What is 2/32 plus 3/7? (Answer: 55/112)

Exact Answer

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Problem: What is 2/32 plus 3/7?
Formula / Expression: 2/32 + 3/7
Final Answer: 55/112
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 7 = 224.
Working: LCD(32, 7) = 224

Step 2: Convert to Equivalent Fractions with Common Denominator 224
Multiply the numerator and denominator of 2/32 by 7, and multiply the numerator and denominator of 3/7 by 32 so both fractions share the common base 224.
Working: 2 × 7/32 × 7 = 14/224 and 3 × 32/7 × 32 = 96/224

Step 3: Add the Numerators
Now add the numerators (14 + 96 = 110) and keep the common denominator 224 unchanged.
Working: 14 + 96/224 = 110/224

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 110 and 224, which is 2. Divide both the numerator and denominator by 2.
Working: 110 ÷ 2/224 ÷ 2 = 55/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 112 produces a repeating decimal (approximately 0.491071, or 49.1071%).
Working: 55 ÷ 112 = 0.491071 (49.1071%)

Key Values:
- Simplified Fraction: 55/112
- Mixed Number Form: 55/112
- Decimal Value: 0.491071
- Percentage: 49.1071%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-32-plus-3-7/
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2/32 + 3/7 = 55/112

Simplified Fraction

55/112

Mixed Number

Proper (55/112)

Decimal Value

0.491071

Percentage

49.1071%

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Step-by-Step Solution: 2/32 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 7 = 224.

LCD(32, 7) = 224

Step 2

Convert to Equivalent Fractions with Common Denominator 224

Multiply the numerator and denominator of 2/32 by 7, and multiply the numerator and denominator of 3/7 by 32 so both fractions share the common base 224.

2 × 7/32 × 7 = 14/224 and 3 × 32/7 × 32 = 96/224

Step 3

Add the Numerators

Now add the numerators (14 + 96 = 110) and keep the common denominator 224 unchanged.

14 + 96/224 = 110/224

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 110 and 224, which is 2. Divide both the numerator and denominator by 2.

110 ÷ 2/224 ÷ 2 = 55/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 112 produces a repeating decimal (approximately 0.491071, or 49.1071%).

55 ÷ 112 = 0.491071 (49.1071%)

Visual Representation

The diagram below illustrates 2/32 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/112`
Mixed Number Form	`55/112`
Decimal Form	`0.491071`
Percentage	`49.1071%`

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Frequently Asked Questions

What is 2/32 plus 3/7 as a fraction?

2/32 + 3/7 in simplest fraction form is 55/112.

What is 2/32 plus 3/7 as a decimal?

2/32 + 3/7 converted to a decimal is 0.491071.

What is 2/32 plus 3/7 as a percentage?

2/32 + 3/7 expressed as a percentage is 49.1071%.

Does 2/32 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.491071...) because the denominator contains prime factors other than 2 and 5.