What is 12/57 plus 7/21? (Answer: 31/57)

Exact Answer

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Problem: What is 12/57 plus 7/21?
Formula / Expression: 12/57 + 7/21
Final Answer: 31/57
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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 12/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.
Working: 12 × 7/57 × 7 = 84/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (84 + 133 = 217) and keep the common denominator 399 unchanged.
Working: 84 + 133/399 = 217/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 217 and 399, which is 7. Divide both the numerator and denominator by 7.
Working: 217 ÷ 7/399 ÷ 7 = 31/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 57 produces a repeating decimal (approximately 0.54386, or 54.386%).
Working: 31 ÷ 57 = 0.54386 (54.386%)

Key Values:
- Simplified Fraction: 31/57
- Mixed Number Form: 31/57
- Decimal Value: 0.54386
- Percentage: 54.386%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-57-plus-7-21/
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12/57 + 7/21 = 31/57

Simplified Fraction

31/57

Mixed Number

Proper (31/57)

Decimal Value

0.54386

Percentage

54.386%

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Step-by-Step Solution: 12/57 + 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 12/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.

12 × 7/57 × 7 = 84/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (84 + 133 = 217) and keep the common denominator 399 unchanged.

84 + 133/399 = 217/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 217 and 399, which is 7. Divide both the numerator and denominator by 7.

217 ÷ 7/399 ÷ 7 = 31/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 57 produces a repeating decimal (approximately 0.54386, or 54.386%).

31 ÷ 57 = 0.54386 (54.386%)

Visual Representation

The diagram below illustrates 12/57 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/57`
Mixed Number Form	`31/57`
Decimal Form	`0.54386`
Percentage	`54.386%`

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Frequently Asked Questions

What is 12/57 plus 7/21 as a fraction?

12/57 + 7/21 in simplest fraction form is 31/57.

What is 12/57 plus 7/21 as a decimal?

12/57 + 7/21 converted to a decimal is 0.54386.

What is 12/57 plus 7/21 as a percentage?

12/57 + 7/21 expressed as a percentage is 54.386%.

Does 12/57 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.54386...) because the denominator contains prime factors other than 2 and 5.