What is 10/34 plus 15/21? (Answer: 120/119)

Exact Answer

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Problem: What is 10/34 plus 15/21?
Formula / Expression: 10/34 + 15/21
Final Answer: 1 1/119 (120/119)
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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 15/21 by 34 so both fractions share the common base 714.
Working: 10 × 21/34 × 21 = 210/714 and 15 × 34/21 × 34 = 510/714

Step 3: Add the Numerators
Now add the numerators (210 + 510 = 720) and keep the common denominator 714 unchanged.
Working: 210 + 510/714 = 720/714

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 720 and 714, which is 6. Divide both the numerator and denominator by 6.
Working: 720 ÷ 6/714 ÷ 6 = 120/119

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (120) is greater than the denominator (119), divide 120 by 119: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/119.
Working: 120/119 = 1 1/119

Step 6: Decimal & Percentage Representation
Dividing the numerator 120 by denominator 119 produces a repeating decimal (approximately 1.008403, or 100.8403%).
Working: 120 ÷ 119 = 1.008403 (100.8403%)

Key Values:
- Simplified Fraction: 120/119
- Mixed Number Form: 1 1/119
- Decimal Value: 1.008403
- Percentage: 100.8403%

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10/34 + 15/21 = 120/119

Simplified Fraction

120/119

Mixed Number

1 1/119

Decimal Value

1.008403

Percentage

100.8403%

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Step-by-Step Solution: 10/34 + 15/21

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 15/21 by 34 so both fractions share the common base 714.

10 × 21/34 × 21 = 210/714 and 15 × 34/21 × 34 = 510/714

Step 3

Add the Numerators

Now add the numerators (210 + 510 = 720) and keep the common denominator 714 unchanged.

210 + 510/714 = 720/714

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 720 and 714, which is 6. Divide both the numerator and denominator by 6.

720 ÷ 6/714 ÷ 6 = 120/119

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (120) is greater than the denominator (119), divide 120 by 119: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/119.

120/119 = 11/119

Step 6

Decimal & Percentage Representation

Dividing the numerator 120 by denominator 119 produces a repeating decimal (approximately 1.008403, or 100.8403%).

120 ÷ 119 = 1.008403 (100.8403%)

Visual Representation

The diagram below illustrates 10/34 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`120/119`
Mixed Number Form	`1 1/119`
Decimal Form	`1.008403`
Percentage	`100.8403%`

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Frequently Asked Questions

What is 10/34 plus 15/21 as a fraction?

10/34 + 15/21 in simplest fraction form is 120/119 (or 1 1/119 as a mixed number).

What is 10/34 plus 15/21 as a decimal?

10/34 + 15/21 converted to a decimal is 1.008403.

What is 10/34 plus 15/21 as a percentage?

10/34 + 15/21 expressed as a percentage is 100.8403%.

How do you write 10/34 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 120/119 can be written as the mixed number 1 1/119.

Does 10/34 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.008403...) because the denominator contains prime factors other than 2 and 5.