What is 8/22 plus 10/21? (Answer: 194/231)

Exact Answer

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Problem: What is 8/22 plus 10/21?
Formula / Expression: 8/22 + 10/21
Final Answer: 194/231
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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 8/22 by 21, and multiply the numerator and denominator of 10/21 by 22 so both fractions share the common base 462.
Working: 8 × 21/22 × 21 = 168/462 and 10 × 22/21 × 22 = 220/462

Step 3: Add the Numerators
Now add the numerators (168 + 220 = 388) and keep the common denominator 462 unchanged.
Working: 168 + 220/462 = 388/462

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 388 and 462, which is 2. Divide both the numerator and denominator by 2.
Working: 388 ÷ 2/462 ÷ 2 = 194/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 194 by denominator 231 produces a repeating decimal (approximately 0.839827, or 83.9827%).
Working: 194 ÷ 231 = 0.839827 (83.9827%)

Key Values:
- Simplified Fraction: 194/231
- Mixed Number Form: 194/231
- Decimal Value: 0.839827
- Percentage: 83.9827%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-22-plus-10-21/
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8/22 + 10/21 = 194/231

Simplified Fraction

194/231

Mixed Number

Proper (194/231)

Decimal Value

0.839827

Percentage

83.9827%

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Step-by-Step Solution: 8/22 + 10/21

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 8/22 by 21, and multiply the numerator and denominator of 10/21 by 22 so both fractions share the common base 462.

8 × 21/22 × 21 = 168/462 and 10 × 22/21 × 22 = 220/462

Step 3

Add the Numerators

Now add the numerators (168 + 220 = 388) and keep the common denominator 462 unchanged.

168 + 220/462 = 388/462

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 388 and 462, which is 2. Divide both the numerator and denominator by 2.

388 ÷ 2/462 ÷ 2 = 194/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 194 by denominator 231 produces a repeating decimal (approximately 0.839827, or 83.9827%).

194 ÷ 231 = 0.839827 (83.9827%)

Visual Representation

The diagram below illustrates 8/22 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`194/231`
Mixed Number Form	`194/231`
Decimal Form	`0.839827`
Percentage	`83.9827%`

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Frequently Asked Questions

What is 8/22 plus 10/21 as a fraction?

8/22 + 10/21 in simplest fraction form is 194/231.

What is 8/22 plus 10/21 as a decimal?

8/22 + 10/21 converted to a decimal is 0.839827.

What is 8/22 plus 10/21 as a percentage?

8/22 + 10/21 expressed as a percentage is 83.9827%.

Does 8/22 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.839827...) because the denominator contains prime factors other than 2 and 5.