What is 5/31 plus 2/7? (Answer: 97/217)

Exact Answer

==================================================
Problem: What is 5/31 plus 2/7?
Formula / Expression: 5/31 + 2/7
Final Answer: 97/217
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 7 = 217.
Working: LCD(31, 7) = 217

Step 2: Convert to Equivalent Fractions with Common Denominator 217
Multiply the numerator and denominator of 5/31 by 7, and multiply the numerator and denominator of 2/7 by 31 so both fractions share the common base 217.
Working: 5 × 7/31 × 7 = 35/217 and 2 × 31/7 × 31 = 62/217

Step 3: Add the Numerators
Now add the numerators (35 + 62 = 97) and keep the common denominator 217 unchanged.
Working: 35 + 62/217 = 97/217

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 217 is 1, confirming that 97/217 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 217 produces a repeating decimal (approximately 0.447005, or 44.7005%).
Working: 97 ÷ 217 = 0.447005 (44.7005%)

Key Values:
- Simplified Fraction: 97/217
- Mixed Number Form: 97/217
- Decimal Value: 0.447005
- Percentage: 44.7005%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-31-plus-2-7/
==================================================

5/31 + 2/7 = 97/217

Simplified Fraction

97/217

Mixed Number

Proper (97/217)

Decimal Value

0.447005

Percentage

44.7005%

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: 5/31 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 7 = 217.

LCD(31, 7) = 217

Step 2

Convert to Equivalent Fractions with Common Denominator 217

Multiply the numerator and denominator of 5/31 by 7, and multiply the numerator and denominator of 2/7 by 31 so both fractions share the common base 217.

5 × 7/31 × 7 = 35/217 and 2 × 31/7 × 31 = 62/217

Step 3

Add the Numerators

Now add the numerators (35 + 62 = 97) and keep the common denominator 217 unchanged.

35 + 62/217 = 97/217

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 217 is 1, confirming that 97/217 cannot be reduced further—it is already in its simplest irreducible form.

97/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 217 produces a repeating decimal (approximately 0.447005, or 44.7005%).

97 ÷ 217 = 0.447005 (44.7005%)

Visual Representation

The diagram below illustrates 5/31 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/217`
Mixed Number Form	`97/217`
Decimal Form	`0.447005`
Percentage	`44.7005%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/31 plus 2/7 as a fraction?

5/31 + 2/7 in simplest fraction form is 97/217.

What is 5/31 plus 2/7 as a decimal?

5/31 + 2/7 converted to a decimal is 0.447005.

What is 5/31 plus 2/7 as a percentage?

5/31 + 2/7 expressed as a percentage is 44.7005%.

Does 5/31 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.447005...) because the denominator contains prime factors other than 2 and 5.