What is 3/40 plus 5/21? (Answer: 263/840)

Exact Answer

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Problem: What is 3/40 plus 5/21?
Formula / Expression: 3/40 + 5/21
Final Answer: 263/840
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.
Working: LCD(40, 21) = 840

Step 2: Convert to Equivalent Fractions with Common Denominator 840
Multiply the numerator and denominator of 3/40 by 21, and multiply the numerator and denominator of 5/21 by 40 so both fractions share the common base 840.
Working: 3 × 21/40 × 21 = 63/840 and 5 × 40/21 × 40 = 200/840

Step 3: Add the Numerators
Now add the numerators (63 + 200 = 263) and keep the common denominator 840 unchanged.
Working: 63 + 200/840 = 263/840

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 263 and 840 is 1, confirming that 263/840 cannot be reduced further—it is already in its simplest irreducible form.
Working: 263/840

Step 5: Decimal & Percentage Representation
Dividing the numerator 263 by denominator 840 produces a repeating decimal (approximately 0.313095, or 31.3095%).
Working: 263 ÷ 840 = 0.313095 (31.3095%)

Key Values:
- Simplified Fraction: 263/840
- Mixed Number Form: 263/840
- Decimal Value: 0.313095
- Percentage: 31.3095%

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Solved with FractionsCalc:
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3/40 + 5/21 = 263/840

Simplified Fraction

263/840

Mixed Number

Proper (263/840)

Decimal Value

0.313095

Percentage

31.3095%

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Step-by-Step Solution: 3/40 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.

LCD(40, 21) = 840

Step 2

Convert to Equivalent Fractions with Common Denominator 840

Multiply the numerator and denominator of 3/40 by 21, and multiply the numerator and denominator of 5/21 by 40 so both fractions share the common base 840.

3 × 21/40 × 21 = 63/840 and 5 × 40/21 × 40 = 200/840

Step 3

Add the Numerators

Now add the numerators (63 + 200 = 263) and keep the common denominator 840 unchanged.

63 + 200/840 = 263/840

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 263 and 840 is 1, confirming that 263/840 cannot be reduced further—it is already in its simplest irreducible form.

263/840

Step 5

Decimal & Percentage Representation

Dividing the numerator 263 by denominator 840 produces a repeating decimal (approximately 0.313095, or 31.3095%).

263 ÷ 840 = 0.313095 (31.3095%)

Visual Representation

The diagram below illustrates 3/40 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`263/840`
Mixed Number Form	`263/840`
Decimal Form	`0.313095`
Percentage	`31.3095%`

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Frequently Asked Questions

What is 3/40 plus 5/21 as a fraction?

3/40 + 5/21 in simplest fraction form is 263/840.

What is 3/40 plus 5/21 as a decimal?

3/40 + 5/21 converted to a decimal is 0.313095.

What is 3/40 plus 5/21 as a percentage?

3/40 + 5/21 expressed as a percentage is 31.3095%.

Does 3/40 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.313095...) because the denominator contains prime factors other than 2 and 5.