Question

Writing  Make a model that shows one fourth
divided by5. Use pencil and paper. Describe a​ real-world situation for which you would want to find that quotient. Describe how you would change the model for one fourth
divided by5 to show one fourth
divided by10.
Question content area bottom
Part 1
Which of these models shows one fourth
divided by5​?
A.
01one fourth



On a number line, tick marks divide the space between 0 and 1 into 20 equal segments. The fifth tick mark to the right of 0 is labeled one fourth. Starting from the left, 5 ovals are each around 1 segment.
B.
01one fifth



On a number line, tick marks divide the space between 0 and 1 into 5 equal segments. The first tick mark to the right of 0 is labeled one fifth. Starting from the left, an oval is around each segment.
C.
01one fifth



On a number line, tick marks divide the space between 0 and 1 into 20 equal segments. The fourth tick mark to the right of 0 is labeled one fifth. Starting from the left, 4 ovals are each around 1 segment.
D.
01one fourth

Answer 1

Answer: A.

Model (pencil-and-paper):
- Draw a number line from 0 to 1 and mark it into 20 equal parts (so each tick = 1/20).
- Label the 5th tick as 1/4 (5/20).
- Circle the five adjacent 1/20 segments that make up 1/4, then separate those five segments into five equal pieces (each is one single 1/20 segment).
This shows 1/4 divided into 5 equal pieces, so each piece = (1/4) ÷ 5 = 1/20.

Real-world situation:
- You have 1/4 of a pizza left and want to share that quarter equally among 5 people. Each person gets 1/20 of the whole pizza.

How to change the model for 1/4 ÷ 10:
- Either redraw the unit into 40 equal parts (so 1/4 = 10/40) and show the ten pieces inside the quarter (each is 1/40), or take the previous model (five pieces of size 1/20) and split each of those five pieces in half to get 10 equal pieces. Each piece then equals (1/4) ÷ 10 = 1/40.

Brief arithmetic check:
(1/4) ÷ 5 = 1/4 × 1/5 = 1/20.
(1/4) ÷ 10 = 1/4 × 1/10 = 1/40.