What is 8/30 plus 8/21? (Answer: 68/105)

Exact Answer

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Problem: What is 8/30 plus 8/21?
Formula / Expression: 8/30 + 8/21
Final Answer: 68/105
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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 8/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.
Working: 8 × 7/30 × 7 = 56/210 and 8 × 10/21 × 10 = 80/210

Step 3: Add the Numerators
Now add the numerators (56 + 80 = 136) and keep the common denominator 210 unchanged.
Working: 56 + 80/210 = 136/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 136 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 136 ÷ 2/210 ÷ 2 = 68/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 105 produces a repeating decimal (approximately 0.647619, or 64.7619%).
Working: 68 ÷ 105 = 0.647619 (64.7619%)

Key Values:
- Simplified Fraction: 68/105
- Mixed Number Form: 68/105
- Decimal Value: 0.647619
- Percentage: 64.7619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-30-plus-8-21/
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8/30 + 8/21 = 68/105

Simplified Fraction

68/105

Mixed Number

Proper (68/105)

Decimal Value

0.647619

Percentage

64.7619%

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Step-by-Step Solution: 8/30 + 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 8/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.

8 × 7/30 × 7 = 56/210 and 8 × 10/21 × 10 = 80/210

Step 3

Add the Numerators

Now add the numerators (56 + 80 = 136) and keep the common denominator 210 unchanged.

56 + 80/210 = 136/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 136 and 210, which is 2. Divide both the numerator and denominator by 2.

136 ÷ 2/210 ÷ 2 = 68/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 105 produces a repeating decimal (approximately 0.647619, or 64.7619%).

68 ÷ 105 = 0.647619 (64.7619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/105`
Mixed Number Form	`68/105`
Decimal Form	`0.647619`
Percentage	`64.7619%`

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Frequently Asked Questions

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

8/30 + 8/21 in simplest fraction form is 68/105.

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

8/30 + 8/21 converted to a decimal is 0.647619.

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

8/30 + 8/21 expressed as a percentage is 64.7619%.

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

It results in a repeating decimal (approximately 0.647619...) because the denominator contains prime factors other than 2 and 5.