What is 7/52 plus 5/21? (Answer: 407/1092)

Exact Answer

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Problem: What is 7/52 plus 5/21?
Formula / Expression: 7/52 + 5/21
Final Answer: 407/1092
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.
Working: LCD(52, 21) = 1092

Step 2: Convert to Equivalent Fractions with Common Denominator 1092
Multiply the numerator and denominator of 7/52 by 21, and multiply the numerator and denominator of 5/21 by 52 so both fractions share the common base 1092.
Working: 7 × 21/52 × 21 = 147/1092 and 5 × 52/21 × 52 = 260/1092

Step 3: Add the Numerators
Now add the numerators (147 + 260 = 407) and keep the common denominator 1092 unchanged.
Working: 147 + 260/1092 = 407/1092

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 407 and 1092 is 1, confirming that 407/1092 cannot be reduced further—it is already in its simplest irreducible form.
Working: 407/1092

Step 5: Decimal & Percentage Representation
Dividing the numerator 407 by denominator 1092 produces a repeating decimal (approximately 0.372711, or 37.2711%).
Working: 407 ÷ 1092 = 0.372711 (37.2711%)

Key Values:
- Simplified Fraction: 407/1092
- Mixed Number Form: 407/1092
- Decimal Value: 0.372711
- Percentage: 37.2711%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-52-plus-5-21/
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7/52 + 5/21 = 407/1092

Simplified Fraction

407/1092

Mixed Number

Proper (407/1092)

Decimal Value

0.372711

Percentage

37.2711%

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Step-by-Step Solution: 7/52 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.

LCD(52, 21) = 1092

Step 2

Convert to Equivalent Fractions with Common Denominator 1092

Multiply the numerator and denominator of 7/52 by 21, and multiply the numerator and denominator of 5/21 by 52 so both fractions share the common base 1092.

7 × 21/52 × 21 = 147/1092 and 5 × 52/21 × 52 = 260/1092

Step 3

Add the Numerators

Now add the numerators (147 + 260 = 407) and keep the common denominator 1092 unchanged.

147 + 260/1092 = 407/1092

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 407 and 1092 is 1, confirming that 407/1092 cannot be reduced further—it is already in its simplest irreducible form.

407/1092

Step 5

Decimal & Percentage Representation

Dividing the numerator 407 by denominator 1092 produces a repeating decimal (approximately 0.372711, or 37.2711%).

407 ÷ 1092 = 0.372711 (37.2711%)

Visual Representation

The diagram below illustrates 7/52 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`407/1092`
Mixed Number Form	`407/1092`
Decimal Form	`0.372711`
Percentage	`37.2711%`

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Frequently Asked Questions

What is 7/52 plus 5/21 as a fraction?

7/52 + 5/21 in simplest fraction form is 407/1092.

What is 7/52 plus 5/21 as a decimal?

7/52 + 5/21 converted to a decimal is 0.372711.

What is 7/52 plus 5/21 as a percentage?

7/52 + 5/21 expressed as a percentage is 37.2711%.

Does 7/52 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.372711...) because the denominator contains prime factors other than 2 and 5.