What is 7/30 plus 8/21? (Answer: 43/70)

Exact Answer

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Problem: What is 7/30 plus 8/21?
Formula / Expression: 7/30 + 8/21
Final Answer: 43/70
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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 7/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.
Working: 7 × 7/30 × 7 = 49/210 and 8 × 10/21 × 10 = 80/210

Step 3: Add the Numerators
Now add the numerators (49 + 80 = 129) and keep the common denominator 210 unchanged.
Working: 49 + 80/210 = 129/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/210 ÷ 3 = 43/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 70 produces a repeating decimal (approximately 0.614286, or 61.4286%).
Working: 43 ÷ 70 = 0.614286 (61.4286%)

Key Values:
- Simplified Fraction: 43/70
- Mixed Number Form: 43/70
- Decimal Value: 0.614286
- Percentage: 61.4286%

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Solved with FractionsCalc:
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7/30 + 8/21 = 43/70

Simplified Fraction

43/70

Mixed Number

Proper (43/70)

Decimal Value

0.614286

Percentage

61.4286%

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

7 × 7/30 × 7 = 49/210 and 8 × 10/21 × 10 = 80/210

Step 3

Add the Numerators

Now add the numerators (49 + 80 = 129) and keep the common denominator 210 unchanged.

49 + 80/210 = 129/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 210, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/210 ÷ 3 = 43/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 70 produces a repeating decimal (approximately 0.614286, or 61.4286%).

43 ÷ 70 = 0.614286 (61.4286%)

Visual Representation

The diagram below illustrates 7/30 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/70`
Mixed Number Form	`43/70`
Decimal Form	`0.614286`
Percentage	`61.4286%`

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Frequently Asked Questions

What is 7/30 plus 8/21 as a fraction?

7/30 + 8/21 in simplest fraction form is 43/70.

What is 7/30 plus 8/21 as a decimal?

7/30 + 8/21 converted to a decimal is 0.614286.

What is 7/30 plus 8/21 as a percentage?

7/30 + 8/21 expressed as a percentage is 61.4286%.

Does 7/30 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.614286...) because the denominator contains prime factors other than 2 and 5.