What is 4/57 plus 7/21? (Answer: 23/57)

Exact Answer

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Problem: What is 4/57 plus 7/21?
Formula / Expression: 4/57 + 7/21
Final Answer: 23/57
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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 4/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.
Working: 4 × 7/57 × 7 = 28/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (28 + 133 = 161) and keep the common denominator 399 unchanged.
Working: 28 + 133/399 = 161/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 161 and 399, which is 7. Divide both the numerator and denominator by 7.
Working: 161 ÷ 7/399 ÷ 7 = 23/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 57 produces a repeating decimal (approximately 0.403509, or 40.3509%).
Working: 23 ÷ 57 = 0.403509 (40.3509%)

Key Values:
- Simplified Fraction: 23/57
- Mixed Number Form: 23/57
- Decimal Value: 0.403509
- Percentage: 40.3509%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-57-plus-7-21/
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4/57 + 7/21 = 23/57

Simplified Fraction

23/57

Mixed Number

Proper (23/57)

Decimal Value

0.403509

Percentage

40.3509%

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Step-by-Step Solution: 4/57 + 7/21

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

4 × 7/57 × 7 = 28/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (28 + 133 = 161) and keep the common denominator 399 unchanged.

28 + 133/399 = 161/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 161 and 399, which is 7. Divide both the numerator and denominator by 7.

161 ÷ 7/399 ÷ 7 = 23/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 57 produces a repeating decimal (approximately 0.403509, or 40.3509%).

23 ÷ 57 = 0.403509 (40.3509%)

Visual Representation

The diagram below illustrates 4/57 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/57`
Mixed Number Form	`23/57`
Decimal Form	`0.403509`
Percentage	`40.3509%`

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Frequently Asked Questions

What is 4/57 plus 7/21 as a fraction?

4/57 + 7/21 in simplest fraction form is 23/57.

What is 4/57 plus 7/21 as a decimal?

4/57 + 7/21 converted to a decimal is 0.403509.

What is 4/57 plus 7/21 as a percentage?

4/57 + 7/21 expressed as a percentage is 40.3509%.

Does 4/57 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.403509...) because the denominator contains prime factors other than 2 and 5.