What is 2/8 plus 9/32? (Answer: 17/32)

Exact Answer

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Problem: What is 2/8 plus 9/32?
Formula / Expression: 2/8 + 9/32
Final Answer: 17/32
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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(8, 32) = 32

Step 2: Convert to Equivalent Fractions with Common Denominator 32
Multiply the numerator and denominator of 2/8 by 4, and multiply the numerator and denominator of 9/32 by 1 so both fractions share the common base 32.
Working: 2 × 4/8 × 4 = 8/32 and 9 × 1/32 × 1 = 9/32

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 32 unchanged.
Working: 8 + 9/32 = 17/32

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 32 is 1, confirming that 17/32 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/32

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 32 yields an exact terminating decimal of 0.53125 (or 53.125%).
Working: 17 ÷ 32 = 0.53125 (53.125%)

Key Values:
- Simplified Fraction: 17/32
- Mixed Number Form: 17/32
- Decimal Value: 0.53125
- Percentage: 53.125%

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Solved with FractionsCalc:
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2/8 + 9/32 = 17/32

Simplified Fraction

17/32

Mixed Number

Proper (17/32)

Decimal Value

0.53125

Percentage

53.125%

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Step-by-Step Solution: 2/8 + 9/32

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(8, 32) = 32

Step 2

Convert to Equivalent Fractions with Common Denominator 32

Multiply the numerator and denominator of 2/8 by 4, and multiply the numerator and denominator of 9/32 by 1 so both fractions share the common base 32.

2 × 4/8 × 4 = 8/32 and 9 × 1/32 × 1 = 9/32

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 32 unchanged.

8 + 9/32 = 17/32

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 32 is 1, confirming that 17/32 cannot be reduced further—it is already in its simplest irreducible form.

17/32

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 32 yields an exact terminating decimal of 0.53125 (or 53.125%).

17 ÷ 32 = 0.53125 (53.125%)

Visual Representation

The diagram below illustrates 2/8 plus 9/32 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/32`
Mixed Number Form	`17/32`
Decimal Form	`0.53125`
Percentage	`53.125%`

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Frequently Asked Questions

What is 2/8 plus 9/32 as a fraction?

2/8 + 9/32 in simplest fraction form is 17/32.

What is 2/8 plus 9/32 as a decimal?

2/8 + 9/32 converted to a decimal is 0.53125.

What is 2/8 plus 9/32 as a percentage?

2/8 + 9/32 expressed as a percentage is 53.125%.

Does 2/8 plus 9/32 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.53125) because the denominator in simplest terms contains only prime factors 2 and/or 5.