What is 9/38 plus 2/8? (Answer: 37/76)

Exact Answer

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Problem: What is 9/38 plus 2/8?
Formula / Expression: 9/38 + 2/8
Final Answer: 37/76
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 152 (which is smaller than their product 38 × 8 = 304, keeping the calculation simpler).
Working: LCD(38, 8) = 152

Step 2: Convert to Equivalent Fractions with Common Denominator 152
Multiply the numerator and denominator of 9/38 by 4, and multiply the numerator and denominator of 2/8 by 19 so both fractions share the common base 152.
Working: 9 × 4/38 × 4 = 36/152 and 2 × 19/8 × 19 = 38/152

Step 3: Add the Numerators
Now add the numerators (36 + 38 = 74) and keep the common denominator 152 unchanged.
Working: 36 + 38/152 = 74/152

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 152, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/152 ÷ 2 = 37/76

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 76 produces a repeating decimal (approximately 0.486842, or 48.6842%).
Working: 37 ÷ 76 = 0.486842 (48.6842%)

Key Values:
- Simplified Fraction: 37/76
- Mixed Number Form: 37/76
- Decimal Value: 0.486842
- Percentage: 48.6842%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-38-plus-2-8/
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9/38 + 2/8 = 37/76

Simplified Fraction

37/76

Mixed Number

Proper (37/76)

Decimal Value

0.486842

Percentage

48.6842%

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Step-by-Step Solution: 9/38 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 152 (which is smaller than their product 38 × 8 = 304, keeping the calculation simpler).

LCD(38, 8) = 152

Step 2

Convert to Equivalent Fractions with Common Denominator 152

Multiply the numerator and denominator of 9/38 by 4, and multiply the numerator and denominator of 2/8 by 19 so both fractions share the common base 152.

9 × 4/38 × 4 = 36/152 and 2 × 19/8 × 19 = 38/152

Step 3

Add the Numerators

Now add the numerators (36 + 38 = 74) and keep the common denominator 152 unchanged.

36 + 38/152 = 74/152

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 152, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/152 ÷ 2 = 37/76

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 76 produces a repeating decimal (approximately 0.486842, or 48.6842%).

37 ÷ 76 = 0.486842 (48.6842%)

Visual Representation

The diagram below illustrates 9/38 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/76`
Mixed Number Form	`37/76`
Decimal Form	`0.486842`
Percentage	`48.6842%`

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Frequently Asked Questions

What is 9/38 plus 2/8 as a fraction?

9/38 + 2/8 in simplest fraction form is 37/76.

What is 9/38 plus 2/8 as a decimal?

9/38 + 2/8 converted to a decimal is 0.486842.

What is 9/38 plus 2/8 as a percentage?

9/38 + 2/8 expressed as a percentage is 48.6842%.

Does 9/38 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.486842...) because the denominator contains prime factors other than 2 and 5.