What is 2/7 plus 3/9? (Answer: 13/21)

Exact Answer

==================================================
Problem: What is 2/7 plus 3/9?
Formula / Expression: 2/7 + 3/9
Final Answer: 13/21
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
Working: LCD(7, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/7 by 9, and multiply the numerator and denominator of 3/9 by 7 so both fractions share the common base 63.
Working: 2 × 9/7 × 9 = 18/63 and 3 × 7/9 × 7 = 21/63

Step 3: Add the Numerators
Now add the numerators (18 + 21 = 39) and keep the common denominator 63 unchanged.
Working: 18 + 21/63 = 39/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/63 ÷ 3 = 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-3-9/
==================================================

2/7 + 3/9 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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: 2/7 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.

LCD(7, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 2/7 by 9, and multiply the numerator and denominator of 3/9 by 7 so both fractions share the common base 63.

2 × 9/7 × 9 = 18/63 and 3 × 7/9 × 7 = 21/63

Step 3

Add the Numerators

Now add the numerators (18 + 21 = 39) and keep the common denominator 63 unchanged.

18 + 21/63 = 39/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 63, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/63 ÷ 3 = 13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 2/7 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/7 plus 3/9 as a fraction?

2/7 + 3/9 in simplest fraction form is 13/21.

What is 2/7 plus 3/9 as a decimal?

2/7 + 3/9 converted to a decimal is 0.619048.

What is 2/7 plus 3/9 as a percentage?

2/7 + 3/9 expressed as a percentage is 61.9048%.

Does 2/7 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.