What is 9/21 plus 15/35? (Answer: 6/7)

Exact Answer

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Problem: What is 9/21 plus 15/35?
Formula / Expression: 9/21 + 15/35
Final Answer: 6/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).
Working: LCD(21, 35) = 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 15/35 by 3 so both fractions share the common base 105.
Working: 9 × 5/21 × 5 = 45/105 and 15 × 3/35 × 3 = 45/105

Step 3: Add the Numerators
Now add the numerators (45 + 45 = 90) and keep the common denominator 105 unchanged.
Working: 45 + 45/105 = 90/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 105, which is 15. Divide both the numerator and denominator by 15.
Working: 90 ÷ 15/105 ÷ 15 = 6/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).
Working: 6 ÷ 7 = 0.857143 (85.7143%)

Key Values:
- Simplified Fraction: 6/7
- Mixed Number Form: 6/7
- Decimal Value: 0.857143
- Percentage: 85.7143%

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Solved with FractionsCalc:
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9/21 + 15/35 = 6/7

Simplified Fraction

6/7

Mixed Number

Proper (6/7)

Decimal Value

0.857143

Percentage

85.7143%

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Step-by-Step Solution: 9/21 + 15/35

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).

LCD(21, 35) = 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 15/35 by 3 so both fractions share the common base 105.

9 × 5/21 × 5 = 45/105 and 15 × 3/35 × 3 = 45/105

Step 3

Add the Numerators

Now add the numerators (45 + 45 = 90) and keep the common denominator 105 unchanged.

45 + 45/105 = 90/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 105, which is 15. Divide both the numerator and denominator by 15.

90 ÷ 15/105 ÷ 15 = 6/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).

6 ÷ 7 = 0.857143 (85.7143%)

Visual Representation

The diagram below illustrates 9/21 plus 15/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/7`
Mixed Number Form	`6/7`
Decimal Form	`0.857143`
Percentage	`85.7143%`

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Frequently Asked Questions

What is 9/21 plus 15/35 as a fraction?

9/21 + 15/35 in simplest fraction form is 6/7.

What is 9/21 plus 15/35 as a decimal?

9/21 + 15/35 converted to a decimal is 0.857143.

What is 9/21 plus 15/35 as a percentage?

9/21 + 15/35 expressed as a percentage is 85.7143%.

Does 9/21 plus 15/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857143...) because the denominator contains prime factors other than 2 and 5.