What is 4/21 plus 4/17?
4/21 plus 4/17 equals 152/357 (or 0.42577 in decimal form). Learn the step-by-step solution to add 4/21 and 4/17 using Least Common Denominator and simplification.
Exact Answer
4/21 + 4/17 = 152/357
Simplified Fraction
152/357
Mixed Number
Proper (152/357)
Decimal Value
0.42577
Percentage
42.577%
Step-by-Step Solution: 4/21 + 4/17
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 17 = 357.
LCD(21, 17) = 357
Step 2
Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 4/21 by 17, and multiply the numerator and denominator of 4/17 by 21 so both fractions share the common base 357.
4 × 17/21 × 17 = 68/357 and 4 × 21/17 × 21 = 84/357
Step 3
Add the Numerators
Now add the numerators (68 + 84 = 152) and keep the common denominator 357 unchanged.
68 + 84/357 = 152/357
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 152 and 357 is 1, confirming that 152/357 cannot be reduced further—it is already in its simplest irreducible form.
152/357
Step 5
Decimal & Percentage Representation
Dividing the numerator 152 by denominator 357 produces a repeating decimal (approximately 0.42577, or 42.577%).
152 ÷ 357 = 0.42577 (42.577%)
Visual Representation
The diagram below illustrates 4/21 plus 4/17 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 152/357 |
| Mixed Number Form | 152/357 |
| Decimal Form | 0.42577 |
| Percentage | 42.577% |
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Frequently Asked Questions
What is 4/21 plus 4/17 as a fraction?
4/21 + 4/17 in simplest fraction form is 152/357.
What is 4/21 plus 4/17 as a decimal?
4/21 + 4/17 converted to a decimal is 0.42577.
What is 4/21 plus 4/17 as a percentage?
4/21 + 4/17 expressed as a percentage is 42.577%.
Does 4/21 plus 4/17 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.42577...) because the denominator contains prime factors other than 2 and 5.