What is 2/23 plus 5/7? (Answer: 129/161)

Exact Answer

==================================================
Problem: What is 2/23 plus 5/7?
Formula / Expression: 2/23 + 5/7
Final Answer: 129/161
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 7 = 161.
Working: LCD(23, 7) = 161

Step 2: Convert to Equivalent Fractions with Common Denominator 161
Multiply the numerator and denominator of 2/23 by 7, and multiply the numerator and denominator of 5/7 by 23 so both fractions share the common base 161.
Working: 2 × 7/23 × 7 = 14/161 and 5 × 23/7 × 23 = 115/161

Step 3: Add the Numerators
Now add the numerators (14 + 115 = 129) and keep the common denominator 161 unchanged.
Working: 14 + 115/161 = 129/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 129 and 161 is 1, confirming that 129/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 129/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 129 by denominator 161 produces a repeating decimal (approximately 0.801242, or 80.1242%).
Working: 129 ÷ 161 = 0.801242 (80.1242%)

Key Values:
- Simplified Fraction: 129/161
- Mixed Number Form: 129/161
- Decimal Value: 0.801242
- Percentage: 80.1242%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-23-plus-5-7/
==================================================

2/23 + 5/7 = 129/161

Simplified Fraction

129/161

Mixed Number

Proper (129/161)

Decimal Value

0.801242

Percentage

80.1242%

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: 2/23 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 7 = 161.

LCD(23, 7) = 161

Step 2

Convert to Equivalent Fractions with Common Denominator 161

Multiply the numerator and denominator of 2/23 by 7, and multiply the numerator and denominator of 5/7 by 23 so both fractions share the common base 161.

2 × 7/23 × 7 = 14/161 and 5 × 23/7 × 23 = 115/161

Step 3

Add the Numerators

Now add the numerators (14 + 115 = 129) and keep the common denominator 161 unchanged.

14 + 115/161 = 129/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 129 and 161 is 1, confirming that 129/161 cannot be reduced further—it is already in its simplest irreducible form.

129/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 129 by denominator 161 produces a repeating decimal (approximately 0.801242, or 80.1242%).

129 ÷ 161 = 0.801242 (80.1242%)

Visual Representation

The diagram below illustrates 2/23 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`129/161`
Mixed Number Form	`129/161`
Decimal Form	`0.801242`
Percentage	`80.1242%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/23 plus 5/7 as a fraction?

2/23 + 5/7 in simplest fraction form is 129/161.

What is 2/23 plus 5/7 as a decimal?

2/23 + 5/7 converted to a decimal is 0.801242.

What is 2/23 plus 5/7 as a percentage?

2/23 + 5/7 expressed as a percentage is 80.1242%.

Does 2/23 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.801242...) because the denominator contains prime factors other than 2 and 5.