What is 9/30 plus 7/21? (Answer: 19/30)

Exact Answer

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Problem: What is 9/30 plus 7/21?
Formula / Expression: 9/30 + 7/21
Final Answer: 19/30
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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 9/30 by 7, and multiply the numerator and denominator of 7/21 by 10 so both fractions share the common base 210.
Working: 9 × 7/30 × 7 = 63/210 and 7 × 10/21 × 10 = 70/210

Step 3: Add the Numerators
Now add the numerators (63 + 70 = 133) and keep the common denominator 210 unchanged.
Working: 63 + 70/210 = 133/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 133 and 210, which is 7. Divide both the numerator and denominator by 7.
Working: 133 ÷ 7/210 ÷ 7 = 19/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).
Working: 19 ÷ 30 = 0.633333 (63.3333%)

Key Values:
- Simplified Fraction: 19/30
- Mixed Number Form: 19/30
- Decimal Value: 0.633333
- Percentage: 63.3333%

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Solved with FractionsCalc:
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9/30 + 7/21 = 19/30

Simplified Fraction

19/30

Mixed Number

Proper (19/30)

Decimal Value

0.633333

Percentage

63.3333%

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Step-by-Step Solution: 9/30 + 7/21

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

9 × 7/30 × 7 = 63/210 and 7 × 10/21 × 10 = 70/210

Step 3

Add the Numerators

Now add the numerators (63 + 70 = 133) and keep the common denominator 210 unchanged.

63 + 70/210 = 133/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 133 and 210, which is 7. Divide both the numerator and denominator by 7.

133 ÷ 7/210 ÷ 7 = 19/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).

19 ÷ 30 = 0.633333 (63.3333%)

Visual Representation

The diagram below illustrates 9/30 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/30`
Mixed Number Form	`19/30`
Decimal Form	`0.633333`
Percentage	`63.3333%`

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Frequently Asked Questions

What is 9/30 plus 7/21 as a fraction?

9/30 + 7/21 in simplest fraction form is 19/30.

What is 9/30 plus 7/21 as a decimal?

9/30 + 7/21 converted to a decimal is 0.633333.

What is 9/30 plus 7/21 as a percentage?

9/30 + 7/21 expressed as a percentage is 63.3333%.

Does 9/30 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.633333...) because the denominator contains prime factors other than 2 and 5.