What is 9/19 plus 4/8? (Answer: 37/38)

Exact Answer

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Problem: What is 9/19 plus 4/8?
Formula / Expression: 9/19 + 4/8
Final Answer: 37/38
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 8 = 152.
Working: LCD(19, 8) = 152

Step 2: Convert to Equivalent Fractions with Common Denominator 152
Multiply the numerator and denominator of 9/19 by 8, and multiply the numerator and denominator of 4/8 by 19 so both fractions share the common base 152.
Working: 9 × 8/19 × 8 = 72/152 and 4 × 19/8 × 19 = 76/152

Step 3: Add the Numerators
Now add the numerators (72 + 76 = 148) and keep the common denominator 152 unchanged.
Working: 72 + 76/152 = 148/152

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 148 and 152, which is 4. Divide both the numerator and denominator by 4.
Working: 148 ÷ 4/152 ÷ 4 = 37/38

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 38 produces a repeating decimal (approximately 0.973684, or 97.3684%).
Working: 37 ÷ 38 = 0.973684 (97.3684%)

Key Values:
- Simplified Fraction: 37/38
- Mixed Number Form: 37/38
- Decimal Value: 0.973684
- Percentage: 97.3684%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-19-plus-4-8/
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9/19 + 4/8 = 37/38

Simplified Fraction

37/38

Mixed Number

Proper (37/38)

Decimal Value

0.973684

Percentage

97.3684%

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Step-by-Step Solution: 9/19 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 8 = 152.

LCD(19, 8) = 152

Step 2

Convert to Equivalent Fractions with Common Denominator 152

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

9 × 8/19 × 8 = 72/152 and 4 × 19/8 × 19 = 76/152

Step 3

Add the Numerators

Now add the numerators (72 + 76 = 148) and keep the common denominator 152 unchanged.

72 + 76/152 = 148/152

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 148 and 152, which is 4. Divide both the numerator and denominator by 4.

148 ÷ 4/152 ÷ 4 = 37/38

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 38 produces a repeating decimal (approximately 0.973684, or 97.3684%).

37 ÷ 38 = 0.973684 (97.3684%)

Visual Representation

The diagram below illustrates 9/19 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/38`
Mixed Number Form	`37/38`
Decimal Form	`0.973684`
Percentage	`97.3684%`

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Frequently Asked Questions

What is 9/19 plus 4/8 as a fraction?

9/19 + 4/8 in simplest fraction form is 37/38.

What is 9/19 plus 4/8 as a decimal?

9/19 + 4/8 converted to a decimal is 0.973684.

What is 9/19 plus 4/8 as a percentage?

9/19 + 4/8 expressed as a percentage is 97.3684%.

Does 9/19 plus 4/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.973684...) because the denominator contains prime factors other than 2 and 5.