What is 1/47 plus 4/21? (Answer: 209/987)

Exact Answer

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Problem: What is 1/47 plus 4/21?
Formula / Expression: 1/47 + 4/21
Final Answer: 209/987
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 47 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 21 = 987.
Working: LCD(47, 21) = 987

Step 2: Convert to Equivalent Fractions with Common Denominator 987
Multiply the numerator and denominator of 1/47 by 21, and multiply the numerator and denominator of 4/21 by 47 so both fractions share the common base 987.
Working: 1 × 21/47 × 21 = 21/987 and 4 × 47/21 × 47 = 188/987

Step 3: Add the Numerators
Now add the numerators (21 + 188 = 209) and keep the common denominator 987 unchanged.
Working: 21 + 188/987 = 209/987

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 987 is 1, confirming that 209/987 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/987

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 987 produces a repeating decimal (approximately 0.211753, or 21.1753%).
Working: 209 ÷ 987 = 0.211753 (21.1753%)

Key Values:
- Simplified Fraction: 209/987
- Mixed Number Form: 209/987
- Decimal Value: 0.211753
- Percentage: 21.1753%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-47-plus-4-21/
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1/47 + 4/21 = 209/987

Simplified Fraction

209/987

Mixed Number

Proper (209/987)

Decimal Value

0.211753

Percentage

21.1753%

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Step-by-Step Solution: 1/47 + 4/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 47 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 21 = 987.

LCD(47, 21) = 987

Step 2

Convert to Equivalent Fractions with Common Denominator 987

Multiply the numerator and denominator of 1/47 by 21, and multiply the numerator and denominator of 4/21 by 47 so both fractions share the common base 987.

1 × 21/47 × 21 = 21/987 and 4 × 47/21 × 47 = 188/987

Step 3

Add the Numerators

Now add the numerators (21 + 188 = 209) and keep the common denominator 987 unchanged.

21 + 188/987 = 209/987

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 987 is 1, confirming that 209/987 cannot be reduced further—it is already in its simplest irreducible form.

209/987

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 987 produces a repeating decimal (approximately 0.211753, or 21.1753%).

209 ÷ 987 = 0.211753 (21.1753%)

Visual Representation

The diagram below illustrates 1/47 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/987`
Mixed Number Form	`209/987`
Decimal Form	`0.211753`
Percentage	`21.1753%`

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Frequently Asked Questions

What is 1/47 plus 4/21 as a fraction?

1/47 + 4/21 in simplest fraction form is 209/987.

What is 1/47 plus 4/21 as a decimal?

1/47 + 4/21 converted to a decimal is 0.211753.

What is 1/47 plus 4/21 as a percentage?

1/47 + 4/21 expressed as a percentage is 21.1753%.

Does 1/47 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.211753...) because the denominator contains prime factors other than 2 and 5.