## Unit 4B

Example: 3/5 can be interpreted as “3 divided by 5 and as 3 shared by 5”.

**MGSE5.NF.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.Example: 3/5 can be interpreted as “3 divided by 5 and as 3 shared by 5”.

**MGSE5.NF.4**Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

**a.**Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction.

*Examples: 𝑎/𝑏 × 𝑞 as 𝑎/𝑏 × 𝑞/1 and 𝑎/𝑏 × 𝑐/𝑑 = 𝑎𝑐/𝑏*

*𝑑*

**b.**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.

**MGSE5.NF.5**Interpret multiplication as scaling (resizing), by:

**a.**Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

*Example 4 x 10 is twice as large as 2 x 10.*

**b.**Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

**MGSE5.NF.6**Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

**MGSE5.NF.7**Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

**a.**Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

**b.**Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

**c.**Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many 1/3-cup servings are 2 cups of raisins?

**MGSE5.MD.2**Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

**Videos**

**Practice Problems**

**Multiplying Fractions**

https://www.commoncoresheets.com/Math/Fractions/Multiplying%20Fractions/English/9.pdf

https://www.commoncoresheets.com/Math/Fractions/Multiplying%20Fractions/English/10.pdf

**Multiplying Mixed Numbers (Word Problems)**

https://www.commoncoresheets.com/Math/Fractions/Multiplying%20Fraction%20Word%20Problems/English/9.pdf

https://www.commoncoresheets.com/Math/Fractions/Multiplying%20Fraction%20Word%20Problems/English/10.pdf

**Interpreting Fractions as Division Problems**

https://www.commoncoresheets.com/Math/Fractions/Division%20as%20Fraction%20-%20Word/English/9.pdf

https://www.commoncoresheets.com/Math/Fractions/Fractions%20as%20Division%20Problems/English/10.pdf