What is 4/22 plus 2/10? (Answer: 21/55)

Exact Answer

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Problem: What is 4/22 plus 2/10?
Formula / Expression: 4/22 + 2/10
Final Answer: 21/55
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 110 (which is smaller than their product 22 × 10 = 220, keeping the calculation simpler).
Working: LCD(22, 10) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 4/22 by 5, and multiply the numerator and denominator of 2/10 by 11 so both fractions share the common base 110.
Working: 4 × 5/22 × 5 = 20/110 and 2 × 11/10 × 11 = 22/110

Step 3: Add the Numerators
Now add the numerators (20 + 22 = 42) and keep the common denominator 110 unchanged.
Working: 20 + 22/110 = 42/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/110 ÷ 2 = 21/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 55 produces a repeating decimal (approximately 0.381818, or 38.1818%).
Working: 21 ÷ 55 = 0.381818 (38.1818%)

Key Values:
- Simplified Fraction: 21/55
- Mixed Number Form: 21/55
- Decimal Value: 0.381818
- Percentage: 38.1818%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-22-plus-2-10/
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4/22 + 2/10 = 21/55

Simplified Fraction

21/55

Mixed Number

Proper (21/55)

Decimal Value

0.381818

Percentage

38.1818%

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Step-by-Step Solution: 4/22 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 110 (which is smaller than their product 22 × 10 = 220, keeping the calculation simpler).

LCD(22, 10) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 4/22 by 5, and multiply the numerator and denominator of 2/10 by 11 so both fractions share the common base 110.

4 × 5/22 × 5 = 20/110 and 2 × 11/10 × 11 = 22/110

Step 3

Add the Numerators

Now add the numerators (20 + 22 = 42) and keep the common denominator 110 unchanged.

20 + 22/110 = 42/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 110, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/110 ÷ 2 = 21/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 55 produces a repeating decimal (approximately 0.381818, or 38.1818%).

21 ÷ 55 = 0.381818 (38.1818%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/55`
Mixed Number Form	`21/55`
Decimal Form	`0.381818`
Percentage	`38.1818%`

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Frequently Asked Questions

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

4/22 + 2/10 in simplest fraction form is 21/55.

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

4/22 + 2/10 converted to a decimal is 0.381818.

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

4/22 + 2/10 expressed as a percentage is 38.1818%.

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

It results in a repeating decimal (approximately 0.381818...) because the denominator contains prime factors other than 2 and 5.