Question

Sofia ate 41 of a pizza and her brother ate 82 of the same pizza. a) Are these amounts equivalent? ___ Yes ___ No. Explain briefly and show a model. b) How much of the pizza did they eat together? Write answer in simplest form and show work.



Use a bar model to show why 43 is equivalent to 10075. Label the model and write one sentence explanation.

Answer 1

I'll assume the fractions were written without slashes. So Sofia ate 4/1 and her brother ate 8/2.

a) Are these amounts equivalent? Yes.

Explanation and model:
- 4/1 = 4 (four whole pizzas).
- 8/2 = 8 ÷ 2 = 4 (eight halves = four whole pizzas).

Bar model (text version):
Sofia (4/1): [🍕][🍕][🍕][🍕] = 4 wholes
Brother (8/2): [1/2][1/2][1/2][1/2][1/2][1/2][1/2][1/2] = 8 halves = (pair them) → [🍕][🍕][🍕][🍕] = 4 wholes

Both show 4 whole pizzas, so they are equivalent.

b) How much did they eat together?
Total = 4 + 4 = 8 pizzas. As a fraction simplest form: 8 (or 8/1).

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Use a bar model to show why 4/3 is equivalent to 100/75

Bar model idea (text version):
- Start with a bar representing 1 whole, divided into 3 equal parts (thirds).
- 4/3 means four of those thirds (one whole plus one extra third).

Now subdivide each third into 25 equal pieces (so the whole bar is divided into 3 × 25 = 75 small equal pieces).
- Each third = 25 small pieces.
- Four thirds = 4 × 25 = 100 small pieces.

So the same shaded amount is 100 of the 75 small pieces, i.e. 100/75.

One-sentence explanation:
Multiplying numerator and denominator of 4/3 by 25 subdivides each third into 25 equal parts, so 4/3 = (4×25)/(3×25) = 100/75.