What is 2/8 plus 9/36? (Answer: 1/2)

Exact Answer

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Problem: What is 2/8 plus 9/36?
Formula / Expression: 2/8 + 9/36
Final Answer: 1/2
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 36 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 8 × 36 = 288, keeping the calculation simpler).
Working: LCD(8, 36) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 2/8 by 9, and multiply the numerator and denominator of 9/36 by 2 so both fractions share the common base 72.
Working: 2 × 9/8 × 9 = 18/72 and 9 × 2/36 × 2 = 18/72

Step 3: Add the Numerators
Now add the numerators (18 + 18 = 36) and keep the common denominator 72 unchanged.
Working: 18 + 18/72 = 36/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 72, which is 36. Divide both the numerator and denominator by 36.
Working: 36 ÷ 36/72 ÷ 36 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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2/8 + 9/36 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 2/8 + 9/36

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 36 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 8 × 36 = 288, keeping the calculation simpler).

LCD(8, 36) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 2/8 by 9, and multiply the numerator and denominator of 9/36 by 2 so both fractions share the common base 72.

2 × 9/8 × 9 = 18/72 and 9 × 2/36 × 2 = 18/72

Step 3

Add the Numerators

Now add the numerators (18 + 18 = 36) and keep the common denominator 72 unchanged.

18 + 18/72 = 36/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 72, which is 36. Divide both the numerator and denominator by 36.

36 ÷ 36/72 ÷ 36 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 2/8 plus 9/36 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 2/8 plus 9/36 as a fraction?

2/8 + 9/36 in simplest fraction form is 1/2.

What is 2/8 plus 9/36 as a decimal?

2/8 + 9/36 converted to a decimal is 0.5.

What is 2/8 plus 9/36 as a percentage?

2/8 + 9/36 expressed as a percentage is 50%.

Does 2/8 plus 9/36 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.