What is 7/52 plus 9/13? (Answer: 43/52)

Exact Answer

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Problem: What is 7/52 plus 9/13?
Formula / Expression: 7/52 + 9/13
Final Answer: 43/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.
Working: LCD(52, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 7/52 by 1, and multiply the numerator and denominator of 9/13 by 4 so both fractions share the common base 52.
Working: 7 × 1/52 × 1 = 7/52 and 9 × 4/13 × 4 = 36/52

Step 3: Add the Numerators
Now add the numerators (7 + 36 = 43) and keep the common denominator 52 unchanged.
Working: 7 + 36/52 = 43/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 52 is 1, confirming that 43/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 52 produces a repeating decimal (approximately 0.826923, or 82.6923%).
Working: 43 ÷ 52 = 0.826923 (82.6923%)

Key Values:
- Simplified Fraction: 43/52
- Mixed Number Form: 43/52
- Decimal Value: 0.826923
- Percentage: 82.6923%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-52-plus-9-13/
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7/52 + 9/13 = 43/52

Simplified Fraction

43/52

Mixed Number

Proper (43/52)

Decimal Value

0.826923

Percentage

82.6923%

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Step-by-Step Solution: 7/52 + 9/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.

LCD(52, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 7/52 by 1, and multiply the numerator and denominator of 9/13 by 4 so both fractions share the common base 52.

7 × 1/52 × 1 = 7/52 and 9 × 4/13 × 4 = 36/52

Step 3

Add the Numerators

Now add the numerators (7 + 36 = 43) and keep the common denominator 52 unchanged.

7 + 36/52 = 43/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 52 is 1, confirming that 43/52 cannot be reduced further—it is already in its simplest irreducible form.

43/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 52 produces a repeating decimal (approximately 0.826923, or 82.6923%).

43 ÷ 52 = 0.826923 (82.6923%)

Visual Representation

The diagram below illustrates 7/52 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/52`
Mixed Number Form	`43/52`
Decimal Form	`0.826923`
Percentage	`82.6923%`

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Frequently Asked Questions

What is 7/52 plus 9/13 as a fraction?

7/52 + 9/13 in simplest fraction form is 43/52.

What is 7/52 plus 9/13 as a decimal?

7/52 + 9/13 converted to a decimal is 0.826923.

What is 7/52 plus 9/13 as a percentage?

7/52 + 9/13 expressed as a percentage is 82.6923%.

Does 7/52 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.826923...) because the denominator contains prime factors other than 2 and 5.