options: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

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?

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

Interpret multiplication as scaling (resizing), by:
- 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.
- 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.
problem_activity: Problem 1
a.   Kyle has 6 Skittles.
$${{1\over3}}$$
of them are red. How many of Kyle's Skittles are red?
b.   Samantha also has 6 Skittles.
$${{2\over3}}$$
of them are red. How many of Samantha’s Skittles are red?
Problem 2
a.   Find the value of each of the following.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:40%"}, "tbody": [{"tr": [{"td": [{"p": [{"_attributes": {"style": "margin-left:40px"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{3}$$"}], "_values": ["i.", "of 9"]}]}, {"p": [{"_attributes": {"style": "margin-left:40px"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{2}{3}$$"}], "_values": ["ii.", "of 9"]}]}]}, {"td": [{"p": [{"_attributes": {"style": "margin-left:40px"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{5}$$"}], "_values": ["iii.", "of 10"]}]}, {"p": [{"_attributes": {"style": "margin-left:40px"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{4}{5}$$"}], "_values": ["iv.", "of 10"]}]}]}, {"td": [{"p": [{"_attributes": {"style": "margin-left:40px"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{4}$$"}], "_values": ["v.", "of 12"]}]}, {"p": [{"_attributes": {"style": "margin-left:40px"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{2}{4}$$"}], "_values": ["vi.", "of 12"]}]}]}]}]}]}
b.   What do you notice about the solutions to the computations in the leftmost column of the table? What do you wonder?
c.   What do you notice about the solutions in each row of the table? What do you wonder?
Problem 3
a.   Mrs. Pham has 8 apples. She wants to give
$${{3\over4}}$$
of the apples to her students. How many apples will her students get?
b.   In a class of 24 students,
$${{5\over6}}$$
of them are boys. How many boys are in the class?


correct_option_index: 0

3