What is 13/51 plus 7/21? (Answer: 10/17)

Exact Answer

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Problem: What is 13/51 plus 7/21?
Formula / Expression: 13/51 + 7/21
Final Answer: 10/17
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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 13/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 13 × 7/51 × 7 = 91/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (91 + 119 = 210) and keep the common denominator 357 unchanged.
Working: 91 + 119/357 = 210/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 210 and 357, which is 21. Divide both the numerator and denominator by 21.
Working: 210 ÷ 21/357 ÷ 21 = 10/17

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 17 produces a repeating decimal (approximately 0.588235, or 58.8235%).
Working: 10 ÷ 17 = 0.588235 (58.8235%)

Key Values:
- Simplified Fraction: 10/17
- Mixed Number Form: 10/17
- Decimal Value: 0.588235
- Percentage: 58.8235%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-51-plus-7-21/
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13/51 + 7/21 = 10/17

Simplified Fraction

10/17

Mixed Number

Proper (10/17)

Decimal Value

0.588235

Percentage

58.8235%

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Step-by-Step Solution: 13/51 + 7/21

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 13/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

13 × 7/51 × 7 = 91/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (91 + 119 = 210) and keep the common denominator 357 unchanged.

91 + 119/357 = 210/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 210 and 357, which is 21. Divide both the numerator and denominator by 21.

210 ÷ 21/357 ÷ 21 = 10/17

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 17 produces a repeating decimal (approximately 0.588235, or 58.8235%).

10 ÷ 17 = 0.588235 (58.8235%)

Visual Representation

The diagram below illustrates 13/51 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/17`
Mixed Number Form	`10/17`
Decimal Form	`0.588235`
Percentage	`58.8235%`

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Frequently Asked Questions

What is 13/51 plus 7/21 as a fraction?

13/51 + 7/21 in simplest fraction form is 10/17.

What is 13/51 plus 7/21 as a decimal?

13/51 + 7/21 converted to a decimal is 0.588235.

What is 13/51 plus 7/21 as a percentage?

13/51 + 7/21 expressed as a percentage is 58.8235%.

Does 13/51 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.588235...) because the denominator contains prime factors other than 2 and 5.