What is 16/62 plus 9/21? (Answer: 149/217)

Exact Answer

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Problem: What is 16/62 plus 9/21?
Formula / Expression: 16/62 + 9/21
Final Answer: 149/217
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 62 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 62 × 21 = 1302.
Working: LCD(62, 21) = 1302

Step 2: Convert to Equivalent Fractions with Common Denominator 1302
Multiply the numerator and denominator of 16/62 by 21, and multiply the numerator and denominator of 9/21 by 62 so both fractions share the common base 1302.
Working: 16 × 21/62 × 21 = 336/1302 and 9 × 62/21 × 62 = 558/1302

Step 3: Add the Numerators
Now add the numerators (336 + 558 = 894) and keep the common denominator 1302 unchanged.
Working: 336 + 558/1302 = 894/1302

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 894 and 1302, which is 6. Divide both the numerator and denominator by 6.
Working: 894 ÷ 6/1302 ÷ 6 = 149/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 217 produces a repeating decimal (approximately 0.686636, or 68.6636%).
Working: 149 ÷ 217 = 0.686636 (68.6636%)

Key Values:
- Simplified Fraction: 149/217
- Mixed Number Form: 149/217
- Decimal Value: 0.686636
- Percentage: 68.6636%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-62-plus-9-21/
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16/62 + 9/21 = 149/217

Simplified Fraction

149/217

Mixed Number

Proper (149/217)

Decimal Value

0.686636

Percentage

68.6636%

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Step-by-Step Solution: 16/62 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 62 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 62 × 21 = 1302.

LCD(62, 21) = 1302

Step 2

Convert to Equivalent Fractions with Common Denominator 1302

Multiply the numerator and denominator of 16/62 by 21, and multiply the numerator and denominator of 9/21 by 62 so both fractions share the common base 1302.

16 × 21/62 × 21 = 336/1302 and 9 × 62/21 × 62 = 558/1302

Step 3

Add the Numerators

Now add the numerators (336 + 558 = 894) and keep the common denominator 1302 unchanged.

336 + 558/1302 = 894/1302

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 894 and 1302, which is 6. Divide both the numerator and denominator by 6.

894 ÷ 6/1302 ÷ 6 = 149/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 217 produces a repeating decimal (approximately 0.686636, or 68.6636%).

149 ÷ 217 = 0.686636 (68.6636%)

Visual Representation

The diagram below illustrates 16/62 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/217`
Mixed Number Form	`149/217`
Decimal Form	`0.686636`
Percentage	`68.6636%`

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Frequently Asked Questions

What is 16/62 plus 9/21 as a fraction?

16/62 + 9/21 in simplest fraction form is 149/217.

What is 16/62 plus 9/21 as a decimal?

16/62 + 9/21 converted to a decimal is 0.686636.

What is 16/62 plus 9/21 as a percentage?

16/62 + 9/21 expressed as a percentage is 68.6636%.

Does 16/62 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.686636...) because the denominator contains prime factors other than 2 and 5.