What is 10/40 plus 10/21? (Answer: 61/84)

Exact Answer

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Problem: What is 10/40 plus 10/21?
Formula / Expression: 10/40 + 10/21
Final Answer: 61/84
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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 10/40 by 21, and multiply the numerator and denominator of 10/21 by 40 so both fractions share the common base 840.
Working: 10 × 21/40 × 21 = 210/840 and 10 × 40/21 × 40 = 400/840

Step 3: Add the Numerators
Now add the numerators (210 + 400 = 610) and keep the common denominator 840 unchanged.
Working: 210 + 400/840 = 610/840

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 610 and 840, which is 10. Divide both the numerator and denominator by 10.
Working: 610 ÷ 10/840 ÷ 10 = 61/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 84 produces a repeating decimal (approximately 0.72619, or 72.619%).
Working: 61 ÷ 84 = 0.72619 (72.619%)

Key Values:
- Simplified Fraction: 61/84
- Mixed Number Form: 61/84
- Decimal Value: 0.72619
- Percentage: 72.619%

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Solved with FractionsCalc:
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10/40 + 10/21 = 61/84

Simplified Fraction

61/84

Mixed Number

Proper (61/84)

Decimal Value

0.72619

Percentage

72.619%

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Step-by-Step Solution: 10/40 + 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 10/40 by 21, and multiply the numerator and denominator of 10/21 by 40 so both fractions share the common base 840.

10 × 21/40 × 21 = 210/840 and 10 × 40/21 × 40 = 400/840

Step 3

Add the Numerators

Now add the numerators (210 + 400 = 610) and keep the common denominator 840 unchanged.

210 + 400/840 = 610/840

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 610 and 840, which is 10. Divide both the numerator and denominator by 10.

610 ÷ 10/840 ÷ 10 = 61/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 84 produces a repeating decimal (approximately 0.72619, or 72.619%).

61 ÷ 84 = 0.72619 (72.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/84`
Mixed Number Form	`61/84`
Decimal Form	`0.72619`
Percentage	`72.619%`

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Frequently Asked Questions

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

10/40 + 10/21 in simplest fraction form is 61/84.

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

10/40 + 10/21 converted to a decimal is 0.72619.

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

10/40 + 10/21 expressed as a percentage is 72.619%.

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

It results in a repeating decimal (approximately 0.72619...) because the denominator contains prime factors other than 2 and 5.