What is 7/51 plus 10/21? (Answer: 73/119)

Exact Answer

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Problem: What is 7/51 plus 10/21?
Formula / Expression: 7/51 + 10/21
Final Answer: 73/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).
Working: LCD(51, 21) = 357

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 7/51 by 7, and multiply the numerator and denominator of 10/21 by 17 so both fractions share the common base 357.
Working: 7 × 7/51 × 7 = 49/357 and 10 × 17/21 × 17 = 170/357

Step 3: Add the Numerators
Now add the numerators (49 + 170 = 219) and keep the common denominator 357 unchanged.
Working: 49 + 170/357 = 219/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 219 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 219 ÷ 3/357 ÷ 3 = 73/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 119 produces a repeating decimal (approximately 0.613445, or 61.3445%).
Working: 73 ÷ 119 = 0.613445 (61.3445%)

Key Values:
- Simplified Fraction: 73/119
- Mixed Number Form: 73/119
- Decimal Value: 0.613445
- Percentage: 61.3445%

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Solved with FractionsCalc:
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7/51 + 10/21 = 73/119

Simplified Fraction

73/119

Mixed Number

Proper (73/119)

Decimal Value

0.613445

Percentage

61.3445%

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Step-by-Step Solution: 7/51 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).

LCD(51, 21) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 7/51 by 7, and multiply the numerator and denominator of 10/21 by 17 so both fractions share the common base 357.

7 × 7/51 × 7 = 49/357 and 10 × 17/21 × 17 = 170/357

Step 3

Add the Numerators

Now add the numerators (49 + 170 = 219) and keep the common denominator 357 unchanged.

49 + 170/357 = 219/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 219 and 357, which is 3. Divide both the numerator and denominator by 3.

219 ÷ 3/357 ÷ 3 = 73/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 119 produces a repeating decimal (approximately 0.613445, or 61.3445%).

73 ÷ 119 = 0.613445 (61.3445%)

Visual Representation

The diagram below illustrates 7/51 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/119`
Mixed Number Form	`73/119`
Decimal Form	`0.613445`
Percentage	`61.3445%`

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Frequently Asked Questions

What is 7/51 plus 10/21 as a fraction?

7/51 + 10/21 in simplest fraction form is 73/119.

What is 7/51 plus 10/21 as a decimal?

7/51 + 10/21 converted to a decimal is 0.613445.

What is 7/51 plus 10/21 as a percentage?

7/51 + 10/21 expressed as a percentage is 61.3445%.

Does 7/51 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.613445...) because the denominator contains prime factors other than 2 and 5.