What is 9/57 plus 9/21? (Answer: 78/133)

Exact Answer

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Problem: What is 9/57 plus 9/21?
Formula / Expression: 9/57 + 9/21
Final Answer: 78/133
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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 9/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 9 × 7/57 × 7 = 63/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (63 + 171 = 234) and keep the common denominator 399 unchanged.
Working: 63 + 171/399 = 234/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 234 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 234 ÷ 3/399 ÷ 3 = 78/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 78 by denominator 133 produces a repeating decimal (approximately 0.586466, or 58.6466%).
Working: 78 ÷ 133 = 0.586466 (58.6466%)

Key Values:
- Simplified Fraction: 78/133
- Mixed Number Form: 78/133
- Decimal Value: 0.586466
- Percentage: 58.6466%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-57-plus-9-21/
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9/57 + 9/21 = 78/133

Simplified Fraction

78/133

Mixed Number

Proper (78/133)

Decimal Value

0.586466

Percentage

58.6466%

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Step-by-Step Solution: 9/57 + 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 9/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

9 × 7/57 × 7 = 63/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (63 + 171 = 234) and keep the common denominator 399 unchanged.

63 + 171/399 = 234/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 234 and 399, which is 3. Divide both the numerator and denominator by 3.

234 ÷ 3/399 ÷ 3 = 78/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 78 by denominator 133 produces a repeating decimal (approximately 0.586466, or 58.6466%).

78 ÷ 133 = 0.586466 (58.6466%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`78/133`
Mixed Number Form	`78/133`
Decimal Form	`0.586466`
Percentage	`58.6466%`

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Frequently Asked Questions

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

9/57 + 9/21 in simplest fraction form is 78/133.

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

9/57 + 9/21 converted to a decimal is 0.586466.

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

9/57 + 9/21 expressed as a percentage is 58.6466%.

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

It results in a repeating decimal (approximately 0.586466...) because the denominator contains prime factors other than 2 and 5.