What is 9/21 plus 7/15? (Answer: 94/105)

Exact Answer

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Problem: What is 9/21 plus 7/15?
Formula / Expression: 9/21 + 7/15
Final Answer: 94/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 15 = 315, keeping the calculation simpler).
Working: LCD(21, 15) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 9/21 by 5, and multiply the numerator and denominator of 7/15 by 7 so both fractions share the common base 105.
Working: 9 × 5/21 × 5 = 45/105 and 7 × 7/15 × 7 = 49/105

Step 3: Add the Numerators
Now add the numerators (45 + 49 = 94) and keep the common denominator 105 unchanged.
Working: 45 + 49/105 = 94/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 94 and 105 is 1, confirming that 94/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 94/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 94 by denominator 105 produces a repeating decimal (approximately 0.895238, or 89.5238%).
Working: 94 ÷ 105 = 0.895238 (89.5238%)

Key Values:
- Simplified Fraction: 94/105
- Mixed Number Form: 94/105
- Decimal Value: 0.895238
- Percentage: 89.5238%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-7-15/
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9/21 + 7/15 = 94/105

Simplified Fraction

94/105

Mixed Number

Proper (94/105)

Decimal Value

0.895238

Percentage

89.5238%

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Step-by-Step Solution: 9/21 + 7/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 15 = 315, keeping the calculation simpler).

LCD(21, 15) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 9/21 by 5, and multiply the numerator and denominator of 7/15 by 7 so both fractions share the common base 105.

9 × 5/21 × 5 = 45/105 and 7 × 7/15 × 7 = 49/105

Step 3

Add the Numerators

Now add the numerators (45 + 49 = 94) and keep the common denominator 105 unchanged.

45 + 49/105 = 94/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 94 and 105 is 1, confirming that 94/105 cannot be reduced further—it is already in its simplest irreducible form.

94/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 94 by denominator 105 produces a repeating decimal (approximately 0.895238, or 89.5238%).

94 ÷ 105 = 0.895238 (89.5238%)

Visual Representation

The diagram below illustrates 9/21 plus 7/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`94/105`
Mixed Number Form	`94/105`
Decimal Form	`0.895238`
Percentage	`89.5238%`

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Frequently Asked Questions

What is 9/21 plus 7/15 as a fraction?

9/21 + 7/15 in simplest fraction form is 94/105.

What is 9/21 plus 7/15 as a decimal?

9/21 + 7/15 converted to a decimal is 0.895238.

What is 9/21 plus 7/15 as a percentage?

9/21 + 7/15 expressed as a percentage is 89.5238%.

Does 9/21 plus 7/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.895238...) because the denominator contains prime factors other than 2 and 5.