What is 2/5 plus 10/22? (Answer: 47/55)

Exact Answer

==================================================
Problem: What is 2/5 plus 10/22?
Formula / Expression: 2/5 + 10/22
Final Answer: 47/55
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 22 = 110.
Working: LCD(5, 22) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/5 by 22, and multiply the numerator and denominator of 10/22 by 5 so both fractions share the common base 110.
Working: 2 × 22/5 × 22 = 44/110 and 10 × 5/22 × 5 = 50/110

Step 3: Add the Numerators
Now add the numerators (44 + 50 = 94) and keep the common denominator 110 unchanged.
Working: 44 + 50/110 = 94/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/110 ÷ 2 = 47/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 55 produces a repeating decimal (approximately 0.854545, or 85.4545%).
Working: 47 ÷ 55 = 0.854545 (85.4545%)

Key Values:
- Simplified Fraction: 47/55
- Mixed Number Form: 47/55
- Decimal Value: 0.854545
- Percentage: 85.4545%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-10-22/
==================================================

2/5 + 10/22 = 47/55

Simplified Fraction

47/55

Mixed Number

Proper (47/55)

Decimal Value

0.854545

Percentage

85.4545%

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: 2/5 + 10/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 22 = 110.

LCD(5, 22) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 2/5 by 22, and multiply the numerator and denominator of 10/22 by 5 so both fractions share the common base 110.

2 × 22/5 × 22 = 44/110 and 10 × 5/22 × 5 = 50/110

Step 3

Add the Numerators

Now add the numerators (44 + 50 = 94) and keep the common denominator 110 unchanged.

44 + 50/110 = 94/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 110, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/110 ÷ 2 = 47/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 55 produces a repeating decimal (approximately 0.854545, or 85.4545%).

47 ÷ 55 = 0.854545 (85.4545%)

Visual Representation

The diagram below illustrates 2/5 plus 10/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/55`
Mixed Number Form	`47/55`
Decimal Form	`0.854545`
Percentage	`85.4545%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/5 plus 10/22 as a fraction?

2/5 + 10/22 in simplest fraction form is 47/55.

What is 2/5 plus 10/22 as a decimal?

2/5 + 10/22 converted to a decimal is 0.854545.

What is 2/5 plus 10/22 as a percentage?

2/5 + 10/22 expressed as a percentage is 85.4545%.

Does 2/5 plus 10/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.854545...) because the denominator contains prime factors other than 2 and 5.