What is 3/5 plus 9/15? (Answer: 6/5)

Exact Answer

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Problem: What is 3/5 plus 9/15?
Formula / Expression: 3/5 + 9/15
Final Answer: 1 1/5 (6/5)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 15 is an exact multiple of 5 (5 × 3 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.
Working: LCD(5, 15) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 3/5 by 3, and multiply the numerator and denominator of 9/15 by 1 so both fractions share the common base 15.
Working: 3 × 3/5 × 3 = 9/15 and 9 × 1/15 × 1 = 9/15

Step 3: Add the Numerators
Now add the numerators (9 + 9 = 18) and keep the common denominator 15 unchanged.
Working: 9 + 9/15 = 18/15

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 15, which is 3. Divide both the numerator and denominator by 3.
Working: 18 ÷ 3/15 ÷ 3 = 6/5

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (6) is greater than the denominator (5), divide 6 by 5: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/5.
Working: 6/5 = 1 1/5

Step 6: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 5 yields an exact terminating decimal of 1.2 (or 120%).
Working: 6 ÷ 5 = 1.2 (120%)

Key Values:
- Simplified Fraction: 6/5
- Mixed Number Form: 1 1/5
- Decimal Value: 1.2
- Percentage: 120%

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3/5 + 9/15 = 6/5

Simplified Fraction

6/5

Mixed Number

1 1/5

Decimal Value

1.2

Percentage

120%

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Step-by-Step Solution: 3/5 + 9/15

Step 1

Find the Least Common Denominator (LCD)

Notice that 15 is an exact multiple of 5 (5 × 3 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.

LCD(5, 15) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 3/5 by 3, and multiply the numerator and denominator of 9/15 by 1 so both fractions share the common base 15.

3 × 3/5 × 3 = 9/15 and 9 × 1/15 × 1 = 9/15

Step 3

Add the Numerators

Now add the numerators (9 + 9 = 18) and keep the common denominator 15 unchanged.

9 + 9/15 = 18/15

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 15, which is 3. Divide both the numerator and denominator by 3.

18 ÷ 3/15 ÷ 3 = 6/5

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (6) is greater than the denominator (5), divide 6 by 5: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/5.

6/5 = 11/5

Step 6

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 5 yields an exact terminating decimal of 1.2 (or 120%).

6 ÷ 5 = 1.2 (120%)

Visual Representation

The diagram below illustrates 3/5 plus 9/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/5`
Mixed Number Form	`1 1/5`
Decimal Form	`1.2`
Percentage	`120%`

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Frequently Asked Questions

What is 3/5 plus 9/15 as a fraction?

3/5 + 9/15 in simplest fraction form is 6/5 (or 1 1/5 as a mixed number).

What is 3/5 plus 9/15 as a decimal?

3/5 + 9/15 converted to a decimal is 1.2.

What is 3/5 plus 9/15 as a percentage?

3/5 + 9/15 expressed as a percentage is 120%.

How do you write 3/5 plus 9/15 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 6/5 can be written as the mixed number 1 1/5.

Does 3/5 plus 9/15 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.2) because the denominator in simplest terms contains only prime factors 2 and/or 5.