What is 2/5 plus 10/21? (Answer: 92/105)

Exact Answer

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Problem: What is 2/5 plus 10/21?
Formula / Expression: 2/5 + 10/21
Final Answer: 92/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.
Working: LCD(5, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/5 by 21, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.
Working: 2 × 21/5 × 21 = 42/105 and 10 × 5/21 × 5 = 50/105

Step 3: Add the Numerators
Now add the numerators (42 + 50 = 92) and keep the common denominator 105 unchanged.
Working: 42 + 50/105 = 92/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 92 and 105 is 1, confirming that 92/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 92/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 92 by denominator 105 produces a repeating decimal (approximately 0.87619, or 87.619%).
Working: 92 ÷ 105 = 0.87619 (87.619%)

Key Values:
- Simplified Fraction: 92/105
- Mixed Number Form: 92/105
- Decimal Value: 0.87619
- Percentage: 87.619%

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2/5 + 10/21 = 92/105

Simplified Fraction

92/105

Mixed Number

Proper (92/105)

Decimal Value

0.87619

Percentage

87.619%

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Step-by-Step Solution: 2/5 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.

LCD(5, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/5 by 21, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.

2 × 21/5 × 21 = 42/105 and 10 × 5/21 × 5 = 50/105

Step 3

Add the Numerators

Now add the numerators (42 + 50 = 92) and keep the common denominator 105 unchanged.

42 + 50/105 = 92/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 92 and 105 is 1, confirming that 92/105 cannot be reduced further—it is already in its simplest irreducible form.

92/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 92 by denominator 105 produces a repeating decimal (approximately 0.87619, or 87.619%).

92 ÷ 105 = 0.87619 (87.619%)

Visual Representation

The diagram below illustrates 2/5 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`92/105`
Mixed Number Form	`92/105`
Decimal Form	`0.87619`
Percentage	`87.619%`

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Frequently Asked Questions

What is 2/5 plus 10/21 as a fraction?

2/5 + 10/21 in simplest fraction form is 92/105.

What is 2/5 plus 10/21 as a decimal?

2/5 + 10/21 converted to a decimal is 0.87619.

What is 2/5 plus 10/21 as a percentage?

2/5 + 10/21 expressed as a percentage is 87.619%.

Does 2/5 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.87619...) because the denominator contains prime factors other than 2 and 5.