Equivalent Fractions Simplifying Fractions Word Problems worksheet ... - Free Printable

Here is the solution to each problem on the worksheet, with clear explanations:

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Problem 1:
> Serenity got $\frac{4}{5}$ on her Mathematics test. What is an equivalent fraction for $\frac{4}{5}$?

✔ Answer: $\frac{8}{10}$ (or any other equivalent like $\frac{12}{15}$, $\frac{16}{20}$, etc.)

Explanation:
An *equivalent fraction* is a fraction that has the same value as another fraction but with different numerator and denominator. To find one, multiply both the numerator and denominator by the same number.

Example:
$$
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
$$

You can also multiply by 3, 4, etc.:
- $\frac{4 \times 3}{5 \times 3} = \frac{12}{15}$
- $\frac{4 \times 4}{5 \times 4} = \frac{16}{20}$

Any of these are correct. The simplest answer to write is often $\frac{8}{10}$.

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Problem 2:
> Samaria ate $\frac{6}{9}$ of her birthday cake. What is an equivalent fraction for $\frac{6}{9}$?

✔ Answer: $\frac{2}{3}$ (this is also the *simplified* form)

Explanation:
We can find an equivalent fraction by multiplying or dividing numerator and denominator by the same number.

But since $\frac{6}{9}$ can be simplified, we usually divide both by their Greatest Common Factor (GCF), which is 3:

$$
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
$$

So $\frac{2}{3}$ is an equivalent fraction — and it’s also in its simplest form.

You could also give $\frac{12}{18}$ as an equivalent fraction (multiply by 2), but $\frac{2}{3}$ is the most common expected answer here.

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Problem 3:
> What is $\frac{2}{10}$ in its simplest form? Simplify the fraction.

✔ Answer: $\frac{1}{5}$

Explanation:
To simplify a fraction, divide both numerator and denominator by their Greatest Common Factor (GCF).

Factors of 2: 1, 2
Factors of 10: 1, 2, 5, 10
→ GCF = 2

$$
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
$$

So, $\frac{2}{10}$ simplifies to $\frac{1}{5}$.

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Problem 4:
> What is $\frac{25}{40}$ in its simplest form? Simplify the fraction.

✔ Answer: $\frac{5}{8}$

Explanation:
Find the GCF of 25 and 40.

Factors of 25: 1, 5, 25
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
→ GCF = 5

Divide both numerator and denominator by 5:

$$
\frac{25 \div 5}{40 \div 5} = \frac{5}{8}
$$

So, $\frac{25}{40}$ simplifies to $\frac{5}{8}$.

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✔ Final Answers Summary:

1. $\boxed{\frac{8}{10}}$ (or any equivalent such as $\frac{12}{15}$)
2. $\boxed{\frac{2}{3}}$
3. $\boxed{\frac{1}{5}}$
4. $\boxed{\frac{5}{8}}$

Let me know if you’d like to see visual models or step-by-step notebook work for these!