What is 4/30 plus 9/39? (Answer: 71/195)

Exact Answer

==================================================
Problem: What is 4/30 plus 9/39?
Formula / Expression: 4/30 + 9/39
Final Answer: 71/195
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 390 (which is smaller than their product 30 × 39 = 1170, keeping the calculation simpler).
Working: LCD(30, 39) = 390

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 4/30 by 13, and multiply the numerator and denominator of 9/39 by 10 so both fractions share the common base 390.
Working: 4 × 13/30 × 13 = 52/390 and 9 × 10/39 × 10 = 90/390

Step 3: Add the Numerators
Now add the numerators (52 + 90 = 142) and keep the common denominator 390 unchanged.
Working: 52 + 90/390 = 142/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 390, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/390 ÷ 2 = 71/195

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 195 produces a repeating decimal (approximately 0.364103, or 36.4103%).
Working: 71 ÷ 195 = 0.364103 (36.4103%)

Key Values:
- Simplified Fraction: 71/195
- Mixed Number Form: 71/195
- Decimal Value: 0.364103
- Percentage: 36.4103%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-30-plus-9-39/
==================================================

4/30 + 9/39 = 71/195

Simplified Fraction

71/195

Mixed Number

Proper (71/195)

Decimal Value

0.364103

Percentage

36.4103%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 4/30 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 390 (which is smaller than their product 30 × 39 = 1170, keeping the calculation simpler).

LCD(30, 39) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

Multiply the numerator and denominator of 4/30 by 13, and multiply the numerator and denominator of 9/39 by 10 so both fractions share the common base 390.

4 × 13/30 × 13 = 52/390 and 9 × 10/39 × 10 = 90/390

Step 3

Add the Numerators

Now add the numerators (52 + 90 = 142) and keep the common denominator 390 unchanged.

52 + 90/390 = 142/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 390, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/390 ÷ 2 = 71/195

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 195 produces a repeating decimal (approximately 0.364103, or 36.4103%).

71 ÷ 195 = 0.364103 (36.4103%)

Visual Representation

The diagram below illustrates 4/30 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/195`
Mixed Number Form	`71/195`
Decimal Form	`0.364103`
Percentage	`36.4103%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/30 plus 9/39 as a fraction?

4/30 + 9/39 in simplest fraction form is 71/195.

What is 4/30 plus 9/39 as a decimal?

4/30 + 9/39 converted to a decimal is 0.364103.

What is 4/30 plus 9/39 as a percentage?

4/30 + 9/39 expressed as a percentage is 36.4103%.

Does 4/30 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.364103...) because the denominator contains prime factors other than 2 and 5.