What is 10/22 plus 2/4? (Answer: 21/22)

Exact Answer

==================================================
Problem: What is 10/22 plus 2/4?
Formula / Expression: 10/22 + 2/4
Final Answer: 21/22
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).
Working: LCD(22, 4) = 44

Step 2: Convert to Equivalent Fractions with Common Denominator 44
Multiply the numerator and denominator of 10/22 by 2, and multiply the numerator and denominator of 2/4 by 11 so both fractions share the common base 44.
Working: 10 × 2/22 × 2 = 20/44 and 2 × 11/4 × 11 = 22/44

Step 3: Add the Numerators
Now add the numerators (20 + 22 = 42) and keep the common denominator 44 unchanged.
Working: 20 + 22/44 = 42/44

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 44, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/44 ÷ 2 = 21/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 22 produces a repeating decimal (approximately 0.954545, or 95.4545%).
Working: 21 ÷ 22 = 0.954545 (95.4545%)

Key Values:
- Simplified Fraction: 21/22
- Mixed Number Form: 21/22
- Decimal Value: 0.954545
- Percentage: 95.4545%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-22-plus-2-4/
==================================================

10/22 + 2/4 = 21/22

Simplified Fraction

21/22

Mixed Number

Proper (21/22)

Decimal Value

0.954545

Percentage

95.4545%

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: 10/22 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).

LCD(22, 4) = 44

Step 2

Convert to Equivalent Fractions with Common Denominator 44

Multiply the numerator and denominator of 10/22 by 2, and multiply the numerator and denominator of 2/4 by 11 so both fractions share the common base 44.

10 × 2/22 × 2 = 20/44 and 2 × 11/4 × 11 = 22/44

Step 3

Add the Numerators

Now add the numerators (20 + 22 = 42) and keep the common denominator 44 unchanged.

20 + 22/44 = 42/44

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 44, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/44 ÷ 2 = 21/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 22 produces a repeating decimal (approximately 0.954545, or 95.4545%).

21 ÷ 22 = 0.954545 (95.4545%)

Visual Representation

The diagram below illustrates 10/22 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/22`
Mixed Number Form	`21/22`
Decimal Form	`0.954545`
Percentage	`95.4545%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/22 plus 2/4 as a fraction?

10/22 + 2/4 in simplest fraction form is 21/22.

What is 10/22 plus 2/4 as a decimal?

10/22 + 2/4 converted to a decimal is 0.954545.

What is 10/22 plus 2/4 as a percentage?

10/22 + 2/4 expressed as a percentage is 95.4545%.

Does 10/22 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.954545...) because the denominator contains prime factors other than 2 and 5.