What is 3/30 plus 9/21? (Answer: 37/70)

Exact Answer

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Problem: What is 3/30 plus 9/21?
Formula / Expression: 3/30 + 9/21
Final Answer: 37/70
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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 3/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.
Working: 3 × 7/30 × 7 = 21/210 and 9 × 10/21 × 10 = 90/210

Step 3: Add the Numerators
Now add the numerators (21 + 90 = 111) and keep the common denominator 210 unchanged.
Working: 21 + 90/210 = 111/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/210 ÷ 3 = 37/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 70 produces a repeating decimal (approximately 0.528571, or 52.8571%).
Working: 37 ÷ 70 = 0.528571 (52.8571%)

Key Values:
- Simplified Fraction: 37/70
- Mixed Number Form: 37/70
- Decimal Value: 0.528571
- Percentage: 52.8571%

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Solved with FractionsCalc:
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3/30 + 9/21 = 37/70

Simplified Fraction

37/70

Mixed Number

Proper (37/70)

Decimal Value

0.528571

Percentage

52.8571%

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Step-by-Step Solution: 3/30 + 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 3/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.

3 × 7/30 × 7 = 21/210 and 9 × 10/21 × 10 = 90/210

Step 3

Add the Numerators

Now add the numerators (21 + 90 = 111) and keep the common denominator 210 unchanged.

21 + 90/210 = 111/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 210, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/210 ÷ 3 = 37/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 70 produces a repeating decimal (approximately 0.528571, or 52.8571%).

37 ÷ 70 = 0.528571 (52.8571%)

Visual Representation

The diagram below illustrates 3/30 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/70`
Mixed Number Form	`37/70`
Decimal Form	`0.528571`
Percentage	`52.8571%`

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Frequently Asked Questions

What is 3/30 plus 9/21 as a fraction?

3/30 + 9/21 in simplest fraction form is 37/70.

What is 3/30 plus 9/21 as a decimal?

3/30 + 9/21 converted to a decimal is 0.528571.

What is 3/30 plus 9/21 as a percentage?

3/30 + 9/21 expressed as a percentage is 52.8571%.

Does 3/30 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.528571...) because the denominator contains prime factors other than 2 and 5.