Dividing by Unit and Non-Unit Fractions

Warmup

To find the value of 6 ÷ , Elena thought, “How many s are in 6? and then she drew this tape diagram below. It shows 6 ones, with each one partitioned into equal pieces.

Explain why your answer is rather more than 6.


Activity #1

Division by Unit Fraction .

  • Use the “whole number” slider to choose a whole number.​
  • Use the “Denominator” slider to choose a fraction.​
  • Note the circles modeling the division.

Activity #2

Write an Equation.

(A). Write an equation for the question below. If you get stuck, consider drawing a diagram.

(B). Write an equation for the question below. If you get stuck, consider drawing a diagram.

(C). Write an equation for the question below. If you get stuck, consider drawing a diagram.

(D). Write an equation for the question below. If you get stuck, consider drawing a diagram.


Activity #3

Divide by Non-Unit Fraction .

  • Use the applets below to carry out the activities described.

To find the value of 6 divided by , Elena started by drawing a diagram for 6 divided by .

For each division expression, complete the diagram using the same method as Elena. Then, find the value of the expression. Think about how you could find that value without counting all the pieces in your diagram.

(1). How many groups of three quarters are in 6?

(2). How many four thirds are in 6?

(3). How many four sixths are in 6?


Challenge #1

Find the value of each expression.

(1). 8 ÷

(2). 12 ÷

(3). a ÷

(4). a ÷


Challenge #2

Here below is a centimeter ruler.

(1). Use the ruler to find 1 ÷ and 4 ÷ 10.

(2). What calculation did you do each time?


Challenge #3

Which expression represents how many s are in 6?

Explain your reasoning.