What is 3/52 plus 9/13? (Answer: 3/4)

Exact Answer

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Problem: What is 3/52 plus 9/13?
Formula / Expression: 3/52 + 9/13
Final Answer: 3/4
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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 3/52 by 1, and multiply the numerator and denominator of 9/13 by 4 so both fractions share the common base 52.
Working: 3 × 1/52 × 1 = 3/52 and 9 × 4/13 × 4 = 36/52

Step 3: Add the Numerators
Now add the numerators (3 + 36 = 39) and keep the common denominator 52 unchanged.
Working: 3 + 36/52 = 39/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 52, which is 13. Divide both the numerator and denominator by 13.
Working: 39 ÷ 13/52 ÷ 13 = 3/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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Solved with FractionsCalc:
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3/52 + 9/13 = 3/4

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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Step-by-Step Solution: 3/52 + 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 3/52 by 1, and multiply the numerator and denominator of 9/13 by 4 so both fractions share the common base 52.

3 × 1/52 × 1 = 3/52 and 9 × 4/13 × 4 = 36/52

Step 3

Add the Numerators

Now add the numerators (3 + 36 = 39) and keep the common denominator 52 unchanged.

3 + 36/52 = 39/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 52, which is 13. Divide both the numerator and denominator by 13.

39 ÷ 13/52 ÷ 13 = 3/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

The diagram below illustrates 3/52 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

What is 3/52 plus 9/13 as a fraction?

3/52 + 9/13 in simplest fraction form is 3/4.

What is 3/52 plus 9/13 as a decimal?

3/52 + 9/13 converted to a decimal is 0.75.

What is 3/52 plus 9/13 as a percentage?

3/52 + 9/13 expressed as a percentage is 75%.

Does 3/52 plus 9/13 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.