3) Fractions Are Division Problems!
5.NF.B.3
5.NF.B.3
I can use and increase my understanding of multiplication and division.
I can understand that fractions are really division problems. For example: Video: Understanding fractions as division
I can solve word problems where I need to divide whole numbers leading to answers that are fractions or mixed numbers. Real-World Problems: Video: Divide Whole Numbers by Fractions Video: Dividing Whole Numbers & Fractions (t-shirts) Practice: Fraction & Whole Number Division Practice: Dividing Fractions (real-world problems) Examples: The following example is from Illustrative Mathematics: 1) After a class potluck, Emily has three equally sized apple pies left and she wants to divide them into eight equal portions to give to eight students who want to take some pie home. a) Draw a picture showing how Emily might divide the pies into eight equal portions. Explain how your picture shows eight equal portions. The picture shows 8 equal portions because each of the 3 pies is divided into 8 equal pieces.
b) What fraction of a pie will each of the eight students get? Each student will get one slice from each pie. for example, Mario will get the red slices. 1 + 1 + 1 = 3 Mario will get 3/8 of the leftovers. 8 8 8 8 In fact, each of the 8 students get 3/8. c) Explain how the answer to (b) is related to the division problem 3 ÷ 8. This task gives us an opportunity to understand that a = a ÷ b in a concrete, real-world example. b In other words, 3 ÷ 8 is the same value as fraction 3. 8 Let's use fact families! a ÷ b = c a = 3 and b = 8 3 ÷ 8 = c so c × 8 = 3 In other words, we can define "3 ÷ 8" in terms of multiplication: "3 ÷ 8" is the same value (number) that you multiply times 8 to get 3. You can then define 3/8 (three-eighths) as unit fractions: 3 = 1 + 1 + 1 8 8 8 8 3/8 is the number you get by making 3 copies of 1/8. So, if b people share a pies equally, then each person gets a/b of a pie. ************ Example #2 12 people students need to survey 100 people. To split up the job equally, how many people will each student survey? The answer needs to give an idea of how many people, so it can be a fraction or a mixed number. In this case, 100 people are being divided equally among 12 students. The fraction will be 100/12. Though it would take a while, you could create a model of this. It might look like 100 squares, and you write "1" over the first square, "2" over the next, and so on until you reach 12. Then you start over, writing "1" over the 13th square, "2" over the the 14th square, and so on until you've gone through 12 again. Repeat this process until all the squares have numbers. Count up all the 1s. You should have nine 1s (8 × 12 = 96, and 100 - 96 = 4, sot you'll have 8 of each number except 1, 2, 3, and 4 will show up 9 times). ************ Example #3 If 9 people want to share a 50-pound sack of rice so that each person has the same amount, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? |
If you want to read the CA State Standards:
Big Idea: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Breaking that apart... Interpret 3/4 as the result of dividing 3 by 4. Note: a) that 3/4 multiplied by 4 equals 3, and b) that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. |