What is 3/22 plus 5/21? (Answer: 173/462)

Exact Answer

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Problem: What is 3/22 plus 5/21?
Formula / Expression: 3/22 + 5/21
Final Answer: 173/462
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 21 = 462.
Working: LCD(22, 21) = 462

Step 2: Convert to Equivalent Fractions with Common Denominator 462
Multiply the numerator and denominator of 3/22 by 21, and multiply the numerator and denominator of 5/21 by 22 so both fractions share the common base 462.
Working: 3 × 21/22 × 21 = 63/462 and 5 × 22/21 × 22 = 110/462

Step 3: Add the Numerators
Now add the numerators (63 + 110 = 173) and keep the common denominator 462 unchanged.
Working: 63 + 110/462 = 173/462

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 173 and 462 is 1, confirming that 173/462 cannot be reduced further—it is already in its simplest irreducible form.
Working: 173/462

Step 5: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 462 produces a repeating decimal (approximately 0.374459, or 37.4459%).
Working: 173 ÷ 462 = 0.374459 (37.4459%)

Key Values:
- Simplified Fraction: 173/462
- Mixed Number Form: 173/462
- Decimal Value: 0.374459
- Percentage: 37.4459%

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Solved with FractionsCalc:
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3/22 + 5/21 = 173/462

Simplified Fraction

173/462

Mixed Number

Proper (173/462)

Decimal Value

0.374459

Percentage

37.4459%

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Step-by-Step Solution: 3/22 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 21 = 462.

LCD(22, 21) = 462

Step 2

Convert to Equivalent Fractions with Common Denominator 462

Multiply the numerator and denominator of 3/22 by 21, and multiply the numerator and denominator of 5/21 by 22 so both fractions share the common base 462.

3 × 21/22 × 21 = 63/462 and 5 × 22/21 × 22 = 110/462

Step 3

Add the Numerators

Now add the numerators (63 + 110 = 173) and keep the common denominator 462 unchanged.

63 + 110/462 = 173/462

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 173 and 462 is 1, confirming that 173/462 cannot be reduced further—it is already in its simplest irreducible form.

173/462

Step 5

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 462 produces a repeating decimal (approximately 0.374459, or 37.4459%).

173 ÷ 462 = 0.374459 (37.4459%)

Visual Representation

The diagram below illustrates 3/22 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/462`
Mixed Number Form	`173/462`
Decimal Form	`0.374459`
Percentage	`37.4459%`

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Frequently Asked Questions

What is 3/22 plus 5/21 as a fraction?

3/22 + 5/21 in simplest fraction form is 173/462.

What is 3/22 plus 5/21 as a decimal?

3/22 + 5/21 converted to a decimal is 0.374459.

What is 3/22 plus 5/21 as a percentage?

3/22 + 5/21 expressed as a percentage is 37.4459%.

Does 3/22 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.374459...) because the denominator contains prime factors other than 2 and 5.