What is 10/39 plus 10/21? (Answer: 200/273)

Exact Answer

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Problem: What is 10/39 plus 10/21?
Formula / Expression: 10/39 + 10/21
Final Answer: 200/273
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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 10/21 by 13 so both fractions share the common base 273.
Working: 10 × 7/39 × 7 = 70/273 and 10 × 13/21 × 13 = 130/273

Step 3: Add the Numerators
Now add the numerators (70 + 130 = 200) and keep the common denominator 273 unchanged.
Working: 70 + 130/273 = 200/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 200 and 273 is 1, confirming that 200/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 200/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 200 by denominator 273 produces a repeating decimal (approximately 0.732601, or 73.2601%).
Working: 200 ÷ 273 = 0.732601 (73.2601%)

Key Values:
- Simplified Fraction: 200/273
- Mixed Number Form: 200/273
- Decimal Value: 0.732601
- Percentage: 73.2601%

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10/39 + 10/21 = 200/273

Simplified Fraction

200/273

Mixed Number

Proper (200/273)

Decimal Value

0.732601

Percentage

73.2601%

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Step-by-Step Solution: 10/39 + 10/21

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 10/21 by 13 so both fractions share the common base 273.

10 × 7/39 × 7 = 70/273 and 10 × 13/21 × 13 = 130/273

Step 3

Add the Numerators

Now add the numerators (70 + 130 = 200) and keep the common denominator 273 unchanged.

70 + 130/273 = 200/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 200 and 273 is 1, confirming that 200/273 cannot be reduced further—it is already in its simplest irreducible form.

200/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 200 by denominator 273 produces a repeating decimal (approximately 0.732601, or 73.2601%).

200 ÷ 273 = 0.732601 (73.2601%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`200/273`
Mixed Number Form	`200/273`
Decimal Form	`0.732601`
Percentage	`73.2601%`

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Frequently Asked Questions

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

10/39 + 10/21 in simplest fraction form is 200/273.

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

10/39 + 10/21 converted to a decimal is 0.732601.

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

10/39 + 10/21 expressed as a percentage is 73.2601%.

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

It results in a repeating decimal (approximately 0.732601...) because the denominator contains prime factors other than 2 and 5.