What is 3/35 plus 8/21? (Answer: 7/15)

Exact Answer

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Problem: What is 3/35 plus 8/21?
Formula / Expression: 3/35 + 8/21
Final Answer: 7/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 3/35 by 3, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.
Working: 3 × 3/35 × 3 = 9/105 and 8 × 5/21 × 5 = 40/105

Step 3: Add the Numerators
Now add the numerators (9 + 40 = 49) and keep the common denominator 105 unchanged.
Working: 9 + 40/105 = 49/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 49 and 105, which is 7. Divide both the numerator and denominator by 7.
Working: 49 ÷ 7/105 ÷ 7 = 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-3-35-plus-8-21/
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3/35 + 8/21 = 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: 3/35 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 3/35 by 3, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.

3 × 3/35 × 3 = 9/105 and 8 × 5/21 × 5 = 40/105

Step 3

Add the Numerators

Now add the numerators (9 + 40 = 49) and keep the common denominator 105 unchanged.

9 + 40/105 = 49/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 49 and 105, which is 7. Divide both the numerator and denominator by 7.

49 ÷ 7/105 ÷ 7 = 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 3/35 plus 8/21 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 3/35 plus 8/21 as a fraction?

3/35 + 8/21 in simplest fraction form is 7/15.

What is 3/35 plus 8/21 as a decimal?

3/35 + 8/21 converted to a decimal is 0.466667.

What is 3/35 plus 8/21 as a percentage?

3/35 + 8/21 expressed as a percentage is 46.6667%.

Does 3/35 plus 8/21 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.