What is 6/57 plus 9/21? (Answer: 71/133)

Exact Answer

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Problem: What is 6/57 plus 9/21?
Formula / Expression: 6/57 + 9/21
Final Answer: 71/133
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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 6/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 6 × 7/57 × 7 = 42/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (42 + 171 = 213) and keep the common denominator 399 unchanged.
Working: 42 + 171/399 = 213/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 213 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 213 ÷ 3/399 ÷ 3 = 71/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 133 produces a repeating decimal (approximately 0.533835, or 53.3835%).
Working: 71 ÷ 133 = 0.533835 (53.3835%)

Key Values:
- Simplified Fraction: 71/133
- Mixed Number Form: 71/133
- Decimal Value: 0.533835
- Percentage: 53.3835%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-57-plus-9-21/
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6/57 + 9/21 = 71/133

Simplified Fraction

71/133

Mixed Number

Proper (71/133)

Decimal Value

0.533835

Percentage

53.3835%

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Step-by-Step Solution: 6/57 + 9/21

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 6/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

6 × 7/57 × 7 = 42/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (42 + 171 = 213) and keep the common denominator 399 unchanged.

42 + 171/399 = 213/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 213 and 399, which is 3. Divide both the numerator and denominator by 3.

213 ÷ 3/399 ÷ 3 = 71/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 133 produces a repeating decimal (approximately 0.533835, or 53.3835%).

71 ÷ 133 = 0.533835 (53.3835%)

Visual Representation

The diagram below illustrates 6/57 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/133`
Mixed Number Form	`71/133`
Decimal Form	`0.533835`
Percentage	`53.3835%`

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Frequently Asked Questions

What is 6/57 plus 9/21 as a fraction?

6/57 + 9/21 in simplest fraction form is 71/133.

What is 6/57 plus 9/21 as a decimal?

6/57 + 9/21 converted to a decimal is 0.533835.

What is 6/57 plus 9/21 as a percentage?

6/57 + 9/21 expressed as a percentage is 53.3835%.

Does 6/57 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.533835...) because the denominator contains prime factors other than 2 and 5.