What is 4/21 plus 10/51? (Answer: 46/119)

Exact Answer

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Problem: What is 4/21 plus 10/51?
Formula / Expression: 4/21 + 10/51
Final Answer: 46/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 51 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 21 × 51 = 1071, keeping the calculation simpler).
Working: LCD(21, 51) = 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 10/51 by 7 so both fractions share the common base 357.
Working: 4 × 17/21 × 17 = 68/357 and 10 × 7/51 × 7 = 70/357

Step 3: Add the Numerators
Now add the numerators (68 + 70 = 138) and keep the common denominator 357 unchanged.
Working: 68 + 70/357 = 138/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 138 ÷ 3/357 ÷ 3 = 46/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 119 produces a repeating decimal (approximately 0.386555, or 38.6555%).
Working: 46 ÷ 119 = 0.386555 (38.6555%)

Key Values:
- Simplified Fraction: 46/119
- Mixed Number Form: 46/119
- Decimal Value: 0.386555
- Percentage: 38.6555%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-10-51/
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4/21 + 10/51 = 46/119

Simplified Fraction

46/119

Mixed Number

Proper (46/119)

Decimal Value

0.386555

Percentage

38.6555%

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Step-by-Step Solution: 4/21 + 10/51

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 51 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 21 × 51 = 1071, keeping the calculation simpler).

LCD(21, 51) = 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 10/51 by 7 so both fractions share the common base 357.

4 × 17/21 × 17 = 68/357 and 10 × 7/51 × 7 = 70/357

Step 3

Add the Numerators

Now add the numerators (68 + 70 = 138) and keep the common denominator 357 unchanged.

68 + 70/357 = 138/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 357, which is 3. Divide both the numerator and denominator by 3.

138 ÷ 3/357 ÷ 3 = 46/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 119 produces a repeating decimal (approximately 0.386555, or 38.6555%).

46 ÷ 119 = 0.386555 (38.6555%)

Visual Representation

The diagram below illustrates 4/21 plus 10/51 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/119`
Mixed Number Form	`46/119`
Decimal Form	`0.386555`
Percentage	`38.6555%`

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Frequently Asked Questions

What is 4/21 plus 10/51 as a fraction?

4/21 + 10/51 in simplest fraction form is 46/119.

What is 4/21 plus 10/51 as a decimal?

4/21 + 10/51 converted to a decimal is 0.386555.

What is 4/21 plus 10/51 as a percentage?

4/21 + 10/51 expressed as a percentage is 38.6555%.

Does 4/21 plus 10/51 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.386555...) because the denominator contains prime factors other than 2 and 5.