What is 16/52 plus 8/21? (Answer: 188/273)

Exact Answer

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Problem: What is 16/52 plus 8/21?
Formula / Expression: 16/52 + 8/21
Final Answer: 188/273
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.
Working: LCD(52, 21) = 1092

Step 2: Convert to Equivalent Fractions with Common Denominator 1092
Multiply the numerator and denominator of 16/52 by 21, and multiply the numerator and denominator of 8/21 by 52 so both fractions share the common base 1092.
Working: 16 × 21/52 × 21 = 336/1092 and 8 × 52/21 × 52 = 416/1092

Step 3: Add the Numerators
Now add the numerators (336 + 416 = 752) and keep the common denominator 1092 unchanged.
Working: 336 + 416/1092 = 752/1092

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 752 and 1092, which is 4. Divide both the numerator and denominator by 4.
Working: 752 ÷ 4/1092 ÷ 4 = 188/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 188 by denominator 273 produces a repeating decimal (approximately 0.688645, or 68.8645%).
Working: 188 ÷ 273 = 0.688645 (68.8645%)

Key Values:
- Simplified Fraction: 188/273
- Mixed Number Form: 188/273
- Decimal Value: 0.688645
- Percentage: 68.8645%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-52-plus-8-21/
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16/52 + 8/21 = 188/273

Simplified Fraction

188/273

Mixed Number

Proper (188/273)

Decimal Value

0.688645

Percentage

68.8645%

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Step-by-Step Solution: 16/52 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.

LCD(52, 21) = 1092

Step 2

Convert to Equivalent Fractions with Common Denominator 1092

Multiply the numerator and denominator of 16/52 by 21, and multiply the numerator and denominator of 8/21 by 52 so both fractions share the common base 1092.

16 × 21/52 × 21 = 336/1092 and 8 × 52/21 × 52 = 416/1092

Step 3

Add the Numerators

Now add the numerators (336 + 416 = 752) and keep the common denominator 1092 unchanged.

336 + 416/1092 = 752/1092

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 752 and 1092, which is 4. Divide both the numerator and denominator by 4.

752 ÷ 4/1092 ÷ 4 = 188/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 188 by denominator 273 produces a repeating decimal (approximately 0.688645, or 68.8645%).

188 ÷ 273 = 0.688645 (68.8645%)

Visual Representation

The diagram below illustrates 16/52 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`188/273`
Mixed Number Form	`188/273`
Decimal Form	`0.688645`
Percentage	`68.8645%`

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Frequently Asked Questions

What is 16/52 plus 8/21 as a fraction?

16/52 + 8/21 in simplest fraction form is 188/273.

What is 16/52 plus 8/21 as a decimal?

16/52 + 8/21 converted to a decimal is 0.688645.

What is 16/52 plus 8/21 as a percentage?

16/52 + 8/21 expressed as a percentage is 68.8645%.

Does 16/52 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.688645...) because the denominator contains prime factors other than 2 and 5.