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#IUNIT FRACTION TRIAL#

Number of terms, so for all I know a 43-term solution awaits. What I did not accomplish was a proof that 42 was the largest possible Of decomposition lead to different solutions.

#IUNIT FRACTION TRIAL#

I decided to restrict myself to unit fractions with two-digitĭenominators, in other words, natural numbers no greater than 99.īy trial and error I managed to find a sum of 42 terms that met the conditions. It's a question I began thinking about around 20 yearsĪgo when I started work on a problem involving unit fractions. Division and multiplication are opposite operations.How long can we make such a sum without repeating any of the unit You can think of multiplication as repeated addition.Īn operation that undoes another operation. For example, a circle can be partitioned into fourths.Ĭombining groups of equal size. For example, 1/5, 1/2 or 1/10Ī mathematical statement that uses an equal sign to show that two expressions are equal. For example, 1/3 or 2/3.Ī fraction with a numerator of 1. To find the answer, you need to solve the equation 8 ÷ 1/4 = ? To divide 8 by 1/4, you change the division equation into the multiplication equation 8 × 4 = ? 8 × 4 = 32, so there are 32 one-fourth pieces.įinding how many equal groups or how many in each group.Ī symbol that describes parts of a whole that is divided into equal parts. Is Delroy correct? ANSWERĭelroy is not correct. Delroy says you have 2 one-fourth pieces because 8 ÷ 4 is 2. You have a piece of ribbon that is 1/3 yard long. What fraction of the pie is each small piece? Write the equation you need to solve, draw a model to solve, and answer the question.ġ/3 ÷ 2 = 1/6. You want to divide that piece into 2 equal pieces to share. I can make 8 birdhouses with the 2-yard-long wood board. I need to find the answer to 2 ÷ 1/4 = ? First, I convert the division problem into a multiplication problem: 2 × 4. How many birdhouse floors can you make from this board? ANSWER You need the length of each board to be 14 yard. You have a board that is 2 yards long and just the right width for the floor of the bird houses you are building. You can count to find the number of half cups of milk you have. Each circle is divided in half and each half represents the 1/2 cup of milk you need for each cake. You need to solve the equation 3 ÷ 1/2 = ? Draw 3 circles to represent the 3 cups of milk. Describe a model that represents this situation and can help you find how many cakes you can make. After Video You need 1/2 cup of milk to make your favorite cake.You find that 1/2 × 5 = 5/2, so 2/5 is the wrong answer. You keep drawing halves until you have five 1/2s. You can draw a circle to represent 1 and divide it in half. How could you use reasoning and/or models to show that Debra's answer is wrong? ANSWER He should have just multiplied the numerator by 5, so the answer is 10/3.ĭebra says that the answer to 1/2 × 5 is 2/5. He multiplied both the numerator and denominator of 2/3 by 5. What fraction of the backyard is planted with tomatoes? ANSWER She plants tomatoes in 3/8 of her garden. The answer is 3/15.Īlma made 1/4 of her backyard into a garden. The answer is represented by the part of the square where the colors overlap. I drew 5 columns and colored three of the columns blue to represent 3/5. Inside a square, I drew 3 rows and colored one of the rows green to represent 1/3.

$iunit fraction$

Explain how the model shows the solution. 8 × 4 = 32, so 32 ÷ 8 = 4.ĭraw a model that shows the solution to 1/3 × 3/5.

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Think what number I can multiply by 8 to get 32, and then use the multiplication fact to find the answer. Before Video How can you use what you know about multiplication to find 32 ÷ 8? ANSWER.

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Iunit fraction