5.NOS.D: Apply and extend previous understanding of multiplication and division to multiply and divide fractions.

Apply and extend previous understanding of multiplication and division to multiply and divide fractions.

5.NOS.D.10Interpret a fraction as division of the numerator by the denominator (c/d = c ÷ d) in context using visual fraction models and equations to represent the problem (e.g., interpret 3/4 as the result of dividing 3 by 4 so when 3 wholes are shared equally among 4 people each person has a share of size 3/4).5.NOS.D.11Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × b). a. Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 3/4 × 2 will be less than 2 because I am creating a fractional part of 2). b. Multiply a whole number by a fraction (e.g., interpret c/d × b as c/d of b when c/d is greater than or less than 1).5.NOS.D.12Apply and extend previous understandings of multiplication to multiply a fraction by a fraction. a. Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 1/2 × 3/4 will be less than 3/4 because I will have one half of 3/4). b. Apply and extend whole number multiplication strategies (e.g. area models). c. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths.5.NOS.D.13Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factors greater than 1. a. Estimate products by reasoning about benchmark numbers and assess reasonableness of answers. b. Apply and extend whole number multiplication strategies (e.g. area model, partial products).5.NOS.D.14Interpret multiplication as scaling (sizing) in context. a. Compare the size of a product to the size of one factor based on the size of the other factor, without performing the indicated multiplication. b. Explain why multiplying a given number by a fraction greater than a 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relate the principle of fraction equivalence to the Identity Property of Multiplication.5.NOS.D.15Solve problems in contexts involving multiplication of fractions and mixed numbers, (e.g., by using visual fraction models or equations to represent the problem).5.NOS.D.16Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions in context. a. Apply estimation strategies to estimate quotients and assess reasonableness of answers. b. Use visual fraction models and equations to interpret division of a unit fraction by a non-zero whole number and compute quotients. c. Use visual fraction models and equations to interpret division of a whole number by a unit fraction and compute quotients. d. Represent and explain the computation by connecting visual fraction models and/or equations to the meaning of division with unit fractions.

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