What is 2/37 plus 2/8? (Answer: 45/148)

Exact Answer

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Problem: What is 2/37 plus 2/8?
Formula / Expression: 2/37 + 2/8
Final Answer: 45/148
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 37 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 8 = 296.
Working: LCD(37, 8) = 296

Step 2: Convert to Equivalent Fractions with Common Denominator 296
Multiply the numerator and denominator of 2/37 by 8, and multiply the numerator and denominator of 2/8 by 37 so both fractions share the common base 296.
Working: 2 × 8/37 × 8 = 16/296 and 2 × 37/8 × 37 = 74/296

Step 3: Add the Numerators
Now add the numerators (16 + 74 = 90) and keep the common denominator 296 unchanged.
Working: 16 + 74/296 = 90/296

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 296, which is 2. Divide both the numerator and denominator by 2.
Working: 90 ÷ 2/296 ÷ 2 = 45/148

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 148 produces a repeating decimal (approximately 0.304054, or 30.4054%).
Working: 45 ÷ 148 = 0.304054 (30.4054%)

Key Values:
- Simplified Fraction: 45/148
- Mixed Number Form: 45/148
- Decimal Value: 0.304054
- Percentage: 30.4054%

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Solved with FractionsCalc:
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2/37 + 2/8 = 45/148

Simplified Fraction

45/148

Mixed Number

Proper (45/148)

Decimal Value

0.304054

Percentage

30.4054%

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Step-by-Step Solution: 2/37 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 37 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 8 = 296.

LCD(37, 8) = 296

Step 2

Convert to Equivalent Fractions with Common Denominator 296

Multiply the numerator and denominator of 2/37 by 8, and multiply the numerator and denominator of 2/8 by 37 so both fractions share the common base 296.

2 × 8/37 × 8 = 16/296 and 2 × 37/8 × 37 = 74/296

Step 3

Add the Numerators

Now add the numerators (16 + 74 = 90) and keep the common denominator 296 unchanged.

16 + 74/296 = 90/296

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 296, which is 2. Divide both the numerator and denominator by 2.

90 ÷ 2/296 ÷ 2 = 45/148

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 148 produces a repeating decimal (approximately 0.304054, or 30.4054%).

45 ÷ 148 = 0.304054 (30.4054%)

Visual Representation

The diagram below illustrates 2/37 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/148`
Mixed Number Form	`45/148`
Decimal Form	`0.304054`
Percentage	`30.4054%`

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Frequently Asked Questions

What is 2/37 plus 2/8 as a fraction?

2/37 + 2/8 in simplest fraction form is 45/148.

What is 2/37 plus 2/8 as a decimal?

2/37 + 2/8 converted to a decimal is 0.304054.

What is 2/37 plus 2/8 as a percentage?

2/37 + 2/8 expressed as a percentage is 30.4054%.

Does 2/37 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.304054...) because the denominator contains prime factors other than 2 and 5.