What is 9/35 plus 9/21? (Answer: 24/35)

Exact Answer

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Problem: What is 9/35 plus 9/21?
Formula / Expression: 9/35 + 9/21
Final Answer: 24/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 9/35 by 3, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.
Working: 9 × 3/35 × 3 = 27/105 and 9 × 5/21 × 5 = 45/105

Step 3: Add the Numerators
Now add the numerators (27 + 45 = 72) and keep the common denominator 105 unchanged.
Working: 27 + 45/105 = 72/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 72 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 72 ÷ 3/105 ÷ 3 = 24/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 24 by denominator 35 produces a repeating decimal (approximately 0.685714, or 68.5714%).
Working: 24 ÷ 35 = 0.685714 (68.5714%)

Key Values:
- Simplified Fraction: 24/35
- Mixed Number Form: 24/35
- Decimal Value: 0.685714
- Percentage: 68.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-35-plus-9-21/
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9/35 + 9/21 = 24/35

Simplified Fraction

24/35

Mixed Number

Proper (24/35)

Decimal Value

0.685714

Percentage

68.5714%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 9/35 by 3, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.

9 × 3/35 × 3 = 27/105 and 9 × 5/21 × 5 = 45/105

Step 3

Add the Numerators

Now add the numerators (27 + 45 = 72) and keep the common denominator 105 unchanged.

27 + 45/105 = 72/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 72 and 105, which is 3. Divide both the numerator and denominator by 3.

72 ÷ 3/105 ÷ 3 = 24/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 24 by denominator 35 produces a repeating decimal (approximately 0.685714, or 68.5714%).

24 ÷ 35 = 0.685714 (68.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`24/35`
Mixed Number Form	`24/35`
Decimal Form	`0.685714`
Percentage	`68.5714%`

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Frequently Asked Questions

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

9/35 + 9/21 in simplest fraction form is 24/35.

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

9/35 + 9/21 converted to a decimal is 0.685714.

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

9/35 + 9/21 expressed as a percentage is 68.5714%.

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

It results in a repeating decimal (approximately 0.685714...) because the denominator contains prime factors other than 2 and 5.