What is 7/57 plus 7/21? (Answer: 26/57)

Exact Answer

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Problem: What is 7/57 plus 7/21?
Formula / Expression: 7/57 + 7/21
Final Answer: 26/57
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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 7/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.
Working: 7 × 7/57 × 7 = 49/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (49 + 133 = 182) and keep the common denominator 399 unchanged.
Working: 49 + 133/399 = 182/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 182 and 399, which is 7. Divide both the numerator and denominator by 7.
Working: 182 ÷ 7/399 ÷ 7 = 26/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 57 produces a repeating decimal (approximately 0.45614, or 45.614%).
Working: 26 ÷ 57 = 0.45614 (45.614%)

Key Values:
- Simplified Fraction: 26/57
- Mixed Number Form: 26/57
- Decimal Value: 0.45614
- Percentage: 45.614%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-57-plus-7-21/
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7/57 + 7/21 = 26/57

Simplified Fraction

26/57

Mixed Number

Proper (26/57)

Decimal Value

0.45614

Percentage

45.614%

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

7 × 7/57 × 7 = 49/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (49 + 133 = 182) and keep the common denominator 399 unchanged.

49 + 133/399 = 182/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 182 and 399, which is 7. Divide both the numerator and denominator by 7.

182 ÷ 7/399 ÷ 7 = 26/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 57 produces a repeating decimal (approximately 0.45614, or 45.614%).

26 ÷ 57 = 0.45614 (45.614%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/57`
Mixed Number Form	`26/57`
Decimal Form	`0.45614`
Percentage	`45.614%`

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Frequently Asked Questions

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

7/57 + 7/21 in simplest fraction form is 26/57.

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

7/57 + 7/21 converted to a decimal is 0.45614.

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

7/57 + 7/21 expressed as a percentage is 45.614%.

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

It results in a repeating decimal (approximately 0.45614...) because the denominator contains prime factors other than 2 and 5.