What is 4/15 plus 8/21? (Answer: 68/105)

Exact Answer

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Problem: What is 4/15 plus 8/21?
Formula / Expression: 4/15 + 8/21
Final Answer: 68/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).
Working: LCD(15, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 4/15 by 7, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.
Working: 4 × 7/15 × 7 = 28/105 and 8 × 5/21 × 5 = 40/105

Step 3: Add the Numerators
Now add the numerators (28 + 40 = 68) and keep the common denominator 105 unchanged.
Working: 28 + 40/105 = 68/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 105 is 1, confirming that 68/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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-4-15-plus-8-21/
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4/15 + 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: 4/15 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).

LCD(15, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 4/15 by 7, and multiply the numerator and denominator of 8/21 by 5 so both fractions share the common base 105.

4 × 7/15 × 7 = 28/105 and 8 × 5/21 × 5 = 40/105

Step 3

Add the Numerators

Now add the numerators (28 + 40 = 68) and keep the common denominator 105 unchanged.

28 + 40/105 = 68/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 105 is 1, confirming that 68/105 cannot be reduced further—it is already in its simplest irreducible form.

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 4/15 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 4/15 plus 8/21 as a fraction?

4/15 + 8/21 in simplest fraction form is 68/105.

What is 4/15 plus 8/21 as a decimal?

4/15 + 8/21 converted to a decimal is 0.647619.

What is 4/15 plus 8/21 as a percentage?

4/15 + 8/21 expressed as a percentage is 64.7619%.

Does 4/15 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.