What is 9/15 plus 5/8? (Answer: 49/40)

Exact Answer

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Problem: What is 9/15 plus 5/8?
Formula / Expression: 9/15 + 5/8
Final Answer: 1 9/40 (49/40)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 9/15 by 8, and multiply the numerator and denominator of 5/8 by 15 so both fractions share the common base 120.
Working: 9 × 8/15 × 8 = 72/120 and 5 × 15/8 × 15 = 75/120

Step 3: Add the Numerators
Now add the numerators (72 + 75 = 147) and keep the common denominator 120 unchanged.
Working: 72 + 75/120 = 147/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 120, which is 3. Divide both the numerator and denominator by 3.
Working: 147 ÷ 3/120 ÷ 3 = 49/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (49) is greater than the denominator (40), divide 49 by 40: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/40.
Working: 49/40 = 1 9/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 40 yields an exact terminating decimal of 1.225 (or 122.5%).
Working: 49 ÷ 40 = 1.225 (122.5%)

Key Values:
- Simplified Fraction: 49/40
- Mixed Number Form: 1 9/40
- Decimal Value: 1.225
- Percentage: 122.5%

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9/15 + 5/8 = 49/40

Simplified Fraction

49/40

Mixed Number

1 9/40

Decimal Value

1.225

Percentage

122.5%

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Step-by-Step Solution: 9/15 + 5/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(15, 8) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 9/15 by 8, and multiply the numerator and denominator of 5/8 by 15 so both fractions share the common base 120.

9 × 8/15 × 8 = 72/120 and 5 × 15/8 × 15 = 75/120

Step 3

Add the Numerators

Now add the numerators (72 + 75 = 147) and keep the common denominator 120 unchanged.

72 + 75/120 = 147/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 120, which is 3. Divide both the numerator and denominator by 3.

147 ÷ 3/120 ÷ 3 = 49/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (49) is greater than the denominator (40), divide 49 by 40: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/40.

49/40 = 19/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 40 yields an exact terminating decimal of 1.225 (or 122.5%).

49 ÷ 40 = 1.225 (122.5%)

Visual Representation

The diagram below illustrates 9/15 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/40`
Mixed Number Form	`1 9/40`
Decimal Form	`1.225`
Percentage	`122.5%`

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Frequently Asked Questions

What is 9/15 plus 5/8 as a fraction?

9/15 + 5/8 in simplest fraction form is 49/40 (or 1 9/40 as a mixed number).

What is 9/15 plus 5/8 as a decimal?

9/15 + 5/8 converted to a decimal is 1.225.

What is 9/15 plus 5/8 as a percentage?

9/15 + 5/8 expressed as a percentage is 122.5%.

How do you write 9/15 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 49/40 can be written as the mixed number 1 9/40.

Does 9/15 plus 5/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.225) because the denominator in simplest terms contains only prime factors 2 and/or 5.