Question

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Part 1
Reasoning  Make a model that shows 9divided bythree fourths
. Use pencil and paper. Describe how the model changes if the divisor is half as big or twice as big.
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Part 1
Which of these models shows 9divided bythree fourths
​?
A.
012345678910



On a number line, tick marks divide the space between 0 and 9 into 36 equal segments. Every fourth tick mark is labeled by ones. 9 ovals each group 4 segments.
B.
012345678910



On a number line, tick marks divide the space between 0 and 9 into 36 equal segments. Every fourth tick mark is labeled by ones. 12 ovals each group 3 segments.
C.
012345



On a number line, tick marks divide the space between 0 and 4 into 36 equal segments. Every ninth tick mark is labeled by ones. 4 ovals each group 9 segments.
D.
012345

Answer 1

Answer: B.

Explanation and model:
- Draw a number line from 0 to 9 and divide each unit into 4 equal parts (so there are 9 × 4 = 36 small equal segments).
- A piece of size 3/4 equals 3 of those small segments. Group the 36 small segments into blocks of 3 — you get 12 blocks.
- So 9 ÷ 3/4 = 12, which is exactly what model B shows (12 ovals each grouping 3 segments).

How the model changes if the divisor is half as big or twice as big:
- Half as big: (3/4) ÷ 2 = 3/8. Now use eighths: divide each unit into 8 parts (9 × 8 = 72 small segments). A 3/8 piece is 3 of those segments, so 72 ÷ 3 = 24 pieces. (Quotient doubles.)
- Twice as big: (3/4) × 2 = 3/2 = 1.5. In quarters, 3/2 = 6 quarter-segments, so on the original 36-quarter-segment line group by 6: 36 ÷ 6 = 6 pieces. (Quotient halves.)

General: making the divisor half as large doubles the number of pieces; making it twice as large halves the number of pieces.