What is 1/23 plus 3/21? (Answer: 30/161)

Exact Answer

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Problem: What is 1/23 plus 3/21?
Formula / Expression: 1/23 + 3/21
Final Answer: 30/161
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.
Working: LCD(23, 21) = 483

Step 2: Convert to Equivalent Fractions with Common Denominator 483
Multiply the numerator and denominator of 1/23 by 21, and multiply the numerator and denominator of 3/21 by 23 so both fractions share the common base 483.
Working: 1 × 21/23 × 21 = 21/483 and 3 × 23/21 × 23 = 69/483

Step 3: Add the Numerators
Now add the numerators (21 + 69 = 90) and keep the common denominator 483 unchanged.
Working: 21 + 69/483 = 90/483

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 483, which is 3. Divide both the numerator and denominator by 3.
Working: 90 ÷ 3/483 ÷ 3 = 30/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 30 by denominator 161 produces a repeating decimal (approximately 0.186335, or 18.6335%).
Working: 30 ÷ 161 = 0.186335 (18.6335%)

Key Values:
- Simplified Fraction: 30/161
- Mixed Number Form: 30/161
- Decimal Value: 0.186335
- Percentage: 18.6335%

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Solved with FractionsCalc:
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1/23 + 3/21 = 30/161

Simplified Fraction

30/161

Mixed Number

Proper (30/161)

Decimal Value

0.186335

Percentage

18.6335%

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Step-by-Step Solution: 1/23 + 3/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.

LCD(23, 21) = 483

Step 2

Convert to Equivalent Fractions with Common Denominator 483

Multiply the numerator and denominator of 1/23 by 21, and multiply the numerator and denominator of 3/21 by 23 so both fractions share the common base 483.

1 × 21/23 × 21 = 21/483 and 3 × 23/21 × 23 = 69/483

Step 3

Add the Numerators

Now add the numerators (21 + 69 = 90) and keep the common denominator 483 unchanged.

21 + 69/483 = 90/483

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 483, which is 3. Divide both the numerator and denominator by 3.

90 ÷ 3/483 ÷ 3 = 30/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 30 by denominator 161 produces a repeating decimal (approximately 0.186335, or 18.6335%).

30 ÷ 161 = 0.186335 (18.6335%)

Visual Representation

The diagram below illustrates 1/23 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`30/161`
Mixed Number Form	`30/161`
Decimal Form	`0.186335`
Percentage	`18.6335%`

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Frequently Asked Questions

What is 1/23 plus 3/21 as a fraction?

1/23 + 3/21 in simplest fraction form is 30/161.

What is 1/23 plus 3/21 as a decimal?

1/23 + 3/21 converted to a decimal is 0.186335.

What is 1/23 plus 3/21 as a percentage?

1/23 + 3/21 expressed as a percentage is 18.6335%.

Does 1/23 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.186335...) because the denominator contains prime factors other than 2 and 5.