What is 4/21 plus 11/57? (Answer: 51/133)

Exact Answer

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Problem: What is 4/21 plus 11/57?
Formula / Expression: 4/21 + 11/57
Final Answer: 51/133
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 4/21 by 19, and multiply the numerator and denominator of 11/57 by 7 so both fractions share the common base 399.
Working: 4 × 19/21 × 19 = 76/399 and 11 × 7/57 × 7 = 77/399

Step 3: Add the Numerators
Now add the numerators (76 + 77 = 153) and keep the common denominator 399 unchanged.
Working: 76 + 77/399 = 153/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 153 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 153 ÷ 3/399 ÷ 3 = 51/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 133 produces a repeating decimal (approximately 0.383459, or 38.3459%).
Working: 51 ÷ 133 = 0.383459 (38.3459%)

Key Values:
- Simplified Fraction: 51/133
- Mixed Number Form: 51/133
- Decimal Value: 0.383459
- Percentage: 38.3459%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-11-57/
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4/21 + 11/57 = 51/133

Simplified Fraction

51/133

Mixed Number

Proper (51/133)

Decimal Value

0.383459

Percentage

38.3459%

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Step-by-Step Solution: 4/21 + 11/57

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 57) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 4/21 by 19, and multiply the numerator and denominator of 11/57 by 7 so both fractions share the common base 399.

4 × 19/21 × 19 = 76/399 and 11 × 7/57 × 7 = 77/399

Step 3

Add the Numerators

Now add the numerators (76 + 77 = 153) and keep the common denominator 399 unchanged.

76 + 77/399 = 153/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 153 and 399, which is 3. Divide both the numerator and denominator by 3.

153 ÷ 3/399 ÷ 3 = 51/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 133 produces a repeating decimal (approximately 0.383459, or 38.3459%).

51 ÷ 133 = 0.383459 (38.3459%)

Visual Representation

The diagram below illustrates 4/21 plus 11/57 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/133`
Mixed Number Form	`51/133`
Decimal Form	`0.383459`
Percentage	`38.3459%`

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Frequently Asked Questions

What is 4/21 plus 11/57 as a fraction?

4/21 + 11/57 in simplest fraction form is 51/133.

What is 4/21 plus 11/57 as a decimal?

4/21 + 11/57 converted to a decimal is 0.383459.

What is 4/21 plus 11/57 as a percentage?

4/21 + 11/57 expressed as a percentage is 38.3459%.

Does 4/21 plus 11/57 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.383459...) because the denominator contains prime factors other than 2 and 5.