Blast Off to Simplifying Ratios! - ArgoPrep - Free Printable

Let's solve each problem on the worksheet step by step and explain the reasoning.

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1. Simplify the ratio 45 : 20

To simplify a ratio, we find the greatest common divisor (GCD) of the two numbers and divide both by it.

- GCD of 45 and 20 is 5.
- Divide both numbers by 5:
- 45 ÷ 5 = 9
- 20 ÷ 5 = 4

✔ Answer: 9 : 4

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2. Leslie receives 120 texts on Monday morning. She responds to 60 of the texts. What is the ratio of texts that Leslie received to the texts that she answered in simplest form?

- Texts received: 120
- Texts answered: 60
- Ratio: 120 : 60

Now simplify:
- GCD of 120 and 60 is 60
- 120 ÷ 60 = 2
- 60 ÷ 60 = 1

✔ Answer: 2 : 1

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3. Simplify the ratio 2 : 16

- GCD of 2 and 16 is 2
- 2 ÷ 2 = 1
- 16 ÷ 2 = 8

✔ Answer: 1 : 8

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4. Which ratio is equal to 15 : 20?

First, simplify 15 : 20:
- GCD of 15 and 20 is 5
- 15 ÷ 5 = 3
- 20 ÷ 5 = 4
- So, 15 : 20 = 3 : 4

Now check which option equals 3 : 4:

A. 3 : 4 → ✔ Yes! This matches.
B. 18 : 25 → Simplify: GCD is 1 → 18/25 ≠ 3/4
C. 21 : 28 → GCD is 7 → 21÷7=3, 28÷7=4 → 3:4 → ✔ Also matches!
Wait — both A and C simplify to 3:4?

Let’s double-check:

- A. 3 : 4 → already simplified → 3:4 ✔
- C. 21 : 28 → 21 ÷ 7 = 3, 28 ÷ 7 = 4 → 3:4 ✔

So both A and C are equivalent to 15:20?

But let’s see if the question asks for which ratio is equal — implying one correct answer.

Let’s verify all:

- A. 3 : 4 → yes, same as 15:20
- B. 18 : 25 → 18/25 = 0.72; 15/20 = 0.75 → no
- C. 21 : 28 → 21/28 = 3/4 = 0.75 → yes
- D. 24 : 30 → 24/30 = 4/5 = 0.8 → no

So both A and C are equivalent to 3:4, but the question says “which ratio” — likely expecting only one choice.

But wait — A is exactly 3:4, and C is 21:28, which simplifies to 3:4.

However, since the original is 15:20, which simplifies to 3:4, then any ratio that simplifies to 3:4 is equal.

But let’s check whether the options are asking for equivalent ratios.

So:

- 15:20 = 3:4
- A. 3:4 → yes
- C. 21:28 → yes

But in multiple-choice questions like this, usually only one option is listed as correct.

Let’s check the values:

Is 15:20 = 21:28?

Cross-multiply:
- 15 × 28 = 420
- 20 × 21 = 420 → yes, they are equal!

So both A and C are correct?

But look again: the options are:

A. 3 : 4
B. 18 : 25
C. 21 : 28
D. 24 : 30

Now, A is the simplified form, and C is an equivalent ratio.

But since the question says "Which ratio is equal to 15:20?", both A and C are mathematically equal.

But typically, such questions expect the simplified version or the one that matches directly.

Wait — let's compare fractions:

- 15/20 = 3/4 → so A is correct.
- 21/28 = 3/4 → also correct.

But maybe the test expects the simplified form.

But the question doesn’t say “simplify”, it says “which ratio is equal”.

So both A and C are correct.

But since it's a single-choice question, and A is the simplest, and often the expected answer, we should check if there's a mistake.

Wait — let’s check if C is really equal:

21:28 → divide both by 7 → 3:4 → yes.

15:20 → divide by 5 → 3:4 → yes.

So both are equal.

But perhaps the question wants the same ratio in different form, and A is the simplified version.

But unless it says "in simplest form", both are valid.

But looking at the format — it's a multiple-choice with one blank.

Most likely, A. 3:4 is the intended answer because it's the simplified form and directly matches.

Alternatively, C could be acceptable.

But let's see what the standard expectation is.

In most cases, when asked “which ratio is equal to 15:20”, the correct answer is any equivalent ratio, but since A is simpler, and C is also equivalent, but A is the reduced form, and often the preferred choice.

But let’s check: Is 21:28 equal to 15:20?

Yes.

But let’s compute:

15/20 = 0.75
21/28 = 0.75 → same.

So both are correct.

But since only one answer can be chosen, and A is the simplest, and most direct, it’s likely A is the expected answer.

Wait — but C is also correct.

This might be a flaw in the question.

But let’s assume the question wants the simplest form.

Then A. 3:4 is the best choice.

✔ Answer: A. 3 : 4

(Though C is also equivalent, A is the simplified version.)

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5. Ms. Wiley’s class has 24 students, 8 of which are girls. What is the ratio of girls to boys in simplest form?

- Total students: 24
- Girls: 8
- Boys: 24 – 8 = 16

So ratio of girls to boys = 8 : 16

Simplify:
- GCD of 8 and 16 is 8
- 8 ÷ 8 = 1
- 16 ÷ 8 = 2

So, 1 : 2

Now check the choices:

A. 16 : 8 → 2:1 → wrong
B. 1 : 2 → ✔ Correct
C. 8 : 24 → girls to total → not what's asked
D. 16 : 24 → boys to total → not what's asked

✔ Answer: B. 1 : 2

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✔ Final Answers:

1. 9 : 4
2. 2 : 1
3. 1 : 8
4. A. 3 : 4
5. B. 1 : 2

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Summary of Solutions:

| Question | Answer |
|--------|--------|
| 1 | 9 : 4 |
| 2 | 2 : 1 |
| 3 | 1 : 8 |
| 4 | A. 3 : 4 |
| 5 | B. 1 : 2 |

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