What is 10/29 plus 2/3? (Answer: 88/87)

Exact Answer

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Problem: What is 10/29 plus 2/3?
Formula / Expression: 10/29 + 2/3
Final Answer: 1 1/87 (88/87)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 3 = 87.
Working: LCD(29, 3) = 87

Step 2: Convert to Equivalent Fractions with Common Denominator 87
Multiply the numerator and denominator of 10/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.
Working: 10 × 3/29 × 3 = 30/87 and 2 × 29/3 × 29 = 58/87

Step 3: Add the Numerators
Now add the numerators (30 + 58 = 88) and keep the common denominator 87 unchanged.
Working: 30 + 58/87 = 88/87

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 88 and 87 is 1, confirming that 88/87 cannot be reduced further—it is already in its simplest irreducible form.
Working: 88/87

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (88) is greater than the denominator (87), divide 88 by 87: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/87.
Working: 88/87 = 1 1/87

Step 6: Decimal & Percentage Representation
Dividing the numerator 88 by denominator 87 produces a repeating decimal (approximately 1.011494, or 101.1494%).
Working: 88 ÷ 87 = 1.011494 (101.1494%)

Key Values:
- Simplified Fraction: 88/87
- Mixed Number Form: 1 1/87
- Decimal Value: 1.011494
- Percentage: 101.1494%

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Solved with FractionsCalc:
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10/29 + 2/3 = 88/87

Simplified Fraction

88/87

Mixed Number

1 1/87

Decimal Value

1.011494

Percentage

101.1494%

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Step-by-Step Solution: 10/29 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 3 = 87.

LCD(29, 3) = 87

Step 2

Convert to Equivalent Fractions with Common Denominator 87

Multiply the numerator and denominator of 10/29 by 3, and multiply the numerator and denominator of 2/3 by 29 so both fractions share the common base 87.

10 × 3/29 × 3 = 30/87 and 2 × 29/3 × 29 = 58/87

Step 3

Add the Numerators

Now add the numerators (30 + 58 = 88) and keep the common denominator 87 unchanged.

30 + 58/87 = 88/87

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 88 and 87 is 1, confirming that 88/87 cannot be reduced further—it is already in its simplest irreducible form.

88/87

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (88) is greater than the denominator (87), divide 88 by 87: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/87.

88/87 = 11/87

Step 6

Decimal & Percentage Representation

Dividing the numerator 88 by denominator 87 produces a repeating decimal (approximately 1.011494, or 101.1494%).

88 ÷ 87 = 1.011494 (101.1494%)

Visual Representation

The diagram below illustrates 10/29 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`88/87`
Mixed Number Form	`1 1/87`
Decimal Form	`1.011494`
Percentage	`101.1494%`

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Frequently Asked Questions

What is 10/29 plus 2/3 as a fraction?

10/29 + 2/3 in simplest fraction form is 88/87 (or 1 1/87 as a mixed number).

What is 10/29 plus 2/3 as a decimal?

10/29 + 2/3 converted to a decimal is 1.011494.

What is 10/29 plus 2/3 as a percentage?

10/29 + 2/3 expressed as a percentage is 101.1494%.

How do you write 10/29 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 88/87 can be written as the mixed number 1 1/87.

Does 10/29 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.011494...) because the denominator contains prime factors other than 2 and 5.