What is 10/30 plus 8/21? (Answer: 5/7)

Exact Answer

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Problem: What is 10/30 plus 8/21?
Formula / Expression: 10/30 + 8/21
Final Answer: 5/7
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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 8/21 by 10 so both fractions share the common base 210.
Working: 10 × 7/30 × 7 = 70/210 and 8 × 10/21 × 10 = 80/210

Step 3: Add the Numerators
Now add the numerators (70 + 80 = 150) and keep the common denominator 210 unchanged.
Working: 70 + 80/210 = 150/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 150 and 210, which is 30. Divide both the numerator and denominator by 30.
Working: 150 ÷ 30/210 ÷ 30 = 5/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 7 produces a repeating decimal (approximately 0.714286, or 71.4286%).
Working: 5 ÷ 7 = 0.714286 (71.4286%)

Key Values:
- Simplified Fraction: 5/7
- Mixed Number Form: 5/7
- Decimal Value: 0.714286
- Percentage: 71.4286%

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10/30 + 8/21 = 5/7

Simplified Fraction

5/7

Mixed Number

Proper (5/7)

Decimal Value

0.714286

Percentage

71.4286%

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Step-by-Step Solution: 10/30 + 8/21

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 8/21 by 10 so both fractions share the common base 210.

10 × 7/30 × 7 = 70/210 and 8 × 10/21 × 10 = 80/210

Step 3

Add the Numerators

Now add the numerators (70 + 80 = 150) and keep the common denominator 210 unchanged.

70 + 80/210 = 150/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 150 and 210, which is 30. Divide both the numerator and denominator by 30.

150 ÷ 30/210 ÷ 30 = 5/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 7 produces a repeating decimal (approximately 0.714286, or 71.4286%).

5 ÷ 7 = 0.714286 (71.4286%)

Visual Representation

The diagram below illustrates 10/30 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/7`
Mixed Number Form	`5/7`
Decimal Form	`0.714286`
Percentage	`71.4286%`

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Frequently Asked Questions

What is 10/30 plus 8/21 as a fraction?

10/30 + 8/21 in simplest fraction form is 5/7.

What is 10/30 plus 8/21 as a decimal?

10/30 + 8/21 converted to a decimal is 0.714286.

What is 10/30 plus 8/21 as a percentage?

10/30 + 8/21 expressed as a percentage is 71.4286%.

Does 10/30 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.714286...) because the denominator contains prime factors other than 2 and 5.