What is 5/30 plus 2/9? (Answer: 7/18)

Exact Answer

==================================================
Problem: What is 5/30 plus 2/9?
Formula / Expression: 5/30 + 2/9
Final Answer: 7/18
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 30 × 9 = 270, keeping the calculation simpler).
Working: LCD(30, 9) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 5/30 by 3, and multiply the numerator and denominator of 2/9 by 10 so both fractions share the common base 90.
Working: 5 × 3/30 × 3 = 15/90 and 2 × 10/9 × 10 = 20/90

Step 3: Add the Numerators
Now add the numerators (15 + 20 = 35) and keep the common denominator 90 unchanged.
Working: 15 + 20/90 = 35/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 90, which is 5. Divide both the numerator and denominator by 5.
Working: 35 ÷ 5/90 ÷ 5 = 7/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 18 produces a repeating decimal (approximately 0.388889, or 38.8889%).
Working: 7 ÷ 18 = 0.388889 (38.8889%)

Key Values:
- Simplified Fraction: 7/18
- Mixed Number Form: 7/18
- Decimal Value: 0.388889
- Percentage: 38.8889%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-30-plus-2-9/
==================================================

5/30 + 2/9 = 7/18

Simplified Fraction

7/18

Mixed Number

Proper (7/18)

Decimal Value

0.388889

Percentage

38.8889%

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: 5/30 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 30 × 9 = 270, keeping the calculation simpler).

LCD(30, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 5/30 by 3, and multiply the numerator and denominator of 2/9 by 10 so both fractions share the common base 90.

5 × 3/30 × 3 = 15/90 and 2 × 10/9 × 10 = 20/90

Step 3

Add the Numerators

Now add the numerators (15 + 20 = 35) and keep the common denominator 90 unchanged.

15 + 20/90 = 35/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 90, which is 5. Divide both the numerator and denominator by 5.

35 ÷ 5/90 ÷ 5 = 7/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 18 produces a repeating decimal (approximately 0.388889, or 38.8889%).

7 ÷ 18 = 0.388889 (38.8889%)

Visual Representation

The diagram below illustrates 5/30 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/18`
Mixed Number Form	`7/18`
Decimal Form	`0.388889`
Percentage	`38.8889%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/30 plus 2/9 as a fraction?

5/30 + 2/9 in simplest fraction form is 7/18.

What is 5/30 plus 2/9 as a decimal?

5/30 + 2/9 converted to a decimal is 0.388889.

What is 5/30 plus 2/9 as a percentage?

5/30 + 2/9 expressed as a percentage is 38.8889%.

Does 5/30 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.388889...) because the denominator contains prime factors other than 2 and 5.