What is 3/10 plus 3/7? (Answer: 51/70)

Exact Answer

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Problem: What is 3/10 plus 3/7?
Formula / Expression: 3/10 + 3/7
Final Answer: 51/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.
Working: LCD(10, 7) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 3/10 by 7, and multiply the numerator and denominator of 3/7 by 10 so both fractions share the common base 70.
Working: 3 × 7/10 × 7 = 21/70 and 3 × 10/7 × 10 = 30/70

Step 3: Add the Numerators
Now add the numerators (21 + 30 = 51) and keep the common denominator 70 unchanged.
Working: 21 + 30/70 = 51/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 51 and 70 is 1, confirming that 51/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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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3/10 + 3/7 = 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 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.

LCD(10, 7) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 3/10 by 7, and multiply the numerator and denominator of 3/7 by 10 so both fractions share the common base 70.

3 × 7/10 × 7 = 21/70 and 3 × 10/7 × 10 = 30/70

Step 3

Add the Numerators

Now add the numerators (21 + 30 = 51) and keep the common denominator 70 unchanged.

21 + 30/70 = 51/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 51 and 70 is 1, confirming that 51/70 cannot be reduced further—it is already in its simplest irreducible form.

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 3/7 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 3/7 as a fraction?

3/10 + 3/7 in simplest fraction form is 51/70.

What is 3/10 plus 3/7 as a decimal?

3/10 + 3/7 converted to a decimal is 0.728571.

What is 3/10 plus 3/7 as a percentage?

3/10 + 3/7 expressed as a percentage is 72.8571%.

Does 3/10 plus 3/7 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.