What is 3/8 plus 9/15? (Answer: 39/40)

Exact Answer

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Problem: What is 3/8 plus 9/15?
Formula / Expression: 3/8 + 9/15
Final Answer: 39/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 15 = 120.
Working: LCD(8, 15) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 3/8 by 15, and multiply the numerator and denominator of 9/15 by 8 so both fractions share the common base 120.
Working: 3 × 15/8 × 15 = 45/120 and 9 × 8/15 × 8 = 72/120

Step 3: Add the Numerators
Now add the numerators (45 + 72 = 117) and keep the common denominator 120 unchanged.
Working: 45 + 72/120 = 117/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 120, which is 3. Divide both the numerator and denominator by 3.
Working: 117 ÷ 3/120 ÷ 3 = 39/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 40 yields an exact terminating decimal of 0.975 (or 97.5%).
Working: 39 ÷ 40 = 0.975 (97.5%)

Key Values:
- Simplified Fraction: 39/40
- Mixed Number Form: 39/40
- Decimal Value: 0.975
- Percentage: 97.5%

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Solved with FractionsCalc:
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3/8 + 9/15 = 39/40

Simplified Fraction

39/40

Mixed Number

Proper (39/40)

Decimal Value

0.975

Percentage

97.5%

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Step-by-Step Solution: 3/8 + 9/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 15 = 120.

LCD(8, 15) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 3/8 by 15, and multiply the numerator and denominator of 9/15 by 8 so both fractions share the common base 120.

3 × 15/8 × 15 = 45/120 and 9 × 8/15 × 8 = 72/120

Step 3

Add the Numerators

Now add the numerators (45 + 72 = 117) and keep the common denominator 120 unchanged.

45 + 72/120 = 117/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 120, which is 3. Divide both the numerator and denominator by 3.

117 ÷ 3/120 ÷ 3 = 39/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 40 yields an exact terminating decimal of 0.975 (or 97.5%).

39 ÷ 40 = 0.975 (97.5%)

Visual Representation

The diagram below illustrates 3/8 plus 9/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/40`
Mixed Number Form	`39/40`
Decimal Form	`0.975`
Percentage	`97.5%`

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Frequently Asked Questions

What is 3/8 plus 9/15 as a fraction?

3/8 + 9/15 in simplest fraction form is 39/40.

What is 3/8 plus 9/15 as a decimal?

3/8 + 9/15 converted to a decimal is 0.975.

What is 3/8 plus 9/15 as a percentage?

3/8 + 9/15 expressed as a percentage is 97.5%.

Does 3/8 plus 9/15 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.975) because the denominator in simplest terms contains only prime factors 2 and/or 5.