What is 18/40 plus 15/21? (Answer: 163/140)

Exact Answer

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Problem: What is 18/40 plus 15/21?
Formula / Expression: 18/40 + 15/21
Final Answer: 1 23/140 (163/140)
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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 18/40 by 21, and multiply the numerator and denominator of 15/21 by 40 so both fractions share the common base 840.
Working: 18 × 21/40 × 21 = 378/840 and 15 × 40/21 × 40 = 600/840

Step 3: Add the Numerators
Now add the numerators (378 + 600 = 978) and keep the common denominator 840 unchanged.
Working: 378 + 600/840 = 978/840

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 978 and 840, which is 6. Divide both the numerator and denominator by 6.
Working: 978 ÷ 6/840 ÷ 6 = 163/140

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (163) is greater than the denominator (140), divide 163 by 140: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/140.
Working: 163/140 = 1 23/140

Step 6: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 140 produces a repeating decimal (approximately 1.164286, or 116.4286%).
Working: 163 ÷ 140 = 1.164286 (116.4286%)

Key Values:
- Simplified Fraction: 163/140
- Mixed Number Form: 1 23/140
- Decimal Value: 1.164286
- Percentage: 116.4286%

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18/40 + 15/21 = 163/140

Simplified Fraction

163/140

Mixed Number

1 23/140

Decimal Value

1.164286

Percentage

116.4286%

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Step-by-Step Solution: 18/40 + 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 18/40 by 21, and multiply the numerator and denominator of 15/21 by 40 so both fractions share the common base 840.

18 × 21/40 × 21 = 378/840 and 15 × 40/21 × 40 = 600/840

Step 3

Add the Numerators

Now add the numerators (378 + 600 = 978) and keep the common denominator 840 unchanged.

378 + 600/840 = 978/840

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 978 and 840, which is 6. Divide both the numerator and denominator by 6.

978 ÷ 6/840 ÷ 6 = 163/140

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (163) is greater than the denominator (140), divide 163 by 140: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/140.

163/140 = 123/140

Step 6

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 140 produces a repeating decimal (approximately 1.164286, or 116.4286%).

163 ÷ 140 = 1.164286 (116.4286%)

Visual Representation

The diagram below illustrates 18/40 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/140`
Mixed Number Form	`1 23/140`
Decimal Form	`1.164286`
Percentage	`116.4286%`

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Frequently Asked Questions

What is 18/40 plus 15/21 as a fraction?

18/40 + 15/21 in simplest fraction form is 163/140 (or 1 23/140 as a mixed number).

What is 18/40 plus 15/21 as a decimal?

18/40 + 15/21 converted to a decimal is 1.164286.

What is 18/40 plus 15/21 as a percentage?

18/40 + 15/21 expressed as a percentage is 116.4286%.

How do you write 18/40 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 163/140 can be written as the mixed number 1 23/140.

Does 18/40 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.164286...) because the denominator contains prime factors other than 2 and 5.