SOLUTION: Number analogy - Studypool - Free Printable

Problem Analysis

The task involves solving number analogy problems. Each problem presents a relationship between two numbers or fractions and asks you to find the corresponding relationship for another pair of numbers or fractions. The key is to identify the underlying pattern or operation that connects the given pairs.

Let's solve each problem step by step.

---

Problem 1:

0.75 is to \( \frac{3}{4} \) as 0.8 is to ____

#### Step 1: Understand the relationship
- \( 0.75 \) is equivalent to \( \frac{3}{4} \).
- This means the relationship is simply converting a decimal to a fraction.

#### Step 2: Apply the same relationship to 0.8
- Convert \( 0.8 \) to a fraction:
\[
0.8 = \frac{8}{10} = \frac{4}{5}
\]

#### Step 3: Match the answer
- The fraction \( \frac{4}{5} \) corresponds to option B.

Answer: B. \( \frac{4}{5} \)

---

Problem 2:

75% is to \( \frac{1}{2} \) as 45% is to ____

#### Step 1: Understand the relationship
- \( 75\% \) is equivalent to \( \frac{75}{100} = \frac{3}{4} \), not \( \frac{1}{2} \). This suggests a different relationship.
- Notice that \( 75\% \) is being compared to \( \frac{1}{2} \), which is half of \( 75\% \):
\[
\frac{75\%}{2} = \frac{75}{2} \% = 37.5\%
\]
However, this doesn't directly match \( \frac{1}{2} \). Instead, it seems the relationship is about simplifying or reducing the percentage to a fraction.

#### Step 2: Simplify 45% to a fraction
- Convert \( 45\% \) to a fraction:
\[
45\% = \frac{45}{100} = \frac{9}{20}
\]

#### Step 3: Match the answer
- The fraction \( \frac{9}{20} \) corresponds to option B.

Answer: B. \( \frac{9}{20} \)

---

Problem 3:

0.25 is to 0.125 as 1.25 is to ____

#### Step 1: Understand the relationship
- \( 0.25 \) is related to \( 0.125 \):
\[
0.125 = \frac{0.25}{2}
\]
So, the relationship is dividing by 2.

#### Step 2: Apply the same relationship to 1.25
- Divide \( 1.25 \) by 2:
\[
\frac{1.25}{2} = 0.625
\]

#### Step 3: Match the answer
- The result \( 0.625 \) corresponds to option A.

Answer: A. 0.625

---

Problem 4:

2 is to 50 as 3.2 is to ____

#### Step 1: Understand the relationship
- \( 2 \) is related to \( 50 \):
\[
50 = 2 \times 25
\]
So, the relationship is multiplying by 25.

#### Step 2: Apply the same relationship to 3.2
- Multiply \( 3.2 \) by 25:
\[
3.2 \times 25 = 80
\]

#### Step 3: Match the answer
- The result \( 80 \) corresponds to option C.

Answer: C. 80

---

Problem 5:

14 is to 28 as 5 is to ____

#### Step 1: Understand the relationship
- \( 14 \) is related to \( 28 \):
\[
28 = 14 \times 2
\]
So, the relationship is multiplying by 2.

#### Step 2: Apply the same relationship to 5
- Multiply \( 5 \) by 2:
\[
5 \times 2 = 10
\]

#### Step 3: Match the answer
- The result \( 10 \) corresponds to option D.

Answer: D. 10

---

Problem 6:

1 is to \( \frac{1}{6} \) as \( \frac{5}{25} \) is to ____

#### Step 1: Understand the relationship
- \( 1 \) is related to \( \frac{1}{6} \):
\[
\frac{1}{6} = 1 \div 6
\]
So, the relationship is dividing by 6.

