What is 4/18 plus 9/39? (Answer: 53/117)

Exact Answer

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Problem: What is 4/18 plus 9/39?
Formula / Expression: 4/18 + 9/39
Final Answer: 53/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 234 (which is smaller than their product 18 × 39 = 702, keeping the calculation simpler).
Working: LCD(18, 39) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 4/18 by 13, and multiply the numerator and denominator of 9/39 by 6 so both fractions share the common base 234.
Working: 4 × 13/18 × 13 = 52/234 and 9 × 6/39 × 6 = 54/234

Step 3: Add the Numerators
Now add the numerators (52 + 54 = 106) and keep the common denominator 234 unchanged.
Working: 52 + 54/234 = 106/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/234 ÷ 2 = 53/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).
Working: 53 ÷ 117 = 0.452991 (45.2991%)

Key Values:
- Simplified Fraction: 53/117
- Mixed Number Form: 53/117
- Decimal Value: 0.452991
- Percentage: 45.2991%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-18-plus-9-39/
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4/18 + 9/39 = 53/117

Simplified Fraction

53/117

Mixed Number

Proper (53/117)

Decimal Value

0.452991

Percentage

45.2991%

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Step-by-Step Solution: 4/18 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 234 (which is smaller than their product 18 × 39 = 702, keeping the calculation simpler).

LCD(18, 39) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 4/18 by 13, and multiply the numerator and denominator of 9/39 by 6 so both fractions share the common base 234.

4 × 13/18 × 13 = 52/234 and 9 × 6/39 × 6 = 54/234

Step 3

Add the Numerators

Now add the numerators (52 + 54 = 106) and keep the common denominator 234 unchanged.

52 + 54/234 = 106/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 234, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/234 ÷ 2 = 53/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).

53 ÷ 117 = 0.452991 (45.2991%)

Visual Representation

The diagram below illustrates 4/18 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/117`
Mixed Number Form	`53/117`
Decimal Form	`0.452991`
Percentage	`45.2991%`

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Frequently Asked Questions

What is 4/18 plus 9/39 as a fraction?

4/18 + 9/39 in simplest fraction form is 53/117.

What is 4/18 plus 9/39 as a decimal?

4/18 + 9/39 converted to a decimal is 0.452991.

What is 4/18 plus 9/39 as a percentage?

4/18 + 9/39 expressed as a percentage is 45.2991%.

Does 4/18 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452991...) because the denominator contains prime factors other than 2 and 5.