What is 4/31 plus 9/39? (Answer: 145/403)

Exact Answer

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Problem: What is 4/31 plus 9/39?
Formula / Expression: 4/31 + 9/39
Final Answer: 145/403
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 39 = 1209.
Working: LCD(31, 39) = 1209

Step 2: Convert to Equivalent Fractions with Common Denominator 1209
Multiply the numerator and denominator of 4/31 by 39, and multiply the numerator and denominator of 9/39 by 31 so both fractions share the common base 1209.
Working: 4 × 39/31 × 39 = 156/1209 and 9 × 31/39 × 31 = 279/1209

Step 3: Add the Numerators
Now add the numerators (156 + 279 = 435) and keep the common denominator 1209 unchanged.
Working: 156 + 279/1209 = 435/1209

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 435 and 1209, which is 3. Divide both the numerator and denominator by 3.
Working: 435 ÷ 3/1209 ÷ 3 = 145/403

Step 5: Decimal & Percentage Representation
Dividing the numerator 145 by denominator 403 produces a repeating decimal (approximately 0.359801, or 35.9801%).
Working: 145 ÷ 403 = 0.359801 (35.9801%)

Key Values:
- Simplified Fraction: 145/403
- Mixed Number Form: 145/403
- Decimal Value: 0.359801
- Percentage: 35.9801%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-31-plus-9-39/
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4/31 + 9/39 = 145/403

Simplified Fraction

145/403

Mixed Number

Proper (145/403)

Decimal Value

0.359801

Percentage

35.9801%

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Step-by-Step Solution: 4/31 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 39 = 1209.

LCD(31, 39) = 1209

Step 2

Convert to Equivalent Fractions with Common Denominator 1209

Multiply the numerator and denominator of 4/31 by 39, and multiply the numerator and denominator of 9/39 by 31 so both fractions share the common base 1209.

4 × 39/31 × 39 = 156/1209 and 9 × 31/39 × 31 = 279/1209

Step 3

Add the Numerators

Now add the numerators (156 + 279 = 435) and keep the common denominator 1209 unchanged.

156 + 279/1209 = 435/1209

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 435 and 1209, which is 3. Divide both the numerator and denominator by 3.

435 ÷ 3/1209 ÷ 3 = 145/403

Step 5

Decimal & Percentage Representation

Dividing the numerator 145 by denominator 403 produces a repeating decimal (approximately 0.359801, or 35.9801%).

145 ÷ 403 = 0.359801 (35.9801%)

Visual Representation

The diagram below illustrates 4/31 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`145/403`
Mixed Number Form	`145/403`
Decimal Form	`0.359801`
Percentage	`35.9801%`

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Frequently Asked Questions

What is 4/31 plus 9/39 as a fraction?

4/31 + 9/39 in simplest fraction form is 145/403.

What is 4/31 plus 9/39 as a decimal?

4/31 + 9/39 converted to a decimal is 0.359801.

What is 4/31 plus 9/39 as a percentage?

4/31 + 9/39 expressed as a percentage is 35.9801%.

Does 4/31 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.359801...) because the denominator contains prime factors other than 2 and 5.