#### Step 2: Simplify \( \frac{5}{25} \)
- Simplify \( \frac{5}{25} \):
\[
\frac{5}{25} = \frac{1}{5}
\]

#### Step 3: Apply the same relationship to \( \frac{1}{5} \)
- Divide \( \frac{1}{5} \) by 6:
\[
\frac{1}{5} \div 6 = \frac{1}{5} \times \frac{1}{6} = \frac{1}{30}
\]

#### Step 4: Match the answer
- The result \( \frac{1}{30} \) corresponds to option D.

Answer: D. \( \frac{1}{30} \)

---

Problem 7:

0.35 is to 7 as 0.45 is to ____

#### Step 1: Understand the relationship
- \( 0.35 \) is related to \( 7 \):
\[
7 = \frac{0.35}{0.05}
\]
So, the relationship is dividing by 0.05.

#### Step 2: Apply the same relationship to 0.45
- Divide \( 0.45 \) by 0.05:
\[
\frac{0.45}{0.05} = 9
\]

#### Step 3: Match the answer
- The result \( 9 \) corresponds to option B.

Answer: B. 9

---

Problem 8:

\( \frac{1}{3} \) is to \( \frac{2}{18} \) as \( \frac{1}{12} \) is to ____

#### Step 1: Understand the relationship
- \( \frac{1}{3} \) is related to \( \frac{2}{18} \):
\[
\frac{2}{18} = \frac{1}{9}
\]
Notice that:
\[
\frac{1}{9} = \frac{1}{3} \times \frac{1}{3}
\]
So, the relationship is squaring the denominator.

#### Step 2: Apply the same relationship to \( \frac{1}{12} \)
- Square the denominator of \( \frac{1}{12} \):
\[
\frac{1}{12} \rightarrow \frac{1}{12^2} = \frac{1}{144}
\]

#### Step 3: Match the answer
- The result \( \frac{1}{144} \) corresponds to option B.

Answer: B. \( \frac{1}{144} \)

---

Problem 9:

\( \frac{3}{8} \) is to \( \frac{12}{32} \) as \( \frac{2}{5} \) is to ____

#### Step 1: Understand the relationship
- \( \frac{3}{8} \) is related to \( \frac{12}{32} \):
\[
\frac{12}{32} = \frac{3}{8} \times \frac{4}{4}
\]
So, the relationship is multiplying both the numerator and the denominator by 4.

#### Step 2: Apply the same relationship to \( \frac{2}{5} \)
- Multiply both the numerator and the denominator of \( \frac{2}{5} \) by 4:
\[
\frac{2}{5} \times \frac{4}{4} = \frac{8}{20}
\]

#### Step 3: Match the answer
- The result \( \frac{8}{20} \) corresponds to option A.

Answer: A. \( \frac{8}{20} \)

---

Problem 10:

\( \frac{1}{3} \) is to \( \frac{3}{7} \) as \( \frac{1}{6} \) is to ____

#### Step 1: Understand the relationship
- \( \frac{1}{3} \) is related to \( \frac{3}{7} \):
\[
\frac{3}{7} = \frac{1}{3} \times \frac{9}{7}
\]
So, the relationship is multiplying by \( \frac{9}{7} \).

#### Step 2: Apply the same relationship to \( \frac{1}{6} \)
- Multiply \( \frac{1}{6} \) by \( \frac{9}{7} \):
\[
\frac{1}{6} \times \frac{9}{7} = \frac{9}{42} = \frac{3}{14}
\]

#### Step 3: Match the answer
- The result \( \frac{3}{14} \) corresponds to option A.

Answer: A. \( \frac{3}{14} \)

---

Final Answers:

1. B. \( \frac{4}{5} \)
2. B. \( \frac{9}{20} \)
3. A. 0.625
4. C. 80
5. D. 10
6. D. \( \frac{1}{30} \)
7. B. 9
8. B. \( \frac{1}{144} \)
9. A. \( \frac{8}{20} \)
10. A. \( \frac{3}{14} \)

Boxed Answer:
\[
\boxed{B, B, A, C, D, D, B, B, A, A}
\]