What is 10/39 plus 11/21? (Answer: 71/91)

Exact Answer

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Problem: What is 10/39 plus 11/21?
Formula / Expression: 10/39 + 11/21
Final Answer: 71/91
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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 10/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.
Working: 10 × 7/39 × 7 = 70/273 and 11 × 13/21 × 13 = 143/273

Step 3: Add the Numerators
Now add the numerators (70 + 143 = 213) and keep the common denominator 273 unchanged.
Working: 70 + 143/273 = 213/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 213 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 213 ÷ 3/273 ÷ 3 = 71/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 91 produces a repeating decimal (approximately 0.78022, or 78.022%).
Working: 71 ÷ 91 = 0.78022 (78.022%)

Key Values:
- Simplified Fraction: 71/91
- Mixed Number Form: 71/91
- Decimal Value: 0.78022
- Percentage: 78.022%

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Solved with FractionsCalc:
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10/39 + 11/21 = 71/91

Simplified Fraction

71/91

Mixed Number

Proper (71/91)

Decimal Value

0.78022

Percentage

78.022%

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Step-by-Step Solution: 10/39 + 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 10/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.

10 × 7/39 × 7 = 70/273 and 11 × 13/21 × 13 = 143/273

Step 3

Add the Numerators

Now add the numerators (70 + 143 = 213) and keep the common denominator 273 unchanged.

70 + 143/273 = 213/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 213 and 273, which is 3. Divide both the numerator and denominator by 3.

213 ÷ 3/273 ÷ 3 = 71/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 91 produces a repeating decimal (approximately 0.78022, or 78.022%).

71 ÷ 91 = 0.78022 (78.022%)

Visual Representation

The diagram below illustrates 10/39 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/91`
Mixed Number Form	`71/91`
Decimal Form	`0.78022`
Percentage	`78.022%`

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Frequently Asked Questions

What is 10/39 plus 11/21 as a fraction?

10/39 + 11/21 in simplest fraction form is 71/91.

What is 10/39 plus 11/21 as a decimal?

10/39 + 11/21 converted to a decimal is 0.78022.

What is 10/39 plus 11/21 as a percentage?

10/39 + 11/21 expressed as a percentage is 78.022%.

Does 10/39 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.78022...) because the denominator contains prime factors other than 2 and 5.