What is 10/30 plus 10/21? (Answer: 17/21)

Exact Answer

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Problem: What is 10/30 plus 10/21?
Formula / Expression: 10/30 + 10/21
Final Answer: 17/21
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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 10/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.
Working: 10 × 7/30 × 7 = 70/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (70 + 100 = 170) and keep the common denominator 210 unchanged.
Working: 70 + 100/210 = 170/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 170 and 210, which is 10. Divide both the numerator and denominator by 10.
Working: 170 ÷ 10/210 ÷ 10 = 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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10/30 + 10/21 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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Step-by-Step Solution: 10/30 + 10/21

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

10 × 7/30 × 7 = 70/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (70 + 100 = 170) and keep the common denominator 210 unchanged.

70 + 100/210 = 170/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 170 and 210, which is 10. Divide both the numerator and denominator by 10.

170 ÷ 10/210 ÷ 10 = 17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 10/30 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

What is 10/30 plus 10/21 as a fraction?

10/30 + 10/21 in simplest fraction form is 17/21.

What is 10/30 plus 10/21 as a decimal?

10/30 + 10/21 converted to a decimal is 0.809524.

What is 10/30 plus 10/21 as a percentage?

10/30 + 10/21 expressed as a percentage is 80.9524%.

Does 10/30 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.