What is 10/57 plus 4/21? (Answer: 146/399)

Exact Answer

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Problem: What is 10/57 plus 4/21?
Formula / Expression: 10/57 + 4/21
Final Answer: 146/399
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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 10/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.
Working: 10 × 7/57 × 7 = 70/399 and 4 × 19/21 × 19 = 76/399

Step 3: Add the Numerators
Now add the numerators (70 + 76 = 146) and keep the common denominator 399 unchanged.
Working: 70 + 76/399 = 146/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 146 and 399 is 1, confirming that 146/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 146/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 399 produces a repeating decimal (approximately 0.365915, or 36.5915%).
Working: 146 ÷ 399 = 0.365915 (36.5915%)

Key Values:
- Simplified Fraction: 146/399
- Mixed Number Form: 146/399
- Decimal Value: 0.365915
- Percentage: 36.5915%

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Solved with FractionsCalc:
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10/57 + 4/21 = 146/399

Simplified Fraction

146/399

Mixed Number

Proper (146/399)

Decimal Value

0.365915

Percentage

36.5915%

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Step-by-Step Solution: 10/57 + 4/21

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 10/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.

10 × 7/57 × 7 = 70/399 and 4 × 19/21 × 19 = 76/399

Step 3

Add the Numerators

Now add the numerators (70 + 76 = 146) and keep the common denominator 399 unchanged.

70 + 76/399 = 146/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 146 and 399 is 1, confirming that 146/399 cannot be reduced further—it is already in its simplest irreducible form.

146/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 399 produces a repeating decimal (approximately 0.365915, or 36.5915%).

146 ÷ 399 = 0.365915 (36.5915%)

Visual Representation

The diagram below illustrates 10/57 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/399`
Mixed Number Form	`146/399`
Decimal Form	`0.365915`
Percentage	`36.5915%`

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Frequently Asked Questions

What is 10/57 plus 4/21 as a fraction?

10/57 + 4/21 in simplest fraction form is 146/399.

What is 10/57 plus 4/21 as a decimal?

10/57 + 4/21 converted to a decimal is 0.365915.

What is 10/57 plus 4/21 as a percentage?

10/57 + 4/21 expressed as a percentage is 36.5915%.

Does 10/57 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.365915...) because the denominator contains prime factors other than 2 and 5.