3rd Grade Equivalent Fractions Task Cards | Equivalent Fractions ... - Free Printable

Let's solve each of the four equivalent fractions problems shown in the image, one by one. I'll explain the reasoning for each.

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Problem 9:

Task: Write the fraction for each model shown. Are they equivalent? Write yes or no.

#### Model 1 (Green Grid):
- The grid is divided into 12 equal parts (3 rows × 4 columns).
- 8 parts are shaded green.
- So, the fraction is:
$$
\frac{8}{12}
$$

#### Model 2 (Yellow Bars):
- The rectangle is divided into 4 equal vertical bars.
- 3 bars are shaded yellow.
- So, the fraction is:
$$
\frac{3}{4}
$$

#### Are they equivalent?
We simplify $\frac{8}{12}$:
$$
\frac{8}{12} = \frac{2}{3} \quad \text{(divide numerator and denominator by 4)}
$$
But $\frac{3}{4}$ is not equal to $\frac{2}{3}$.

So, no, they are not equivalent.

✔ Answer:
- Fraction 1: $\frac{8}{12}$
- Fraction 2: $\frac{3}{4}$
- Are they equivalent? No

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Problem 10:

Task: Are the fractions equivalent? Write yes or no.

#### Top Bar (Orange):
- Divided into 5 equal parts.
- 2 parts shaded orange.
- Fraction: $\frac{2}{5}$

#### Bottom Bar (Blue):
- Divided into 8 equal parts.
- 4 parts shaded blue.
- Fraction: $\frac{4}{8} = \frac{1}{2}$

Now compare:
- $\frac{2}{5} = 0.4$
- $\frac{4}{8} = 0.5$

They are not equal.

✔ Answer: No

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Problem 11:

Task: Shade in the second fraction to make it equivalent to the model shown.
Given:
$$
\frac{1}{5} = ?
$$

#### First Pentagon:
- Divided into 5 equal parts.
- 1 part shaded red → $\frac{1}{5}$

#### Second Pentagon:
- Divided into 10 equal parts (since it has 10 triangles).
- We need to shade a number of parts so that the fraction equals $\frac{1}{5}$.

To find an equivalent fraction:
$$
\frac{1}{5} = \frac{?}{10}
$$
Multiply numerator and denominator by 2:
$$
\frac{1 \times 2}{5 \times 2} = \frac{2}{10}
$$

So, we must shade 2 out of the 10 parts in the second pentagon.

✔ Answer: Shade 2 sections in the second pentagon.

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Problem 12:

Task: Draw a fraction equivalent to the given model.

#### Given Model (Orange Octagon):
- A circle divided into 8 equal parts (like an octagon).
- 3 parts shaded orange.
- So, the fraction is: $\frac{3}{8}$

Now, draw a fraction equivalent to $\frac{3}{8}$.

There are many possible answers. For example:

- $\frac{6}{16}$: double both numerator and denominator.
- $\frac{9}{24}$: triple them.
- Or you could draw a shape divided into 16 parts with 6 shaded.

But since the task says "draw", and only one shape is provided, you can create another shape (e.g., a rectangle or circle) divided into more parts and shade the correct amount.

✔ Example Answer:
Draw a circle divided into 16 equal parts and shade 6 parts → $\frac{6}{16} = \frac{3}{8}$

Or draw a rectangle divided into 4 parts and shade 1.5 parts — but that’s not possible with whole parts.

So better to use a shape with multiples of 8.

✔ Best choice: Divide a shape into 16 parts, shade 6 → $\frac{6}{16} = \frac{3}{8}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 9 | $\frac{8}{12}$, $\frac{3}{4}$, No |
| 10 | No |
| 11 | Shade 2 out of 10 parts in the second pentagon |
| 12 | Draw a shape (e.g., circle) divided into 16 parts, shade 6 (or any equivalent like $\frac{6}{16}$, $\frac{9}{24}$, etc.) |

Let me know if you'd like a visual explanation or printable version!