What is 9/35 plus 12/21? (Answer: 29/35)

Exact Answer

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Problem: What is 9/35 plus 12/21?
Formula / Expression: 9/35 + 12/21
Final Answer: 29/35
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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 12/21 by 5 so both fractions share the common base 105.
Working: 9 × 3/35 × 3 = 27/105 and 12 × 5/21 × 5 = 60/105

Step 3: Add the Numerators
Now add the numerators (27 + 60 = 87) and keep the common denominator 105 unchanged.
Working: 27 + 60/105 = 87/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 87 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 87 ÷ 3/105 ÷ 3 = 29/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).
Working: 29 ÷ 35 = 0.828571 (82.8571%)

Key Values:
- Simplified Fraction: 29/35
- Mixed Number Form: 29/35
- Decimal Value: 0.828571
- Percentage: 82.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-35-plus-12-21/
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9/35 + 12/21 = 29/35

Simplified Fraction

29/35

Mixed Number

Proper (29/35)

Decimal Value

0.828571

Percentage

82.8571%

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Step-by-Step Solution: 9/35 + 12/21

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 12/21 by 5 so both fractions share the common base 105.

9 × 3/35 × 3 = 27/105 and 12 × 5/21 × 5 = 60/105

Step 3

Add the Numerators

Now add the numerators (27 + 60 = 87) and keep the common denominator 105 unchanged.

27 + 60/105 = 87/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 87 and 105, which is 3. Divide both the numerator and denominator by 3.

87 ÷ 3/105 ÷ 3 = 29/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).

29 ÷ 35 = 0.828571 (82.8571%)

Visual Representation

The diagram below illustrates 9/35 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/35`
Mixed Number Form	`29/35`
Decimal Form	`0.828571`
Percentage	`82.8571%`

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Frequently Asked Questions

What is 9/35 plus 12/21 as a fraction?

9/35 + 12/21 in simplest fraction form is 29/35.

What is 9/35 plus 12/21 as a decimal?

9/35 + 12/21 converted to a decimal is 0.828571.

What is 9/35 plus 12/21 as a percentage?

9/35 + 12/21 expressed as a percentage is 82.8571%.

Does 9/35 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.828571...) because the denominator contains prime factors other than 2 and 5.