What is 9/45 plus 15/21? (Answer: 32/35)

Exact Answer

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Problem: What is 9/45 plus 15/21?
Formula / Expression: 9/45 + 15/21
Final Answer: 32/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 9/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.
Working: 9 × 7/45 × 7 = 63/315 and 15 × 15/21 × 15 = 225/315

Step 3: Add the Numerators
Now add the numerators (63 + 225 = 288) and keep the common denominator 315 unchanged.
Working: 63 + 225/315 = 288/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 288 and 315, which is 9. Divide both the numerator and denominator by 9.
Working: 288 ÷ 9/315 ÷ 9 = 32/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 35 produces a repeating decimal (approximately 0.914286, or 91.4286%).
Working: 32 ÷ 35 = 0.914286 (91.4286%)

Key Values:
- Simplified Fraction: 32/35
- Mixed Number Form: 32/35
- Decimal Value: 0.914286
- Percentage: 91.4286%

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Solved with FractionsCalc:
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9/45 + 15/21 = 32/35

Simplified Fraction

32/35

Mixed Number

Proper (32/35)

Decimal Value

0.914286

Percentage

91.4286%

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Step-by-Step Solution: 9/45 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 9/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.

9 × 7/45 × 7 = 63/315 and 15 × 15/21 × 15 = 225/315

Step 3

Add the Numerators

Now add the numerators (63 + 225 = 288) and keep the common denominator 315 unchanged.

63 + 225/315 = 288/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 288 and 315, which is 9. Divide both the numerator and denominator by 9.

288 ÷ 9/315 ÷ 9 = 32/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 35 produces a repeating decimal (approximately 0.914286, or 91.4286%).

32 ÷ 35 = 0.914286 (91.4286%)

Visual Representation

The diagram below illustrates 9/45 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/35`
Mixed Number Form	`32/35`
Decimal Form	`0.914286`
Percentage	`91.4286%`

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Frequently Asked Questions

What is 9/45 plus 15/21 as a fraction?

9/45 + 15/21 in simplest fraction form is 32/35.

What is 9/45 plus 15/21 as a decimal?

9/45 + 15/21 converted to a decimal is 0.914286.

What is 9/45 plus 15/21 as a percentage?

9/45 + 15/21 expressed as a percentage is 91.4286%.

Does 9/45 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.914286...) because the denominator contains prime factors other than 2 and 5.