What is 7/30 plus 5/21? (Answer: 33/70)

Exact Answer

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Problem: What is 7/30 plus 5/21?
Formula / Expression: 7/30 + 5/21
Final Answer: 33/70
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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 5/21 by 10 so both fractions share the common base 210.
Working: 7 × 7/30 × 7 = 49/210 and 5 × 10/21 × 10 = 50/210

Step 3: Add the Numerators
Now add the numerators (49 + 50 = 99) and keep the common denominator 210 unchanged.
Working: 49 + 50/210 = 99/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 99 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 99 ÷ 3/210 ÷ 3 = 33/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 70 produces a repeating decimal (approximately 0.471429, or 47.1429%).
Working: 33 ÷ 70 = 0.471429 (47.1429%)

Key Values:
- Simplified Fraction: 33/70
- Mixed Number Form: 33/70
- Decimal Value: 0.471429
- Percentage: 47.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-30-plus-5-21/
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7/30 + 5/21 = 33/70

Simplified Fraction

33/70

Mixed Number

Proper (33/70)

Decimal Value

0.471429

Percentage

47.1429%

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Step-by-Step Solution: 7/30 + 5/21

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 5/21 by 10 so both fractions share the common base 210.

7 × 7/30 × 7 = 49/210 and 5 × 10/21 × 10 = 50/210

Step 3

Add the Numerators

Now add the numerators (49 + 50 = 99) and keep the common denominator 210 unchanged.

49 + 50/210 = 99/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 99 and 210, which is 3. Divide both the numerator and denominator by 3.

99 ÷ 3/210 ÷ 3 = 33/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 70 produces a repeating decimal (approximately 0.471429, or 47.1429%).

33 ÷ 70 = 0.471429 (47.1429%)

Visual Representation

The diagram below illustrates 7/30 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/70`
Mixed Number Form	`33/70`
Decimal Form	`0.471429`
Percentage	`47.1429%`

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Frequently Asked Questions

What is 7/30 plus 5/21 as a fraction?

7/30 + 5/21 in simplest fraction form is 33/70.

What is 7/30 plus 5/21 as a decimal?

7/30 + 5/21 converted to a decimal is 0.471429.

What is 7/30 plus 5/21 as a percentage?

7/30 + 5/21 expressed as a percentage is 47.1429%.

Does 7/30 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.471429...) because the denominator contains prime factors other than 2 and 5.