What is 2/32 plus 3/4? (Answer: 13/16)

Exact Answer

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Problem: What is 2/32 plus 3/4?
Formula / Expression: 2/32 + 3/4
Final Answer: 13/16
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 32 is an exact multiple of 4 (4 × 8 = 32). The Least Common Denominator (LCD) is simply 32, meaning we only need to scale one fraction.
Working: LCD(32, 4) = 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 3/4 by 8 so both fractions share the common base 32.
Working: 2 × 1/32 × 1 = 2/32 and 3 × 8/4 × 8 = 24/32

Step 3: Add the Numerators
Now add the numerators (2 + 24 = 26) and keep the common denominator 32 unchanged.
Working: 2 + 24/32 = 26/32

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 32, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/32 ÷ 2 = 13/16

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 16 yields an exact terminating decimal of 0.8125 (or 81.25%).
Working: 13 ÷ 16 = 0.8125 (81.25%)

Key Values:
- Simplified Fraction: 13/16
- Mixed Number Form: 13/16
- Decimal Value: 0.8125
- Percentage: 81.25%

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2/32 + 3/4 = 13/16

Simplified Fraction

13/16

Mixed Number

Proper (13/16)

Decimal Value

0.8125

Percentage

81.25%

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Step-by-Step Solution: 2/32 + 3/4

Step 1

Find the Least Common Denominator (LCD)

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

LCD(32, 4) = 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 3/4 by 8 so both fractions share the common base 32.

2 × 1/32 × 1 = 2/32 and 3 × 8/4 × 8 = 24/32

Step 3

Add the Numerators

Now add the numerators (2 + 24 = 26) and keep the common denominator 32 unchanged.

2 + 24/32 = 26/32

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 32, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/32 ÷ 2 = 13/16

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 16 yields an exact terminating decimal of 0.8125 (or 81.25%).

13 ÷ 16 = 0.8125 (81.25%)

Visual Representation

The diagram below illustrates 2/32 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/16`
Mixed Number Form	`13/16`
Decimal Form	`0.8125`
Percentage	`81.25%`

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Frequently Asked Questions

What is 2/32 plus 3/4 as a fraction?

2/32 + 3/4 in simplest fraction form is 13/16.

What is 2/32 plus 3/4 as a decimal?

2/32 + 3/4 converted to a decimal is 0.8125.

What is 2/32 plus 3/4 as a percentage?

2/32 + 3/4 expressed as a percentage is 81.25%.

Does 2/32 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.8125) because the denominator in simplest terms contains only prime factors 2 and/or 5.