What is 7/31 plus 10/21? (Answer: 457/651)

Exact Answer

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Problem: What is 7/31 plus 10/21?
Formula / Expression: 7/31 + 10/21
Final Answer: 457/651
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.
Working: LCD(31, 21) = 651

Step 2: Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 7/31 by 21, and multiply the numerator and denominator of 10/21 by 31 so both fractions share the common base 651.
Working: 7 × 21/31 × 21 = 147/651 and 10 × 31/21 × 31 = 310/651

Step 3: Add the Numerators
Now add the numerators (147 + 310 = 457) and keep the common denominator 651 unchanged.
Working: 147 + 310/651 = 457/651

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 457 and 651 is 1, confirming that 457/651 cannot be reduced further—it is already in its simplest irreducible form.
Working: 457/651

Step 5: Decimal & Percentage Representation
Dividing the numerator 457 by denominator 651 produces a repeating decimal (approximately 0.701997, or 70.1997%).
Working: 457 ÷ 651 = 0.701997 (70.1997%)

Key Values:
- Simplified Fraction: 457/651
- Mixed Number Form: 457/651
- Decimal Value: 0.701997
- Percentage: 70.1997%

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Solved with FractionsCalc:
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7/31 + 10/21 = 457/651

Simplified Fraction

457/651

Mixed Number

Proper (457/651)

Decimal Value

0.701997

Percentage

70.1997%

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Step-by-Step Solution: 7/31 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.

LCD(31, 21) = 651

Step 2

Convert to Equivalent Fractions with Common Denominator 651

Multiply the numerator and denominator of 7/31 by 21, and multiply the numerator and denominator of 10/21 by 31 so both fractions share the common base 651.

7 × 21/31 × 21 = 147/651 and 10 × 31/21 × 31 = 310/651

Step 3

Add the Numerators

Now add the numerators (147 + 310 = 457) and keep the common denominator 651 unchanged.

147 + 310/651 = 457/651

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 457 and 651 is 1, confirming that 457/651 cannot be reduced further—it is already in its simplest irreducible form.

457/651

Step 5

Decimal & Percentage Representation

Dividing the numerator 457 by denominator 651 produces a repeating decimal (approximately 0.701997, or 70.1997%).

457 ÷ 651 = 0.701997 (70.1997%)

Visual Representation

The diagram below illustrates 7/31 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`457/651`
Mixed Number Form	`457/651`
Decimal Form	`0.701997`
Percentage	`70.1997%`

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Frequently Asked Questions

What is 7/31 plus 10/21 as a fraction?

7/31 + 10/21 in simplest fraction form is 457/651.

What is 7/31 plus 10/21 as a decimal?

7/31 + 10/21 converted to a decimal is 0.701997.

What is 7/31 plus 10/21 as a percentage?

7/31 + 10/21 expressed as a percentage is 70.1997%.

Does 7/31 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.701997...) because the denominator contains prime factors other than 2 and 5.