Understanding Fractions as Division
What does the numerator represent in a fraction when thinking about it as a division problem?
The numerator represents the dividend in a division problem.
How is division connected to the multiplication of a whole number by a non-unit fraction?
Division is the inverse of multiplication, so dividing by a fraction is the same as multiplying by its reciprocal.
What does it mean to multiply a whole number by a fraction?
To multiply a whole number by a fraction, you scale the whole number by the fraction.
How do you find the area of a rectangle when one side length is a whole number and the other side length is a fraction?
Multiply the whole number by the fraction.
Write the numerical expression for the multiplication of 6 by 2/3.
6 × 2/3
If you have 6 cookies and want to share them equally among 3 friends and yourself, what fraction of cookies will each friend get?
Each friend will get 6/4 or 1 1/2 cookies.
Provide an example of a situation where division is connected to the multiplication of a whole number by a unit fraction.
Dividing a quantity by a unit fraction is the same as multiplying the quantity by the reciprocal of the unit fraction.
Express 3/4 as a product of a whole number and a unit fraction.
3/4 is the same as 3 × 1/4.
If the length of a rectangle is 8 units and the width is 1/2, what is the area?
The area is 8 × 1/2 or 4 square units.
Interpret the expression 4 × 1/2 in a real-world context.
Multiply 4 by half of something.
Ex: 4 bananas cut in half to share with 8 people.
Explain the relationship between division and fractions using a real-life example.
Division is the process of sharing or partitioning a whole into equal parts, which is represented by fractions.
Explain the relationship between multiplication and division, using both words and a mathematical expression.
Multiplication is repeated addition, and division is the inverse operation. a×b=c is related to c÷a=b.
How is the multiplication of a whole number by a mixed number similar to the multiplication of a whole number by a fraction?
Both involve scaling a whole number by a part of a whole.
Create a word problem involving finding the area of a rectangle with a whole number and a fraction as side lengths.
(Example) Sarah has a garden that is 5 meters long and 3/4 meters wide. Find the area of her garden.
Evaluate the expression 9 × 3/4.
9 × 3/4 equals 27/4 or 6 3/4.
If you divide 15 by 3, what fraction is equivalent to the quotient?
15/3 equals 5, so the fraction is 5/1.
If you know that 5 ÷ 1/4 equals 20, what is 20 × 1/4?
20 × 1/4 equals 5.
Solve: 5 × 2/3
5 × 2/3 equals 10/3 or 3 1/3.
If the area of a rectangle is 3/4 square units and the length is 2 units, what is the width?
The width is 3/8 units.
Create a numerical expression that represents the problem: "Divide 15 apples equally among 5 friends."
15 ÷ 5
Solve the problem: You have 24 apples, and you want to divide them equally among 8 baskets. What fraction of apples is in each basket?
24/8 equals 3/1 or 3.
Solve the problem: If 30 pencils are distributed equally among 6 students, how many pencils does each student get? Express your answer as a fraction.
30/6 equals 5 pencils per student.
Represent the multiplication of 4 by 5/6 using a visual model.
Draw a rectangle representing 4 and partition it into 6 equal parts. Shade 5 of those parts.
Solve: 7 × 4/5 and represent it as the area of a rectangle.
The product is 28/5 or 5 3/5. Represent this as a rectangle with a length of 7 units and a width of 4/5 units.
Write an expression that represents finding the area of a rectangle with a length of 5 units and a width of 2/3.
5 x 2/3