What is 8/30 plus 2/7? (Answer: 58/105)

Exact Answer

==================================================
Problem: What is 8/30 plus 2/7?
Formula / Expression: 8/30 + 2/7
Final Answer: 58/105
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 30 × 7 = 210.
Working: LCD(30, 7) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 8/30 by 7, and multiply the numerator and denominator of 2/7 by 30 so both fractions share the common base 210.
Working: 8 × 7/30 × 7 = 56/210 and 2 × 30/7 × 30 = 60/210

Step 3: Add the Numerators
Now add the numerators (56 + 60 = 116) and keep the common denominator 210 unchanged.
Working: 56 + 60/210 = 116/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 116 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 116 ÷ 2/210 ÷ 2 = 58/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 105 produces a repeating decimal (approximately 0.552381, or 55.2381%).
Working: 58 ÷ 105 = 0.552381 (55.2381%)

Key Values:
- Simplified Fraction: 58/105
- Mixed Number Form: 58/105
- Decimal Value: 0.552381
- Percentage: 55.2381%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-30-plus-2-7/
==================================================

8/30 + 2/7 = 58/105

Simplified Fraction

58/105

Mixed Number

Proper (58/105)

Decimal Value

0.552381

Percentage

55.2381%

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: 8/30 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 30 × 7 = 210.

LCD(30, 7) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 8/30 by 7, and multiply the numerator and denominator of 2/7 by 30 so both fractions share the common base 210.

8 × 7/30 × 7 = 56/210 and 2 × 30/7 × 30 = 60/210

Step 3

Add the Numerators

Now add the numerators (56 + 60 = 116) and keep the common denominator 210 unchanged.

56 + 60/210 = 116/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 116 and 210, which is 2. Divide both the numerator and denominator by 2.

116 ÷ 2/210 ÷ 2 = 58/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 105 produces a repeating decimal (approximately 0.552381, or 55.2381%).

58 ÷ 105 = 0.552381 (55.2381%)

Visual Representation

The diagram below illustrates 8/30 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/105`
Mixed Number Form	`58/105`
Decimal Form	`0.552381`
Percentage	`55.2381%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 8/30 plus 2/7 as a fraction?

8/30 + 2/7 in simplest fraction form is 58/105.

What is 8/30 plus 2/7 as a decimal?

8/30 + 2/7 converted to a decimal is 0.552381.

What is 8/30 plus 2/7 as a percentage?

8/30 + 2/7 expressed as a percentage is 55.2381%.

Does 8/30 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.552381...) because the denominator contains prime factors other than 2 and 5.