What is 12/40 plus 15/21? (Answer: 71/70)

Exact Answer

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Problem: What is 12/40 plus 15/21?
Formula / Expression: 12/40 + 15/21
Final Answer: 1 1/70 (71/70)
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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 15/21 by 40 so both fractions share the common base 840.
Working: 12 × 21/40 × 21 = 252/840 and 15 × 40/21 × 40 = 600/840

Step 3: Add the Numerators
Now add the numerators (252 + 600 = 852) and keep the common denominator 840 unchanged.
Working: 252 + 600/840 = 852/840

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 852 and 840, which is 12. Divide both the numerator and denominator by 12.
Working: 852 ÷ 12/840 ÷ 12 = 71/70

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (70), divide 71 by 70: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/70.
Working: 71/70 = 1 1/70

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 70 produces a repeating decimal (approximately 1.014286, or 101.4286%).
Working: 71 ÷ 70 = 1.014286 (101.4286%)

Key Values:
- Simplified Fraction: 71/70
- Mixed Number Form: 1 1/70
- Decimal Value: 1.014286
- Percentage: 101.4286%

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12/40 + 15/21 = 71/70

Simplified Fraction

71/70

Mixed Number

1 1/70

Decimal Value

1.014286

Percentage

101.4286%

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Step-by-Step Solution: 12/40 + 15/21

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 15/21 by 40 so both fractions share the common base 840.

12 × 21/40 × 21 = 252/840 and 15 × 40/21 × 40 = 600/840

Step 3

Add the Numerators

Now add the numerators (252 + 600 = 852) and keep the common denominator 840 unchanged.

252 + 600/840 = 852/840

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 852 and 840, which is 12. Divide both the numerator and denominator by 12.

852 ÷ 12/840 ÷ 12 = 71/70

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (70), divide 71 by 70: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/70.

71/70 = 11/70

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 70 produces a repeating decimal (approximately 1.014286, or 101.4286%).

71 ÷ 70 = 1.014286 (101.4286%)

Visual Representation

The diagram below illustrates 12/40 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/70`
Mixed Number Form	`1 1/70`
Decimal Form	`1.014286`
Percentage	`101.4286%`

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Frequently Asked Questions

What is 12/40 plus 15/21 as a fraction?

12/40 + 15/21 in simplest fraction form is 71/70 (or 1 1/70 as a mixed number).

What is 12/40 plus 15/21 as a decimal?

12/40 + 15/21 converted to a decimal is 1.014286.

What is 12/40 plus 15/21 as a percentage?

12/40 + 15/21 expressed as a percentage is 101.4286%.

How do you write 12/40 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/70 can be written as the mixed number 1 1/70.

Does 12/40 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.014286...) because the denominator contains prime factors other than 2 and 5.