What is 4/40 plus 8/21? (Answer: 101/210)

Exact Answer

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Problem: What is 4/40 plus 8/21?
Formula / Expression: 4/40 + 8/21
Final Answer: 101/210
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.
Working: LCD(40, 21) = 840

Step 2: Convert to Equivalent Fractions with Common Denominator 840
Multiply the numerator and denominator of 4/40 by 21, and multiply the numerator and denominator of 8/21 by 40 so both fractions share the common base 840.
Working: 4 × 21/40 × 21 = 84/840 and 8 × 40/21 × 40 = 320/840

Step 3: Add the Numerators
Now add the numerators (84 + 320 = 404) and keep the common denominator 840 unchanged.
Working: 84 + 320/840 = 404/840

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 404 and 840, which is 4. Divide both the numerator and denominator by 4.
Working: 404 ÷ 4/840 ÷ 4 = 101/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 210 produces a repeating decimal (approximately 0.480952, or 48.0952%).
Working: 101 ÷ 210 = 0.480952 (48.0952%)

Key Values:
- Simplified Fraction: 101/210
- Mixed Number Form: 101/210
- Decimal Value: 0.480952
- Percentage: 48.0952%

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Solved with FractionsCalc:
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4/40 + 8/21 = 101/210

Simplified Fraction

101/210

Mixed Number

Proper (101/210)

Decimal Value

0.480952

Percentage

48.0952%

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Step-by-Step Solution: 4/40 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.

LCD(40, 21) = 840

Step 2

Convert to Equivalent Fractions with Common Denominator 840

Multiply the numerator and denominator of 4/40 by 21, and multiply the numerator and denominator of 8/21 by 40 so both fractions share the common base 840.

4 × 21/40 × 21 = 84/840 and 8 × 40/21 × 40 = 320/840

Step 3

Add the Numerators

Now add the numerators (84 + 320 = 404) and keep the common denominator 840 unchanged.

84 + 320/840 = 404/840

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 404 and 840, which is 4. Divide both the numerator and denominator by 4.

404 ÷ 4/840 ÷ 4 = 101/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 210 produces a repeating decimal (approximately 0.480952, or 48.0952%).

101 ÷ 210 = 0.480952 (48.0952%)

Visual Representation

The diagram below illustrates 4/40 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/210`
Mixed Number Form	`101/210`
Decimal Form	`0.480952`
Percentage	`48.0952%`

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Frequently Asked Questions

What is 4/40 plus 8/21 as a fraction?

4/40 + 8/21 in simplest fraction form is 101/210.

What is 4/40 plus 8/21 as a decimal?

4/40 + 8/21 converted to a decimal is 0.480952.

What is 4/40 plus 8/21 as a percentage?

4/40 + 8/21 expressed as a percentage is 48.0952%.

Does 4/40 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.480952...) because the denominator contains prime factors other than 2 and 5.