What is 7/57 plus 6/21? (Answer: 163/399)

Exact Answer

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Problem: What is 7/57 plus 6/21?
Formula / Expression: 7/57 + 6/21
Final Answer: 163/399
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 7/57 by 7, and multiply the numerator and denominator of 6/21 by 19 so both fractions share the common base 399.
Working: 7 × 7/57 × 7 = 49/399 and 6 × 19/21 × 19 = 114/399

Step 3: Add the Numerators
Now add the numerators (49 + 114 = 163) and keep the common denominator 399 unchanged.
Working: 49 + 114/399 = 163/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 399 is 1, confirming that 163/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 399 produces a repeating decimal (approximately 0.408521, or 40.8521%).
Working: 163 ÷ 399 = 0.408521 (40.8521%)

Key Values:
- Simplified Fraction: 163/399
- Mixed Number Form: 163/399
- Decimal Value: 0.408521
- Percentage: 40.8521%

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Solved with FractionsCalc:
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7/57 + 6/21 = 163/399

Simplified Fraction

163/399

Mixed Number

Proper (163/399)

Decimal Value

0.408521

Percentage

40.8521%

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Step-by-Step Solution: 7/57 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 7/57 by 7, and multiply the numerator and denominator of 6/21 by 19 so both fractions share the common base 399.

7 × 7/57 × 7 = 49/399 and 6 × 19/21 × 19 = 114/399

Step 3

Add the Numerators

Now add the numerators (49 + 114 = 163) and keep the common denominator 399 unchanged.

49 + 114/399 = 163/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 399 is 1, confirming that 163/399 cannot be reduced further—it is already in its simplest irreducible form.

163/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 399 produces a repeating decimal (approximately 0.408521, or 40.8521%).

163 ÷ 399 = 0.408521 (40.8521%)

Visual Representation

The diagram below illustrates 7/57 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/399`
Mixed Number Form	`163/399`
Decimal Form	`0.408521`
Percentage	`40.8521%`

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Frequently Asked Questions

What is 7/57 plus 6/21 as a fraction?

7/57 + 6/21 in simplest fraction form is 163/399.

What is 7/57 plus 6/21 as a decimal?

7/57 + 6/21 converted to a decimal is 0.408521.

What is 7/57 plus 6/21 as a percentage?

7/57 + 6/21 expressed as a percentage is 40.8521%.

Does 7/57 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.408521...) because the denominator contains prime factors other than 2 and 5.