What is 4/30 plus 7/21? (Answer: 7/15)

Exact Answer

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Problem: What is 4/30 plus 7/21?
Formula / Expression: 4/30 + 7/21
Final Answer: 7/15
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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 4/30 by 7, and multiply the numerator and denominator of 7/21 by 10 so both fractions share the common base 210.
Working: 4 × 7/30 × 7 = 28/210 and 7 × 10/21 × 10 = 70/210

Step 3: Add the Numerators
Now add the numerators (28 + 70 = 98) and keep the common denominator 210 unchanged.
Working: 28 + 70/210 = 98/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 98 and 210, which is 14. Divide both the numerator and denominator by 14.
Working: 98 ÷ 14/210 ÷ 14 = 7/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).
Working: 7 ÷ 15 = 0.466667 (46.6667%)

Key Values:
- Simplified Fraction: 7/15
- Mixed Number Form: 7/15
- Decimal Value: 0.466667
- Percentage: 46.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-30-plus-7-21/
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4/30 + 7/21 = 7/15

Simplified Fraction

7/15

Mixed Number

Proper (7/15)

Decimal Value

0.466667

Percentage

46.6667%

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Step-by-Step Solution: 4/30 + 7/21

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 4/30 by 7, and multiply the numerator and denominator of 7/21 by 10 so both fractions share the common base 210.

4 × 7/30 × 7 = 28/210 and 7 × 10/21 × 10 = 70/210

Step 3

Add the Numerators

Now add the numerators (28 + 70 = 98) and keep the common denominator 210 unchanged.

28 + 70/210 = 98/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 98 and 210, which is 14. Divide both the numerator and denominator by 14.

98 ÷ 14/210 ÷ 14 = 7/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).

7 ÷ 15 = 0.466667 (46.6667%)

Visual Representation

The diagram below illustrates 4/30 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/15`
Mixed Number Form	`7/15`
Decimal Form	`0.466667`
Percentage	`46.6667%`

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Frequently Asked Questions

What is 4/30 plus 7/21 as a fraction?

4/30 + 7/21 in simplest fraction form is 7/15.

What is 4/30 plus 7/21 as a decimal?

4/30 + 7/21 converted to a decimal is 0.466667.

What is 4/30 plus 7/21 as a percentage?

4/30 + 7/21 expressed as a percentage is 46.6667%.

Does 4/30 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.466667...) because the denominator contains prime factors other than 2 and 5.