proportions of percent Worksheets - Free Printable

The worksheet titled "Finding Amounts with Proportional Relationship" asks you to find the missing value in each proportion so that the two fractions are equivalent. Each problem is of the form:

$$
\frac{a}{b} = \frac{c}{100}
$$

We need to solve for $ a $ or $ c $, depending on what's missing. In this case, all problems have the right-hand side as a fraction over 100, and we are solving for the numerator on the left side (or sometimes the denominator, but here it's mostly the numerator). The goal is to use proportional reasoning — cross-multiplying or simplifying to make the fractions equal.

Let’s go through each problem step by step and explain how to solve them.

---

Problem 1:

$$
\frac{12}{48} = \frac{25}{100}
$$

We check if these are equal:
- Simplify $ \frac{12}{48} = \frac{1}{4} $
- $ \frac{25}{100} = \frac{1}{4} $

✔ Yes, they are equal. But the question says “find the missing value.” Wait — actually, looking at the format, the answer key shows 12, which suggests that the missing value is the numerator on the left, but the equation is already written as $ \frac{12}{48} = \frac{25}{100} $. So perhaps the task is to verify or possibly find a missing numerator?

Wait — let’s look more carefully.

Actually, re-examining: The equations are given, and the missing value is in the numerator on the left side, but in some cases, the numerator is already filled in. But from the answer key, it seems like the missing value is being found such that the left side equals the right side (which is always over 100).

But wait — in problem 1, it's:
$$
\frac{12}{48} = \frac{25}{100}
$$
This is true, but the missing value is not shown — unless the blank is in the numerator? No, both numerators are present.

Ah! I think there's confusion. Let's look again at the structure.

Looking at the layout, the equations are written with a blank in the numerator on the left side, but in the image, the numerators are filled in. For example:

1) $ \frac{12}{48} = \frac{25}{100} $ → Answer: 12

So maybe the original worksheet had a blank like:
$$
\frac{?}{48} = \frac{25}{100}
$$
And we're supposed to find the missing numerator.

But in the image, the numerator is already filled in. So likely, the student is to verify or compute the missing value based on proportionality.

But since the answer key is provided, and the answers are listed, it seems the task is to solve for the unknown numerator such that the two fractions are proportional.

Let’s assume that in each problem, the numerator on the left is missing, and we’re solving for it.

But in the image, the numerator is already written. So perhaps the student is to check whether the equation is correct, or compute the missing value.

Alternatively, maybe the problem is to find the numerator on the left such that the ratio is equal to the one on the right.

Let’s reinterpret:

Each problem is of the form:
$$
\frac{x}{\text{denominator}} = \frac{\text{some number}}{100}
$$

And we must solve for $ x $.

But in the image, $ x $ is already filled in. However, the answer key has numbers listed, matching the values in the numerator on the left.

So, likely, the original worksheet had blanks, and the student fills in the missing numerator.

For example, Problem 1 might be:
$$
\frac{?}{48} = \frac{25}{100}
$$
We solve:
$$
x = \frac{25}{100} \times 48 = 0.25 \times 48 = 12
$$
✔ So the missing numerator is 12 — matches answer key.

Similarly, let’s do each one.

---

Problem 1:

$$
\frac{?}{48} = \frac{25}{100}
$$
$$
x = \frac{25}{100} \times 48 = 0.25 \times 48 = 12
$$
✔ Answer: 12

---

Problem 2:

$$
\frac{?}{35} = \frac{20}{100}
$$
$$
x = \frac{20}{100} \times 35 = 0.2 \times 35 = 7
$$
✔ Answer: 7

---

Problem 3:

$$
\frac{?}{30} = \frac{10}{100}
$$
$$
x = \frac{10}{100} \times 30 = 0.1 \times 30 = 3
$$
✔ Answer: 3

---

Problem 4:

$$
\frac{?}{32} = \frac{25}{100}
$$
$$
x = 0.25 \times 32 = 8
$$
✔ Answer: 8

---

Problem 5:

$$
\frac{?}{36} = \frac{25}{100}
$$
$$
x = 0.25 \times 36 = 9
$$
✔ Answer: 9

---

Problem 6:

$$
\frac{?}{40} = \frac{5}{100}
$$
$$
x = 0.05 \times 40 = 2
$$
✔ Answer: 2

---

Problem 7:

$$
\frac{?}{64} = \frac{25}{100}
$$
$$
x = 0.25 \times 64 = 16
$$
✔ Answer: 16

---

Problem 8:

$$
\frac{?}{68} = \frac{25}{100}
$$
$$
x = 0.25 \times 68 = 17
$$
✔ Answer: 17

---

Problem 9:

$$
\frac{?}{56} = \frac{25}{100}
$$
$$
x = 0.25 \times 56 = 14
$$
✔ Answer: 14

---

Problem 10:

$$
\frac{?}{44} = \frac{25}{100}
$$
$$
x = 0.25 \times 44 = 11
$$
✔ Answer: 11

---

Problem 11:

$$
\frac{?}{45} = \frac{20}{100}
$$
$$
x = 0.2 \times 45 = 9
$$
✔ Answer: 9

---

Problem 12:

$$
\frac{?}{55} = \frac{20}{100}
$$
$$
x = 0.2 \times 55 = 11
$$
✔ Answer: 11

---

Problem 13:

$$
\frac{?}{70} = \frac{10}{100}
$$
$$
x = 0.1 \times 70 = 7
$$
✔ Answer: 7

---

Problem 14:

$$
\frac{?}{20} = \frac{5}{100}
$$
$$
x = 0.05 \times 20 = 1
$$
✔ Answer: 1

---

Problem 15:

$$
\frac{?}{50} = \frac{2}{100}
$$
$$
x = 0.02 \times 50 = 1
$$
✔ Answer: 1

---

Problem 16:

$$
\frac{?}{60} = \frac{5}{100}
$$
$$
x = 0.05 \times 60 = 3
$$
✔ Answer: 3

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✔ Summary of Method:

To solve each problem:
1. Recognize that $ \frac{x}{d} = \frac{n}{100} $
2. Solve for $ x $ using:
$$
x = \frac{n}{100} \times d
$$
Or equivalently:
$$
x = n \times \frac{d}{100}
$$

This uses proportional reasoning: the fraction on the left should be equivalent to the fraction on the right.

---

Final Answers (as per answer key):

1. 12
2. 7
3. 3
4. 8
5. 9
6. 2
7. 16
8. 17
9. 14
10. 11
11. 9
12. 11
13. 7
14. 1
15. 1
16. 3

All match the calculations above.

✔ All problems solved correctly using proportional relationships.

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💡 Key Concept:

This is about finding equivalent fractions where one side is expressed as a percent (over 100), and the other is a simplified fraction. You can convert between them by multiplying the percentage (as a decimal) by the denominator.

Example:
If $ \frac{x}{48} = 25\% $, then $ x = 0.25 \times 48 = 12 $.

This is foundational for understanding percentages and proportions.