What is 16/39 plus 11/21? (Answer: 85/91)

Exact Answer

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Problem: What is 16/39 plus 11/21?
Formula / Expression: 16/39 + 11/21
Final Answer: 85/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 16/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.
Working: 16 × 7/39 × 7 = 112/273 and 11 × 13/21 × 13 = 143/273

Step 3: Add the Numerators
Now add the numerators (112 + 143 = 255) and keep the common denominator 273 unchanged.
Working: 112 + 143/273 = 255/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 255 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 255 ÷ 3/273 ÷ 3 = 85/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 91 produces a repeating decimal (approximately 0.934066, or 93.4066%).
Working: 85 ÷ 91 = 0.934066 (93.4066%)

Key Values:
- Simplified Fraction: 85/91
- Mixed Number Form: 85/91
- Decimal Value: 0.934066
- Percentage: 93.4066%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-39-plus-11-21/
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16/39 + 11/21 = 85/91

Simplified Fraction

85/91

Mixed Number

Proper (85/91)

Decimal Value

0.934066

Percentage

93.4066%

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Step-by-Step Solution: 16/39 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 16/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.

16 × 7/39 × 7 = 112/273 and 11 × 13/21 × 13 = 143/273

Step 3

Add the Numerators

Now add the numerators (112 + 143 = 255) and keep the common denominator 273 unchanged.

112 + 143/273 = 255/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 255 and 273, which is 3. Divide both the numerator and denominator by 3.

255 ÷ 3/273 ÷ 3 = 85/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 91 produces a repeating decimal (approximately 0.934066, or 93.4066%).

85 ÷ 91 = 0.934066 (93.4066%)

Visual Representation

The diagram below illustrates 16/39 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/91`
Mixed Number Form	`85/91`
Decimal Form	`0.934066`
Percentage	`93.4066%`

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Frequently Asked Questions

What is 16/39 plus 11/21 as a fraction?

16/39 + 11/21 in simplest fraction form is 85/91.

What is 16/39 plus 11/21 as a decimal?

16/39 + 11/21 converted to a decimal is 0.934066.

What is 16/39 plus 11/21 as a percentage?

16/39 + 11/21 expressed as a percentage is 93.4066%.

Does 16/39 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.934066...) because the denominator contains prime factors other than 2 and 5.