What is 9/38 plus 2/4? (Answer: 14/19)

Exact Answer

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Problem: What is 9/38 plus 2/4?
Formula / Expression: 9/38 + 2/4
Final Answer: 14/19
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 76 (which is smaller than their product 38 × 4 = 152, keeping the calculation simpler).
Working: LCD(38, 4) = 76

Step 2: Convert to Equivalent Fractions with Common Denominator 76
Multiply the numerator and denominator of 9/38 by 2, and multiply the numerator and denominator of 2/4 by 19 so both fractions share the common base 76.
Working: 9 × 2/38 × 2 = 18/76 and 2 × 19/4 × 19 = 38/76

Step 3: Add the Numerators
Now add the numerators (18 + 38 = 56) and keep the common denominator 76 unchanged.
Working: 18 + 38/76 = 56/76

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 56 and 76, which is 4. Divide both the numerator and denominator by 4.
Working: 56 ÷ 4/76 ÷ 4 = 14/19

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 19 produces a repeating decimal (approximately 0.736842, or 73.6842%).
Working: 14 ÷ 19 = 0.736842 (73.6842%)

Key Values:
- Simplified Fraction: 14/19
- Mixed Number Form: 14/19
- Decimal Value: 0.736842
- Percentage: 73.6842%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-38-plus-2-4/
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9/38 + 2/4 = 14/19

Simplified Fraction

14/19

Mixed Number

Proper (14/19)

Decimal Value

0.736842

Percentage

73.6842%

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Step-by-Step Solution: 9/38 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 76 (which is smaller than their product 38 × 4 = 152, keeping the calculation simpler).

LCD(38, 4) = 76

Step 2

Convert to Equivalent Fractions with Common Denominator 76

Multiply the numerator and denominator of 9/38 by 2, and multiply the numerator and denominator of 2/4 by 19 so both fractions share the common base 76.

9 × 2/38 × 2 = 18/76 and 2 × 19/4 × 19 = 38/76

Step 3

Add the Numerators

Now add the numerators (18 + 38 = 56) and keep the common denominator 76 unchanged.

18 + 38/76 = 56/76

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 56 and 76, which is 4. Divide both the numerator and denominator by 4.

56 ÷ 4/76 ÷ 4 = 14/19

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 19 produces a repeating decimal (approximately 0.736842, or 73.6842%).

14 ÷ 19 = 0.736842 (73.6842%)

Visual Representation

The diagram below illustrates 9/38 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/19`
Mixed Number Form	`14/19`
Decimal Form	`0.736842`
Percentage	`73.6842%`

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Frequently Asked Questions

What is 9/38 plus 2/4 as a fraction?

9/38 + 2/4 in simplest fraction form is 14/19.

What is 9/38 plus 2/4 as a decimal?

9/38 + 2/4 converted to a decimal is 0.736842.

What is 9/38 plus 2/4 as a percentage?

9/38 + 2/4 expressed as a percentage is 73.6842%.

Does 9/38 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.736842...) because the denominator contains prime factors other than 2 and 5.