What is 16/57 plus 7/21? (Answer: 35/57)

Exact Answer

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Problem: What is 16/57 plus 7/21?
Formula / Expression: 16/57 + 7/21
Final Answer: 35/57
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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 16/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.
Working: 16 × 7/57 × 7 = 112/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (112 + 133 = 245) and keep the common denominator 399 unchanged.
Working: 112 + 133/399 = 245/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 245 and 399, which is 7. Divide both the numerator and denominator by 7.
Working: 245 ÷ 7/399 ÷ 7 = 35/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 57 produces a repeating decimal (approximately 0.614035, or 61.4035%).
Working: 35 ÷ 57 = 0.614035 (61.4035%)

Key Values:
- Simplified Fraction: 35/57
- Mixed Number Form: 35/57
- Decimal Value: 0.614035
- Percentage: 61.4035%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-57-plus-7-21/
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16/57 + 7/21 = 35/57

Simplified Fraction

35/57

Mixed Number

Proper (35/57)

Decimal Value

0.614035

Percentage

61.4035%

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Step-by-Step Solution: 16/57 + 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 16/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.

16 × 7/57 × 7 = 112/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (112 + 133 = 245) and keep the common denominator 399 unchanged.

112 + 133/399 = 245/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 245 and 399, which is 7. Divide both the numerator and denominator by 7.

245 ÷ 7/399 ÷ 7 = 35/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 57 produces a repeating decimal (approximately 0.614035, or 61.4035%).

35 ÷ 57 = 0.614035 (61.4035%)

Visual Representation

The diagram below illustrates 16/57 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/57`
Mixed Number Form	`35/57`
Decimal Form	`0.614035`
Percentage	`61.4035%`

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Frequently Asked Questions

What is 16/57 plus 7/21 as a fraction?

16/57 + 7/21 in simplest fraction form is 35/57.

What is 16/57 plus 7/21 as a decimal?

16/57 + 7/21 converted to a decimal is 0.614035.

What is 16/57 plus 7/21 as a percentage?

16/57 + 7/21 expressed as a percentage is 61.4035%.

Does 16/57 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.614035...) because the denominator contains prime factors other than 2 and 5.