What is 3/10 plus 9/21? (Answer: 51/70)

Exact Answer

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Problem: What is 3/10 plus 9/21?
Formula / Expression: 3/10 + 9/21
Final Answer: 51/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 21 = 210.
Working: LCD(10, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 3/10 by 21, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.
Working: 3 × 21/10 × 21 = 63/210 and 9 × 10/21 × 10 = 90/210

Step 3: Add the Numerators
Now add the numerators (63 + 90 = 153) and keep the common denominator 210 unchanged.
Working: 63 + 90/210 = 153/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 153 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 153 ÷ 3/210 ÷ 3 = 51/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 70 produces a repeating decimal (approximately 0.728571, or 72.8571%).
Working: 51 ÷ 70 = 0.728571 (72.8571%)

Key Values:
- Simplified Fraction: 51/70
- Mixed Number Form: 51/70
- Decimal Value: 0.728571
- Percentage: 72.8571%

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Solved with FractionsCalc:
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3/10 + 9/21 = 51/70

Simplified Fraction

51/70

Mixed Number

Proper (51/70)

Decimal Value

0.728571

Percentage

72.8571%

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Step-by-Step Solution: 3/10 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 21 = 210.

LCD(10, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 3/10 by 21, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.

3 × 21/10 × 21 = 63/210 and 9 × 10/21 × 10 = 90/210

Step 3

Add the Numerators

Now add the numerators (63 + 90 = 153) and keep the common denominator 210 unchanged.

63 + 90/210 = 153/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 153 and 210, which is 3. Divide both the numerator and denominator by 3.

153 ÷ 3/210 ÷ 3 = 51/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 70 produces a repeating decimal (approximately 0.728571, or 72.8571%).

51 ÷ 70 = 0.728571 (72.8571%)

Visual Representation

The diagram below illustrates 3/10 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/70`
Mixed Number Form	`51/70`
Decimal Form	`0.728571`
Percentage	`72.8571%`

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Frequently Asked Questions

What is 3/10 plus 9/21 as a fraction?

3/10 + 9/21 in simplest fraction form is 51/70.

What is 3/10 plus 9/21 as a decimal?

3/10 + 9/21 converted to a decimal is 0.728571.

What is 3/10 plus 9/21 as a percentage?

3/10 + 9/21 expressed as a percentage is 72.8571%.

Does 3/10 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.728571...) because the denominator contains prime factors other than 2 and 5.