4. the dashed line divides the same area model into 6 equal parts. what is the missing numerator?
shaded parts
total parts (\frac{square}{6})
5. when the area model is divided into thirds, the shaded part represents ______.
when the area model is divided into sixths, the shaded part represents ______.
since the same part of the whole area is shaded in both models,
______ and ______ are equivalent fractions.
on the back!
6. draw an area model for (\frac{3}{4}). write an equivalent fraction for (\frac{3}{4}). show the equivalent fraction on your model.

Question

Accepted Answer

### Question 4:
# Explanation:
## Step1: Analyze the diagram (assuming the shaded parts: from the image, the shaded part is 2 out of 3 parts when divided into thirds? Wait, no, the total parts are 6. Wait, maybe the original model (before dashed line) was divided into 3 parts, shaded 1? Wait, no, let's re-express. Wait, the dashed line divides into 6 equal parts. Let's see, if originally, maybe the shaded part was 2 when divided into 3? Wait, no, the problem says "the dashed line divides the same area model into 6 equal parts. What is the missing numerator? Shaded parts, Total parts $\frac{\square}{6}$". Wait, maybe the original shaded part was 1 when total was 3? Wait, no, let's think of equivalent fractions. If the original was $\frac{1}{3}$, then to get denominator 6, multiply numerator and denominator by 2: $\frac{1	imes2}{3	imes2}=\frac{2}{6}$. Wait, or maybe the shaded part in the original (before dashed) was 2 out of 3? No, maybe the diagram shows that when divided into 3 parts, shaded is 1, so when divided into 6, shaded is 2. Wait, let's check: $\frac{1}{3}=\frac{2}{6}$. So the missing numerator is 2.

## Step1: Identify original fraction (assume original was $\frac{1}{3}$ from context, since dividing into 3 and then 6).
## Step2: Find equivalent fraction with denominator 6. Multiply numerator and denominator of $\frac{1}{3}$ by 2: $\frac{1	imes2}{3	imes2}=\frac{2}{6}$.
# Answer: 2

### Question 5:
# Explanation:
## Step1: When divided into thirds, the shaded part: let's assume the shaded part is 1 (if original was $\frac{1}{3}$). So when divided into thirds, the shaded part represents $\frac{1}{3}$.
## Step2: When divided into sixths, the shaded part (equivalent) is $\frac{2}{6}$, so represents $\frac{2}{6}$ (or simplified $\frac{1}{3}$, but as a fraction with denominator 6, it's $\frac{2}{6}$). Then, since the same part is shaded, $\frac{1}{3}$ and $\frac{2}{6}$ are equivalent fractions.
## Step1: Determine fraction for thirds: If shaded is 1 out of 3, it's $\frac{1}{3}$.
## Step2: Determine fraction for sixths: Equivalent to $\frac{1}{3}$ is $\frac{2}{6}$.
## Step3: State equivalent fractions: $\frac{1}{3}$ and $\frac{2}{6}$ (or whatever the actual shaded was, but based on equivalent, if original shaded was 1/3, then sixths is 2/6).
# Answer: When divided into thirds, shaded part represents $\frac{1}{3}$; when divided into sixths, represents $\frac{2}{6}$; and $\frac{1}{3}$ and $\frac{2}{6}$ are equivalent fractions. (But the blanks: first blank when divided into thirds: $\frac{1}{3}$, second when into sixths: $\frac{2}{6}$, and the two fractions are $\frac{1}{3}$ and $\frac{2}{6}$ (or other equivalent pair, but likely $\frac{1}{3}$ and $\frac{2}{6}$ or similar).

### Question 6:
# Explanation:
## Step1: Draw a rectangle (area model) and divide it into 4 equal parts. Shade 3 of them (for $\frac{3}{4}$).
## Step2: To find an equivalent fraction, multiply numerator and denominator by 2: $\frac{3	imes2}{4	imes2}=\frac{6}{8}$. So draw another rectangle, divide into 8 equal parts, shade 6.
## Step1: Draw for $\frac{3}{4}$: Rectangle with 4 columns, shade 3.
## Step2: Equivalent fraction: $\frac{3}{4}=\frac{6}{8}$ (multiply numerator and denominator by 2). Draw rectangle with 8 columns, shade 6.
# Answer: (Drawing: first rectangle divided into 4, shaded 3; second divided into 8, shaded 6. Equivalent fraction: $\frac{6}{8}$ (or other, like $\frac{9}{12}$ etc.))

(Note: For question 6, the equivalent fraction can be $\frac{6}{8}$, $\frac{9}{12}$, etc. The key is to show the area model and the equivalent fraction by multiplying numerator and denominator by the same non - zero integer.)

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Question

Explanation:

Question 4:

Step1: Identify original fraction (assume original was $\frac{1}{3}$ from context, since dividing into 3 and then 6).

Step2: Find equivalent fraction with denominator 6. Multiply numerator and denominator of $\frac{1}{3}$ by 2: $\frac{1\times2}{3\times2}=\frac{2}{6}$.

Step1: When divided into thirds, the shaded part: let's assume the shaded part is 1 (if original was $\frac{1}{3}$). So when divided into thirds, the shaded part represents $\frac{1}{3}$.

Step2: When divided into sixths, the shaded part (equivalent) is $\frac{2}{6}$, so represents $\frac{2}{6}$ (or simplified $\frac{1}{3}$, but as a fraction with denominator 6, it's $\frac{2}{6}$). Then, since the same part is shaded, $\frac{1}{3}$ and $\frac{2}{6}$ are equivalent fractions.

Step1: Determine fraction for thirds: If shaded is 1 out of 3, it's $\frac{1}{3}$.

Step2: Determine fraction for sixths: Equivalent to $\frac{1}{3}$ is $\frac{2}{6}$.

Step3: State equivalent fractions: $\frac{1}{3}$ and $\frac{2}{6}$ (or whatever the actual shaded was, but based on equivalent, if original shaded was 1/3, then sixths is 2/6).

Step1: Draw a rectangle (area model) and divide it into 4 equal parts. Shade 3 of them (for $\frac{3}{4}$).

Step2: To find an equivalent fraction, multiply numerator and denominator by 2: $\frac{3\times2}{4\times2}=\frac{6}{8}$. So draw another rectangle, divide into 8 equal parts, shade 6.

Step1: Draw for $\frac{3}{4}$: Rectangle with 4 columns, shade 3.

Step2: Equivalent fraction: $\frac{3}{4}=\frac{6}{8}$ (multiply numerator and denominator by 2). Draw rectangle with 8 columns, shade 6.

Answer:

Question 5: