What is 7/51 plus 7/21? (Answer: 8/17)

Exact Answer

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Problem: What is 7/51 plus 7/21?
Formula / Expression: 7/51 + 7/21
Final Answer: 8/17
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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 7/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 7 × 7/51 × 7 = 49/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (49 + 119 = 168) and keep the common denominator 357 unchanged.
Working: 49 + 119/357 = 168/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 168 and 357, which is 21. Divide both the numerator and denominator by 21.
Working: 168 ÷ 21/357 ÷ 21 = 8/17

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 17 produces a repeating decimal (approximately 0.470588, or 47.0588%).
Working: 8 ÷ 17 = 0.470588 (47.0588%)

Key Values:
- Simplified Fraction: 8/17
- Mixed Number Form: 8/17
- Decimal Value: 0.470588
- Percentage: 47.0588%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-51-plus-7-21/
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7/51 + 7/21 = 8/17

Simplified Fraction

8/17

Mixed Number

Proper (8/17)

Decimal Value

0.470588

Percentage

47.0588%

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Step-by-Step Solution: 7/51 + 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 7/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

7 × 7/51 × 7 = 49/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (49 + 119 = 168) and keep the common denominator 357 unchanged.

49 + 119/357 = 168/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 168 and 357, which is 21. Divide both the numerator and denominator by 21.

168 ÷ 21/357 ÷ 21 = 8/17

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 17 produces a repeating decimal (approximately 0.470588, or 47.0588%).

8 ÷ 17 = 0.470588 (47.0588%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/17`
Mixed Number Form	`8/17`
Decimal Form	`0.470588`
Percentage	`47.0588%`

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Frequently Asked Questions

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

7/51 + 7/21 in simplest fraction form is 8/17.

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

7/51 + 7/21 converted to a decimal is 0.470588.

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

7/51 + 7/21 expressed as a percentage is 47.0588%.

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

It results in a repeating decimal (approximately 0.470588...) because the denominator contains prime factors other than 2 and 5.