What is 5/57 plus 4/21? (Answer: 37/133)

Exact Answer

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Problem: What is 5/57 plus 4/21?
Formula / Expression: 5/57 + 4/21
Final Answer: 37/133
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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 5/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.
Working: 5 × 7/57 × 7 = 35/399 and 4 × 19/21 × 19 = 76/399

Step 3: Add the Numerators
Now add the numerators (35 + 76 = 111) and keep the common denominator 399 unchanged.
Working: 35 + 76/399 = 111/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/399 ÷ 3 = 37/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 133 produces a repeating decimal (approximately 0.278195, or 27.8195%).
Working: 37 ÷ 133 = 0.278195 (27.8195%)

Key Values:
- Simplified Fraction: 37/133
- Mixed Number Form: 37/133
- Decimal Value: 0.278195
- Percentage: 27.8195%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-57-plus-4-21/
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5/57 + 4/21 = 37/133

Simplified Fraction

37/133

Mixed Number

Proper (37/133)

Decimal Value

0.278195

Percentage

27.8195%

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Step-by-Step Solution: 5/57 + 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 5/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.

5 × 7/57 × 7 = 35/399 and 4 × 19/21 × 19 = 76/399

Step 3

Add the Numerators

Now add the numerators (35 + 76 = 111) and keep the common denominator 399 unchanged.

35 + 76/399 = 111/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 399, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/399 ÷ 3 = 37/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 133 produces a repeating decimal (approximately 0.278195, or 27.8195%).

37 ÷ 133 = 0.278195 (27.8195%)

Visual Representation

The diagram below illustrates 5/57 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/133`
Mixed Number Form	`37/133`
Decimal Form	`0.278195`
Percentage	`27.8195%`

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Frequently Asked Questions

What is 5/57 plus 4/21 as a fraction?

5/57 + 4/21 in simplest fraction form is 37/133.

What is 5/57 plus 4/21 as a decimal?

5/57 + 4/21 converted to a decimal is 0.278195.

What is 5/57 plus 4/21 as a percentage?

5/57 + 4/21 expressed as a percentage is 27.8195%.

Does 5/57 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.278195...) because the denominator contains prime factors other than 2 and 5.