What is 9/21 plus 16/37? (Answer: 223/259)

Exact Answer

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Problem: What is 9/21 plus 16/37?
Formula / Expression: 9/21 + 16/37
Final Answer: 223/259
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 37 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 37 = 777.
Working: LCD(21, 37) = 777

Step 2: Convert to Equivalent Fractions with Common Denominator 777
Multiply the numerator and denominator of 9/21 by 37, and multiply the numerator and denominator of 16/37 by 21 so both fractions share the common base 777.
Working: 9 × 37/21 × 37 = 333/777 and 16 × 21/37 × 21 = 336/777

Step 3: Add the Numerators
Now add the numerators (333 + 336 = 669) and keep the common denominator 777 unchanged.
Working: 333 + 336/777 = 669/777

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 669 and 777, which is 3. Divide both the numerator and denominator by 3.
Working: 669 ÷ 3/777 ÷ 3 = 223/259

Step 5: Decimal & Percentage Representation
Dividing the numerator 223 by denominator 259 produces a repeating decimal (approximately 0.861004, or 86.1004%).
Working: 223 ÷ 259 = 0.861004 (86.1004%)

Key Values:
- Simplified Fraction: 223/259
- Mixed Number Form: 223/259
- Decimal Value: 0.861004
- Percentage: 86.1004%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-16-37/
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9/21 + 16/37 = 223/259

Simplified Fraction

223/259

Mixed Number

Proper (223/259)

Decimal Value

0.861004

Percentage

86.1004%

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Step-by-Step Solution: 9/21 + 16/37

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 37 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 37 = 777.

LCD(21, 37) = 777

Step 2

Convert to Equivalent Fractions with Common Denominator 777

Multiply the numerator and denominator of 9/21 by 37, and multiply the numerator and denominator of 16/37 by 21 so both fractions share the common base 777.

9 × 37/21 × 37 = 333/777 and 16 × 21/37 × 21 = 336/777

Step 3

Add the Numerators

Now add the numerators (333 + 336 = 669) and keep the common denominator 777 unchanged.

333 + 336/777 = 669/777

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 669 and 777, which is 3. Divide both the numerator and denominator by 3.

669 ÷ 3/777 ÷ 3 = 223/259

Step 5

Decimal & Percentage Representation

Dividing the numerator 223 by denominator 259 produces a repeating decimal (approximately 0.861004, or 86.1004%).

223 ÷ 259 = 0.861004 (86.1004%)

Visual Representation

The diagram below illustrates 9/21 plus 16/37 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`223/259`
Mixed Number Form	`223/259`
Decimal Form	`0.861004`
Percentage	`86.1004%`

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Frequently Asked Questions

What is 9/21 plus 16/37 as a fraction?

9/21 + 16/37 in simplest fraction form is 223/259.

What is 9/21 plus 16/37 as a decimal?

9/21 + 16/37 converted to a decimal is 0.861004.

What is 9/21 plus 16/37 as a percentage?

9/21 + 16/37 expressed as a percentage is 86.1004%.

Does 9/21 plus 16/37 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.861004...) because the denominator contains prime factors other than 2 and 5.