What is 4/10 plus 10/21? (Answer: 92/105)

Exact Answer

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Problem: What is 4/10 plus 10/21?
Formula / Expression: 4/10 + 10/21
Final Answer: 92/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 21 = 210.
Working: LCD(10, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 4/10 by 21, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.
Working: 4 × 21/10 × 21 = 84/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (84 + 100 = 184) and keep the common denominator 210 unchanged.
Working: 84 + 100/210 = 184/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 184 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 184 ÷ 2/210 ÷ 2 = 92/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 92 by denominator 105 produces a repeating decimal (approximately 0.87619, or 87.619%).
Working: 92 ÷ 105 = 0.87619 (87.619%)

Key Values:
- Simplified Fraction: 92/105
- Mixed Number Form: 92/105
- Decimal Value: 0.87619
- Percentage: 87.619%

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4/10 + 10/21 = 92/105

Simplified Fraction

92/105

Mixed Number

Proper (92/105)

Decimal Value

0.87619

Percentage

87.619%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 21 = 210.

LCD(10, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 4/10 by 21, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.

4 × 21/10 × 21 = 84/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (84 + 100 = 184) and keep the common denominator 210 unchanged.

84 + 100/210 = 184/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 184 and 210, which is 2. Divide both the numerator and denominator by 2.

184 ÷ 2/210 ÷ 2 = 92/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 92 by denominator 105 produces a repeating decimal (approximately 0.87619, or 87.619%).

92 ÷ 105 = 0.87619 (87.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`92/105`
Mixed Number Form	`92/105`
Decimal Form	`0.87619`
Percentage	`87.619%`

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Frequently Asked Questions

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

4/10 + 10/21 in simplest fraction form is 92/105.

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

4/10 + 10/21 converted to a decimal is 0.87619.

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

4/10 + 10/21 expressed as a percentage is 87.619%.

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

It results in a repeating decimal (approximately 0.87619...) because the denominator contains prime factors other than 2 and 5.