What is 10/34 plus 9/21? (Answer: 86/119)

Exact Answer

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Problem: What is 10/34 plus 9/21?
Formula / Expression: 10/34 + 9/21
Final Answer: 86/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 21 = 714.
Working: LCD(34, 21) = 714

Step 2: Convert to Equivalent Fractions with Common Denominator 714
Multiply the numerator and denominator of 10/34 by 21, and multiply the numerator and denominator of 9/21 by 34 so both fractions share the common base 714.
Working: 10 × 21/34 × 21 = 210/714 and 9 × 34/21 × 34 = 306/714

Step 3: Add the Numerators
Now add the numerators (210 + 306 = 516) and keep the common denominator 714 unchanged.
Working: 210 + 306/714 = 516/714

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 516 and 714, which is 6. Divide both the numerator and denominator by 6.
Working: 516 ÷ 6/714 ÷ 6 = 86/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 119 produces a repeating decimal (approximately 0.722689, or 72.2689%).
Working: 86 ÷ 119 = 0.722689 (72.2689%)

Key Values:
- Simplified Fraction: 86/119
- Mixed Number Form: 86/119
- Decimal Value: 0.722689
- Percentage: 72.2689%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-34-plus-9-21/
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10/34 + 9/21 = 86/119

Simplified Fraction

86/119

Mixed Number

Proper (86/119)

Decimal Value

0.722689

Percentage

72.2689%

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Step-by-Step Solution: 10/34 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 21 = 714.

LCD(34, 21) = 714

Step 2

Convert to Equivalent Fractions with Common Denominator 714

Multiply the numerator and denominator of 10/34 by 21, and multiply the numerator and denominator of 9/21 by 34 so both fractions share the common base 714.

10 × 21/34 × 21 = 210/714 and 9 × 34/21 × 34 = 306/714

Step 3

Add the Numerators

Now add the numerators (210 + 306 = 516) and keep the common denominator 714 unchanged.

210 + 306/714 = 516/714

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 516 and 714, which is 6. Divide both the numerator and denominator by 6.

516 ÷ 6/714 ÷ 6 = 86/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 119 produces a repeating decimal (approximately 0.722689, or 72.2689%).

86 ÷ 119 = 0.722689 (72.2689%)

Visual Representation

The diagram below illustrates 10/34 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/119`
Mixed Number Form	`86/119`
Decimal Form	`0.722689`
Percentage	`72.2689%`

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Frequently Asked Questions

What is 10/34 plus 9/21 as a fraction?

10/34 + 9/21 in simplest fraction form is 86/119.

What is 10/34 plus 9/21 as a decimal?

10/34 + 9/21 converted to a decimal is 0.722689.

What is 10/34 plus 9/21 as a percentage?

10/34 + 9/21 expressed as a percentage is 72.2689%.

Does 10/34 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.722689...) because the denominator contains prime factors other than 2 and 5.