What is 2/32 plus 2/8? (Answer: 5/16)

Exact Answer

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Problem: What is 2/32 plus 2/8?
Formula / Expression: 2/32 + 2/8
Final Answer: 5/16
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 32 is an exact multiple of 8 (8 × 4 = 32). The Least Common Denominator (LCD) is simply 32, meaning we only need to scale one fraction.
Working: LCD(32, 8) = 32

Step 2: Convert to Equivalent Fractions with Common Denominator 32
Multiply the numerator and denominator of 2/32 by 1, and multiply the numerator and denominator of 2/8 by 4 so both fractions share the common base 32.
Working: 2 × 1/32 × 1 = 2/32 and 2 × 4/8 × 4 = 8/32

Step 3: Add the Numerators
Now add the numerators (2 + 8 = 10) and keep the common denominator 32 unchanged.
Working: 2 + 8/32 = 10/32

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 32, which is 2. Divide both the numerator and denominator by 2.
Working: 10 ÷ 2/32 ÷ 2 = 5/16

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 16 yields an exact terminating decimal of 0.3125 (or 31.25%).
Working: 5 ÷ 16 = 0.3125 (31.25%)

Key Values:
- Simplified Fraction: 5/16
- Mixed Number Form: 5/16
- Decimal Value: 0.3125
- Percentage: 31.25%

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Solved with FractionsCalc:
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2/32 + 2/8 = 5/16

Simplified Fraction

5/16

Mixed Number

Proper (5/16)

Decimal Value

0.3125

Percentage

31.25%

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Step-by-Step Solution: 2/32 + 2/8

Step 1

Find the Least Common Denominator (LCD)

Notice that 32 is an exact multiple of 8 (8 × 4 = 32). The Least Common Denominator (LCD) is simply 32, meaning we only need to scale one fraction.

LCD(32, 8) = 32

Step 2

Convert to Equivalent Fractions with Common Denominator 32

Multiply the numerator and denominator of 2/32 by 1, and multiply the numerator and denominator of 2/8 by 4 so both fractions share the common base 32.

2 × 1/32 × 1 = 2/32 and 2 × 4/8 × 4 = 8/32

Step 3

Add the Numerators

Now add the numerators (2 + 8 = 10) and keep the common denominator 32 unchanged.

2 + 8/32 = 10/32

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 32, which is 2. Divide both the numerator and denominator by 2.

10 ÷ 2/32 ÷ 2 = 5/16

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 16 yields an exact terminating decimal of 0.3125 (or 31.25%).

5 ÷ 16 = 0.3125 (31.25%)

Visual Representation

The diagram below illustrates 2/32 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/16`
Mixed Number Form	`5/16`
Decimal Form	`0.3125`
Percentage	`31.25%`

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Frequently Asked Questions

What is 2/32 plus 2/8 as a fraction?

2/32 + 2/8 in simplest fraction form is 5/16.

What is 2/32 plus 2/8 as a decimal?

2/32 + 2/8 converted to a decimal is 0.3125.

What is 2/32 plus 2/8 as a percentage?

2/32 + 2/8 expressed as a percentage is 31.25%.

Does 2/32 plus 2/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.3125) because the denominator in simplest terms contains only prime factors 2 and/or 5.