit. So for 2 whole units, I have 1, 2, 3, 4, 5, 6, one third units. I can also model this pictorially by representing my first fraction, my dividend, and dividing it into groups of one third. I have 1 group, 2 groups, 3 groups, 4 groups, 5, groups and a total of 6 groups, 2 divided by one third is 6. We�re now going to model dividing fractions by another fraction. Our problem is one third divided by one sixth. The meaning of this is, how many groups of one sixth are in one third? In division we represent our first number our dividend with our fraction strip one third unit. We then need to find out how many groups of our one sixth we can fit into that one third unit. We take our fraction strips and we see that there are 2 groups of one sixth in one third.

This problem can be modeled pictorially by drawing the one third fraction bar, and the 2 groups of one sixth underneath. I have a total of 2 groups, 2 groups of one sixth. The next problem we�re going to model is two thirds divided by one twelfth. The meaning of the problem is, how many groups of one twelfth are in two thirds? When we are modeling division multiplication we represent our first fraction. I have my two thirds or 2, one third units. I need to divide that into groups of one twelfth. So I�m going to place my pink fraction strips from my manipulative kit underneath my one third units to see how many groups of one twelfth are in two thirds. I have 1, 2, 3, 4, 5, 6, 7, 8. I can model this pictorially by drawing my 2 one third fraction strips and then drawing the one twelfth units underneath to show that there are 8. I�m then going to add those up for a total of 8. How many groups of one twelfth are in two thirds unit, 8 groups of one twelfth.

We are now gong to model the problem three fourths divided by one half. In division we always start with our first fraction or our dividend. The meaning of or problem is, how many groups of one half are in three fourths? I�m going to take my one half units and place them underneath my one fourth units. You can see that we have a second brown strip that goes beyond our 3, one fourth units. What we�re going to do is we�re going to take the one half unit and underneath that I�m going to place the legal trade of two fourths. Now I have completely covered my three fourths unit, 1 full one half unit covers my two fourths and one half of my brown unit covers my third fourth in this picture. Because we�ve divided the one half into 2 sections, 1 out of the 2 makes up the third fourth. When we go up to the pictorial model we have our 3 fourths and we are dividing into groups of one half. Our one half extends over the last fourth so we divide the one half into 2 pieces, one out of those two pieces or one half of the one half completes our model.

So we have 1 whole group of one half, and then one half of a group which is our one fourth. How many groups of one half are in three fourths? 1 and one half groups of one half. We are going to talk about a method of dividing fractions without using models. We are going to be learning about reciprocals. One fourth and 4 are reciprocals because they have a product of 1. Any whole number can b e written as a fraction by placing it over one, so the 4 whole number can be written as an improper faction of 4 over 1. A number is considered to be a reciprocal if the product of 2 fractions is equal to 1. We found the reciprocal of one fourth by inverting the fraction, that is flipping the fraction so that the denominator is now the numerator and the numerator is now the denominator. In example 2, we�re going to look at one fifth and 5. These 2 values are reciprocals. Remember we are going to first change our whole number to an improper fraction by writing it over 1.

Any whole number can be written as a fraction by placing it over 1 as the denominator because 5 divided by 1 is still 5. When we multiply one fifth times 5 over 1 we see that our product is 1. These 2 numbers are reciprocals. The last example we�re going to look at is example 3. The question is what is the reciprocal of two thirds. The reciprocal of two thirds is 3 halves. We have inverted or flipped our fraction so that the denominator is now the numerator and the numerator is now the denominator. We know that these two values are reciprocals because when we multiply them because our product is 1. We�re going to model a division of fraction problems using reciprocals. Remember a reciprocal is any two pairs of fractions that are multiplied with a product of 1. We find the reciprocal of the fractions by inverting it. We are going to start our problem three fourths divided by five sixth by rewriting it vertically.

Remember we have two fractions here but that the fraction line is also an indicator of the operation of division, 3 / 4 is actually 3 divided by 4, five sixths is actually 5 divided by 6, and we can change this division sign to the vertical model. When we are dividing two values we need to get a denominator of 1 here. We can do that by multiplying five sixths by it�s reciprocal which is six fifths. Remember you find the reciprocal by inverting the fraction. If we�re going to multiply by six fifths we also to have to multiply our numerator by six fifths, and we can do that because if we look at these two values six fifths divided by six fifths is the value of 1. If we divide something by 1 we do not change the final value. We�re going to go ahead and multiply our numerator�s, 3 times 6 is 18, 4 times 5 is 20, 5 times 6 is 30, 6 times 5 is 30, 30 over 30 is equivalent to 1.

Our value of 18 over 20 divided by 1 is that same value 18 over 20. We�re going to simplify our fraction by dividing 2 over 2 and again this is the value of 1 so we�re not changing the value of the fraction we�re simply simplifying it, 18 divided by 2 is 9, 20 divided by 2 is 10. And our simplified answer is nine tenths. This is the information that you should include on the division section of your fraction book. You want to start by writing what the division means, �how many groups of blank are in blank?� In division we represent the first fraction and divide it by the value of the second fraction, � how many groups of one fourth are in one half?� Then what we�re going to do is we�re going to show one half and we place one fourth units underneath it and we count the number of groups of one-fourth in one half. There are 2 groups of one fourth in one half. We are going back to our SOLVE problem from the beginning of the lesson. Ms. Sherrill has three fourths of a yard of red material.

She needs to cut the material into pieces that are one eighth of a yard in length. How many pieces of material will she have? We S the problem, we study the problem, we underline the question and we completed the sentence this problem is asking me to find the number of pieces of material. We�re now moving to O, we are going to organize our facts. First we are going to identify the facts. Ms. Sherrill has three fourths of a yard of red material. She needs to cut the material into pieces that are one eighth of a yard in length. The second step is to eliminate the unnecessary facts. Ms. Sherrill has three fourths of a yard of material. We need to know how much material she has, so that fact will be necessary. She needs to cut them into pieces that are one eighth of a yard. We also need to know that so we have no unnecessary facts in this problem. Then we�re going to list the necessary facts. We have three fourths of a yard of material, and we need one eighth yard pieces. We�re going to line up our plan by choosing an operation or operations.

Since we�re cutting material, we�re actually dividing it into pieces we�re going to choose division. Our plan of action will be to divide the total quantity of material by the length of each piece. We are now moving to our V step and we are going to begin to verify our plan with action by estimating our answer. We know we have three fourths of a yard, and we know each piece needs to be one eighth in length, so our estimate is going to be about 5. We�re now going to carry out our plan. We take our three fourths yard and divide it into pieces that are one eighth in length. We�re going to use the concept of reciprocals, remember we divided by one eighth we were multiplying both the fractions by 8 over 1, 3 times 8 is 24, 4 times 1 is 4, when we divide and simplify we have 6 pieces of material. To complete our word problem we are going to go back to the E step and examine our results. Does our answer make sense? We had 6 pieces of material and we were looking for the number of pieces of material. So, yes our answer makes sense. Is your answer reasonable?

Our estimate was 5 and our answer is 6. So, yes our answer is reasonable because our answer is close to our answer of about 5. Is your answer accurate? We�re going to go back and recheck our work and the answer is yes. Then we are going to complete the E step by writing our answer in a complete sentence. Ms. Sherrill will have 6 pieces of material. Now we are going to go back and answer the essential questions from the beginning of our lesson. Why is it important to know how to build a model for division of fractions? So we will know what the problems mean. What does a division sentence mean? How many groups of blank are in blank? What are the steps for dividing a fraction by a fraction? We create a reciprocal of the second fraction and then multiply.

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Question: What is two-thirds divided by one-third?
Answer: 2