What is 7/27 plus 2/7? (Answer: 103/189)

Exact Answer

==================================================
Problem: What is 7/27 plus 2/7?
Formula / Expression: 7/27 + 2/7
Final Answer: 103/189
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 7 = 189.
Working: LCD(27, 7) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 7/27 by 7, and multiply the numerator and denominator of 2/7 by 27 so both fractions share the common base 189.
Working: 7 × 7/27 × 7 = 49/189 and 2 × 27/7 × 27 = 54/189

Step 3: Add the Numerators
Now add the numerators (49 + 54 = 103) and keep the common denominator 189 unchanged.
Working: 49 + 54/189 = 103/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 189 is 1, confirming that 103/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 189 produces a repeating decimal (approximately 0.544974, or 54.4974%).
Working: 103 ÷ 189 = 0.544974 (54.4974%)

Key Values:
- Simplified Fraction: 103/189
- Mixed Number Form: 103/189
- Decimal Value: 0.544974
- Percentage: 54.4974%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-27-plus-2-7/
==================================================

7/27 + 2/7 = 103/189

Simplified Fraction

103/189

Mixed Number

Proper (103/189)

Decimal Value

0.544974

Percentage

54.4974%

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: 7/27 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 7 = 189.

LCD(27, 7) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 7/27 by 7, and multiply the numerator and denominator of 2/7 by 27 so both fractions share the common base 189.

7 × 7/27 × 7 = 49/189 and 2 × 27/7 × 27 = 54/189

Step 3

Add the Numerators

Now add the numerators (49 + 54 = 103) and keep the common denominator 189 unchanged.

49 + 54/189 = 103/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 189 is 1, confirming that 103/189 cannot be reduced further—it is already in its simplest irreducible form.

103/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 189 produces a repeating decimal (approximately 0.544974, or 54.4974%).

103 ÷ 189 = 0.544974 (54.4974%)

Visual Representation

The diagram below illustrates 7/27 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/189`
Mixed Number Form	`103/189`
Decimal Form	`0.544974`
Percentage	`54.4974%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/27 plus 2/7 as a fraction?

7/27 + 2/7 in simplest fraction form is 103/189.

What is 7/27 plus 2/7 as a decimal?

7/27 + 2/7 converted to a decimal is 0.544974.

What is 7/27 plus 2/7 as a percentage?

7/27 + 2/7 expressed as a percentage is 54.4974%.

Does 7/27 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.544974...) because the denominator contains prime factors other than 2 and 5.