What is 3/22 plus 2/10? (Answer: 37/110)

Exact Answer

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Problem: What is 3/22 plus 2/10?
Formula / Expression: 3/22 + 2/10
Final Answer: 37/110
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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 3/22 by 5, and multiply the numerator and denominator of 2/10 by 11 so both fractions share the common base 110.
Working: 3 × 5/22 × 5 = 15/110 and 2 × 11/10 × 11 = 22/110

Step 3: Add the Numerators
Now add the numerators (15 + 22 = 37) and keep the common denominator 110 unchanged.
Working: 15 + 22/110 = 37/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 110 is 1, confirming that 37/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 110 produces a repeating decimal (approximately 0.336364, or 33.6364%).
Working: 37 ÷ 110 = 0.336364 (33.6364%)

Key Values:
- Simplified Fraction: 37/110
- Mixed Number Form: 37/110
- Decimal Value: 0.336364
- Percentage: 33.6364%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-22-plus-2-10/
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3/22 + 2/10 = 37/110

Simplified Fraction

37/110

Mixed Number

Proper (37/110)

Decimal Value

0.336364

Percentage

33.6364%

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Step-by-Step Solution: 3/22 + 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 3/22 by 5, and multiply the numerator and denominator of 2/10 by 11 so both fractions share the common base 110.

3 × 5/22 × 5 = 15/110 and 2 × 11/10 × 11 = 22/110

Step 3

Add the Numerators

Now add the numerators (15 + 22 = 37) and keep the common denominator 110 unchanged.

15 + 22/110 = 37/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 110 is 1, confirming that 37/110 cannot be reduced further—it is already in its simplest irreducible form.

37/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 110 produces a repeating decimal (approximately 0.336364, or 33.6364%).

37 ÷ 110 = 0.336364 (33.6364%)

Visual Representation

The diagram below illustrates 3/22 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/110`
Mixed Number Form	`37/110`
Decimal Form	`0.336364`
Percentage	`33.6364%`

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Frequently Asked Questions

What is 3/22 plus 2/10 as a fraction?

3/22 + 2/10 in simplest fraction form is 37/110.

What is 3/22 plus 2/10 as a decimal?

3/22 + 2/10 converted to a decimal is 0.336364.

What is 3/22 plus 2/10 as a percentage?

3/22 + 2/10 expressed as a percentage is 33.6364%.

Does 3/22 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.336364...) because the denominator contains prime factors other than 2 and 5.