What is 2/52 plus 2/22? (Answer: 37/286)

Exact Answer

==================================================
Problem: What is 2/52 plus 2/22?
Formula / Expression: 2/52 + 2/22
Final Answer: 37/286
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 572 (which is smaller than their product 52 × 22 = 1144, keeping the calculation simpler).
Working: LCD(52, 22) = 572

Step 2: Convert to Equivalent Fractions with Common Denominator 572
Multiply the numerator and denominator of 2/52 by 11, and multiply the numerator and denominator of 2/22 by 26 so both fractions share the common base 572.
Working: 2 × 11/52 × 11 = 22/572 and 2 × 26/22 × 26 = 52/572

Step 3: Add the Numerators
Now add the numerators (22 + 52 = 74) and keep the common denominator 572 unchanged.
Working: 22 + 52/572 = 74/572

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 572, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/572 ÷ 2 = 37/286

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 286 produces a repeating decimal (approximately 0.129371, or 12.9371%).
Working: 37 ÷ 286 = 0.129371 (12.9371%)

Key Values:
- Simplified Fraction: 37/286
- Mixed Number Form: 37/286
- Decimal Value: 0.129371
- Percentage: 12.9371%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-52-plus-2-22/
==================================================

2/52 + 2/22 = 37/286

Simplified Fraction

37/286

Mixed Number

Proper (37/286)

Decimal Value

0.129371

Percentage

12.9371%

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: 2/52 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 572 (which is smaller than their product 52 × 22 = 1144, keeping the calculation simpler).

LCD(52, 22) = 572

Step 2

Convert to Equivalent Fractions with Common Denominator 572

Multiply the numerator and denominator of 2/52 by 11, and multiply the numerator and denominator of 2/22 by 26 so both fractions share the common base 572.

2 × 11/52 × 11 = 22/572 and 2 × 26/22 × 26 = 52/572

Step 3

Add the Numerators

Now add the numerators (22 + 52 = 74) and keep the common denominator 572 unchanged.

22 + 52/572 = 74/572

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 572, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/572 ÷ 2 = 37/286

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 286 produces a repeating decimal (approximately 0.129371, or 12.9371%).

37 ÷ 286 = 0.129371 (12.9371%)

Visual Representation

The diagram below illustrates 2/52 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/286`
Mixed Number Form	`37/286`
Decimal Form	`0.129371`
Percentage	`12.9371%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/52 plus 2/22 as a fraction?

2/52 + 2/22 in simplest fraction form is 37/286.

What is 2/52 plus 2/22 as a decimal?

2/52 + 2/22 converted to a decimal is 0.129371.

What is 2/52 plus 2/22 as a percentage?

2/52 + 2/22 expressed as a percentage is 12.9371%.

Does 2/52 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.129371...) because the denominator contains prime factors other than 2 and 5.