Question

sharon is making latkes, a kind of potato pancake. she needs \\(\frac{3}{4}\\) lb of potatoes for each batch. sharon has 4 lb of potatoes. which model represents the number of pounds of potatoes in one batch?

Explanation:

Step1: Analyze the fraction

The amount of potatoes per batch is $\frac{3}{4}$ lb. We need to check which number line (or model) has intervals representing fourths, since the denominator is 4.

Step2: Check the number lines

• The first number line: Let's see the intervals between 0 and 1. If we count the ticks, from 0 to 1, how many equal parts? Wait, the key is that $\frac{3}{4}$ means dividing a whole (1 lb) into 4 equal parts and taking 3. So the number line should have each whole divided into 4 parts (since the fraction is quarters).
• The second number line: Wait, no, wait. Wait, the first model (top) – the rectangle is divided into 4 parts? Wait, no, the first rectangle has 3 dashed lines? Wait, no, the problem is about the number line and the rectangle. Wait, actually, the fraction is $\frac{3}{4}$, so the unit (1 lb) should be divided into 4 equal segments. Let's check the number lines:
• In the first number line (top), between 0 and 1, how many segments? Let's see the ticks. From 0 to 1, there are 4 small ticks? Wait, no, the first number line: from 0 to 1, the distance is divided into 4 parts? Wait, no, maybe the rectangle: the top rectangle is divided into 4 parts (3 dashed lines, so 4 sections), and the number line has each whole (1 unit) divided into 4 parts? Wait, no, the second number line: between 0 and 1, how many segments? Wait, maybe I got it wrong. Wait, the fraction is $\frac{3}{4}$, so the model should represent a whole divided into 4 equal parts, with 3 parts shaded (or the number line showing $\frac{3}{4}$). Wait, but the question is which model represents the number of pounds in one batch, which is $\frac{3}{4}$ lb. So we need to see which number line (or the combination of rectangle and number line) has the unit divided into 4 parts (since denominator is 4) and the length corresponding to $\frac{3}{4}$.
• Looking at the two models: the top one (first) – the rectangle is divided into 4 parts (3 dashed lines, so 4 sections), and the number line: let's check the intervals. From 0 to 1, how many ticks? If the first number line has each 1 unit divided into 4 parts (so each tick is $\frac{1}{4}$), then $\frac{3}{4}$ would be 3 ticks from 0. Wait, but the problem is about the model for $\frac{3}{4}$ lb. So the correct model should have the whole (1 lb) divided into 4 equal parts, and the length representing $\frac{3}{4}$. So the first model (top) – the rectangle is divided into 4 parts (so each part is $\frac{1}{4}$), and the number line: let's see, the first number line, between 0 and 1, how many segments? Wait, maybe the first model (top) has the rectangle divided into 4 equal parts (so 3 dashed lines, making 4 sections), which matches the denominator 4 of $\frac{3}{4}$. The second model's rectangle has 3 dashed lines? Wait, no, the second rectangle has 2 dashed lines, making 3 sections? Wait, no, looking at the image: top rectangle has 3 vertical dashed lines, so 4 columns. Bottom rectangle has 2 vertical dashed lines, so 3 columns. So the top rectangle is divided into 4 parts (since 3 dashes create 4 sections), which is correct for a fraction with denominator 4. So the top model (first one) represents $\frac{3}{4}$ because it divides the whole into 4 equal parts (matching the denominator of $\frac{3}{4}$) and the number line also has intervals that would correspond to fourths.

Answer:

The top model (the first one with the rectangle divided into 4 parts and the corresponding number line) represents the number of pounds of potatoes in one batch.