What is 5/16 plus 10/21? (Answer: 265/336)

Exact Answer

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Problem: What is 5/16 plus 10/21?
Formula / Expression: 5/16 + 10/21
Final Answer: 265/336
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 21 = 336.
Working: LCD(16, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 5/16 by 21, and multiply the numerator and denominator of 10/21 by 16 so both fractions share the common base 336.
Working: 5 × 21/16 × 21 = 105/336 and 10 × 16/21 × 16 = 160/336

Step 3: Add the Numerators
Now add the numerators (105 + 160 = 265) and keep the common denominator 336 unchanged.
Working: 105 + 160/336 = 265/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 265 and 336 is 1, confirming that 265/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 265/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 265 by denominator 336 produces a repeating decimal (approximately 0.78869, or 78.869%).
Working: 265 ÷ 336 = 0.78869 (78.869%)

Key Values:
- Simplified Fraction: 265/336
- Mixed Number Form: 265/336
- Decimal Value: 0.78869
- Percentage: 78.869%

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Solved with FractionsCalc:
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5/16 + 10/21 = 265/336

Simplified Fraction

265/336

Mixed Number

Proper (265/336)

Decimal Value

0.78869

Percentage

78.869%

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Step-by-Step Solution: 5/16 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 21 = 336.

LCD(16, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 5/16 by 21, and multiply the numerator and denominator of 10/21 by 16 so both fractions share the common base 336.

5 × 21/16 × 21 = 105/336 and 10 × 16/21 × 16 = 160/336

Step 3

Add the Numerators

Now add the numerators (105 + 160 = 265) and keep the common denominator 336 unchanged.

105 + 160/336 = 265/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 265 and 336 is 1, confirming that 265/336 cannot be reduced further—it is already in its simplest irreducible form.

265/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 265 by denominator 336 produces a repeating decimal (approximately 0.78869, or 78.869%).

265 ÷ 336 = 0.78869 (78.869%)

Visual Representation

The diagram below illustrates 5/16 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`265/336`
Mixed Number Form	`265/336`
Decimal Form	`0.78869`
Percentage	`78.869%`

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Frequently Asked Questions

What is 5/16 plus 10/21 as a fraction?

5/16 + 10/21 in simplest fraction form is 265/336.

What is 5/16 plus 10/21 as a decimal?

5/16 + 10/21 converted to a decimal is 0.78869.

What is 5/16 plus 10/21 as a percentage?

5/16 + 10/21 expressed as a percentage is 78.869%.

Does 5/16 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.78869...) because the denominator contains prime factors other than 2 and 5.