What is 6/30 plus 9/21? (Answer: 22/35)

Exact Answer

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Problem: What is 6/30 plus 9/21?
Formula / Expression: 6/30 + 9/21
Final Answer: 22/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 6/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.
Working: 6 × 7/30 × 7 = 42/210 and 9 × 10/21 × 10 = 90/210

Step 3: Add the Numerators
Now add the numerators (42 + 90 = 132) and keep the common denominator 210 unchanged.
Working: 42 + 90/210 = 132/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 132 and 210, which is 6. Divide both the numerator and denominator by 6.
Working: 132 ÷ 6/210 ÷ 6 = 22/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 35 produces a repeating decimal (approximately 0.628571, or 62.8571%).
Working: 22 ÷ 35 = 0.628571 (62.8571%)

Key Values:
- Simplified Fraction: 22/35
- Mixed Number Form: 22/35
- Decimal Value: 0.628571
- Percentage: 62.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-30-plus-9-21/
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6/30 + 9/21 = 22/35

Simplified Fraction

22/35

Mixed Number

Proper (22/35)

Decimal Value

0.628571

Percentage

62.8571%

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Step-by-Step Solution: 6/30 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 6/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.

6 × 7/30 × 7 = 42/210 and 9 × 10/21 × 10 = 90/210

Step 3

Add the Numerators

Now add the numerators (42 + 90 = 132) and keep the common denominator 210 unchanged.

42 + 90/210 = 132/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 132 and 210, which is 6. Divide both the numerator and denominator by 6.

132 ÷ 6/210 ÷ 6 = 22/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 35 produces a repeating decimal (approximately 0.628571, or 62.8571%).

22 ÷ 35 = 0.628571 (62.8571%)

Visual Representation

The diagram below illustrates 6/30 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/35`
Mixed Number Form	`22/35`
Decimal Form	`0.628571`
Percentage	`62.8571%`

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Frequently Asked Questions

What is 6/30 plus 9/21 as a fraction?

6/30 + 9/21 in simplest fraction form is 22/35.

What is 6/30 plus 9/21 as a decimal?

6/30 + 9/21 converted to a decimal is 0.628571.

What is 6/30 plus 9/21 as a percentage?

6/30 + 9/21 expressed as a percentage is 62.8571%.

Does 6/30 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.628571...) because the denominator contains prime factors other than 2 and 5.