What is 12/40 plus 10/21? (Answer: 163/210)

Exact Answer

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Problem: What is 12/40 plus 10/21?
Formula / Expression: 12/40 + 10/21
Final Answer: 163/210
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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 12/40 by 21, and multiply the numerator and denominator of 10/21 by 40 so both fractions share the common base 840.
Working: 12 × 21/40 × 21 = 252/840 and 10 × 40/21 × 40 = 400/840

Step 3: Add the Numerators
Now add the numerators (252 + 400 = 652) and keep the common denominator 840 unchanged.
Working: 252 + 400/840 = 652/840

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 652 and 840, which is 4. Divide both the numerator and denominator by 4.
Working: 652 ÷ 4/840 ÷ 4 = 163/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 210 produces a repeating decimal (approximately 0.77619, or 77.619%).
Working: 163 ÷ 210 = 0.77619 (77.619%)

Key Values:
- Simplified Fraction: 163/210
- Mixed Number Form: 163/210
- Decimal Value: 0.77619
- Percentage: 77.619%

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Solved with FractionsCalc:
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12/40 + 10/21 = 163/210

Simplified Fraction

163/210

Mixed Number

Proper (163/210)

Decimal Value

0.77619

Percentage

77.619%

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Step-by-Step Solution: 12/40 + 10/21

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 12/40 by 21, and multiply the numerator and denominator of 10/21 by 40 so both fractions share the common base 840.

12 × 21/40 × 21 = 252/840 and 10 × 40/21 × 40 = 400/840

Step 3

Add the Numerators

Now add the numerators (252 + 400 = 652) and keep the common denominator 840 unchanged.

252 + 400/840 = 652/840

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 652 and 840, which is 4. Divide both the numerator and denominator by 4.

652 ÷ 4/840 ÷ 4 = 163/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 210 produces a repeating decimal (approximately 0.77619, or 77.619%).

163 ÷ 210 = 0.77619 (77.619%)

Visual Representation

The diagram below illustrates 12/40 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/210`
Mixed Number Form	`163/210`
Decimal Form	`0.77619`
Percentage	`77.619%`

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Frequently Asked Questions

What is 12/40 plus 10/21 as a fraction?

12/40 + 10/21 in simplest fraction form is 163/210.

What is 12/40 plus 10/21 as a decimal?

12/40 + 10/21 converted to a decimal is 0.77619.

What is 12/40 plus 10/21 as a percentage?

12/40 + 10/21 expressed as a percentage is 77.619%.

Does 12/40 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.77619...) because the denominator contains prime factors other than 2 and 5.