What is 2/32 plus 2/5? (Answer: 37/80)

Exact Answer

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Problem: What is 2/32 plus 2/5?
Formula / Expression: 2/32 + 2/5
Final Answer: 37/80
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 5 = 160.
Working: LCD(32, 5) = 160

Step 2: Convert to Equivalent Fractions with Common Denominator 160
Multiply the numerator and denominator of 2/32 by 5, and multiply the numerator and denominator of 2/5 by 32 so both fractions share the common base 160.
Working: 2 × 5/32 × 5 = 10/160 and 2 × 32/5 × 32 = 64/160

Step 3: Add the Numerators
Now add the numerators (10 + 64 = 74) and keep the common denominator 160 unchanged.
Working: 10 + 64/160 = 74/160

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 160, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/160 ÷ 2 = 37/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 80 yields an exact terminating decimal of 0.4625 (or 46.25%).
Working: 37 ÷ 80 = 0.4625 (46.25%)

Key Values:
- Simplified Fraction: 37/80
- Mixed Number Form: 37/80
- Decimal Value: 0.4625
- Percentage: 46.25%

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2/32 + 2/5 = 37/80

Simplified Fraction

37/80

Mixed Number

Proper (37/80)

Decimal Value

0.4625

Percentage

46.25%

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Step-by-Step Solution: 2/32 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 5 = 160.

LCD(32, 5) = 160

Step 2

Convert to Equivalent Fractions with Common Denominator 160

Multiply the numerator and denominator of 2/32 by 5, and multiply the numerator and denominator of 2/5 by 32 so both fractions share the common base 160.

2 × 5/32 × 5 = 10/160 and 2 × 32/5 × 32 = 64/160

Step 3

Add the Numerators

Now add the numerators (10 + 64 = 74) and keep the common denominator 160 unchanged.

10 + 64/160 = 74/160

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 160, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/160 ÷ 2 = 37/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 80 yields an exact terminating decimal of 0.4625 (or 46.25%).

37 ÷ 80 = 0.4625 (46.25%)

Visual Representation

The diagram below illustrates 2/32 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/80`
Mixed Number Form	`37/80`
Decimal Form	`0.4625`
Percentage	`46.25%`

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Frequently Asked Questions

What is 2/32 plus 2/5 as a fraction?

2/32 + 2/5 in simplest fraction form is 37/80.

What is 2/32 plus 2/5 as a decimal?

2/32 + 2/5 converted to a decimal is 0.4625.

What is 2/32 plus 2/5 as a percentage?

2/32 + 2/5 expressed as a percentage is 46.25%.

Does 2/32 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.4625) because the denominator in simplest terms contains only prime factors 2 and/or 5.