What is 2/3 plus 5/7? (Answer: 29/21)

Exact Answer

==================================================
Problem: What is 2/3 plus 5/7?
Formula / Expression: 2/3 + 5/7
Final Answer: 1 8/21 (29/21)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 7 = 21.
Working: LCD(3, 7) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 2/3 by 7, and multiply the numerator and denominator of 5/7 by 3 so both fractions share the common base 21.
Working: 2 × 7/3 × 7 = 14/21 and 5 × 3/7 × 3 = 15/21

Step 3: Add the Numerators
Now add the numerators (14 + 15 = 29) and keep the common denominator 21 unchanged.
Working: 14 + 15/21 = 29/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 21 is 1, confirming that 29/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (21), divide 29 by 21: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/21.
Working: 29/21 = 1 8/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 21 produces a repeating decimal (approximately 1.380952, or 138.0952%).
Working: 29 ÷ 21 = 1.380952 (138.0952%)

Key Values:
- Simplified Fraction: 29/21
- Mixed Number Form: 1 8/21
- Decimal Value: 1.380952
- Percentage: 138.0952%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-plus-5-7/
==================================================

2/3 + 5/7 = 29/21

Simplified Fraction

29/21

Mixed Number

1 8/21

Decimal Value

1.380952

Percentage

138.0952%

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: 2/3 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 7 = 21.

LCD(3, 7) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 2/3 by 7, and multiply the numerator and denominator of 5/7 by 3 so both fractions share the common base 21.

2 × 7/3 × 7 = 14/21 and 5 × 3/7 × 3 = 15/21

Step 3

Add the Numerators

Now add the numerators (14 + 15 = 29) and keep the common denominator 21 unchanged.

14 + 15/21 = 29/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 21 is 1, confirming that 29/21 cannot be reduced further—it is already in its simplest irreducible form.

29/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (29) is greater than the denominator (21), divide 29 by 21: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/21.

29/21 = 18/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 21 produces a repeating decimal (approximately 1.380952, or 138.0952%).

29 ÷ 21 = 1.380952 (138.0952%)

Visual Representation

The diagram below illustrates 2/3 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/21`
Mixed Number Form	`1 8/21`
Decimal Form	`1.380952`
Percentage	`138.0952%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/3 plus 5/7 as a fraction?

2/3 + 5/7 in simplest fraction form is 29/21 (or 1 8/21 as a mixed number).

What is 2/3 plus 5/7 as a decimal?

2/3 + 5/7 converted to a decimal is 1.380952.

What is 2/3 plus 5/7 as a percentage?

2/3 + 5/7 expressed as a percentage is 138.0952%.

How do you write 2/3 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 29/21 can be written as the mixed number 1 8/21.

Does 2/3 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.380952...) because the denominator contains prime factors other than 2 and 5.