What is 19/40 plus 10/21?
19/40 plus 10/21 equals 799/840 (or 0.95119 in decimal form). Learn the step-by-step solution to add 19/40 and 10/21 using Least Common Denominator and simplification.
Exact Answer
19/40 + 10/21 = 799/840
Simplified Fraction
799/840
Mixed Number
Proper (799/840)
Decimal Value
0.95119
Percentage
95.119%
Step-by-Step Solution: 19/40 + 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 19/40 by 21, and multiply the numerator and denominator of 10/21 by 40 so both fractions share the common base 840.
19 × 21/40 × 21 = 399/840 and 10 × 40/21 × 40 = 400/840
Step 3
Add the Numerators
Now add the numerators (399 + 400 = 799) and keep the common denominator 840 unchanged.
399 + 400/840 = 799/840
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 799 and 840 is 1, confirming that 799/840 cannot be reduced further—it is already in its simplest irreducible form.
799/840
Step 5
Decimal & Percentage Representation
Dividing the numerator 799 by denominator 840 produces a repeating decimal (approximately 0.95119, or 95.119%).
799 ÷ 840 = 0.95119 (95.119%)
Visual Representation
The diagram below illustrates 19/40 plus 10/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 799/840 |
| Mixed Number Form | 799/840 |
| Decimal Form | 0.95119 |
| Percentage | 95.119% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 19/40 plus 10/21 as a fraction?
19/40 + 10/21 in simplest fraction form is 799/840.
What is 19/40 plus 10/21 as a decimal?
19/40 + 10/21 converted to a decimal is 0.95119.
What is 19/40 plus 10/21 as a percentage?
19/40 + 10/21 expressed as a percentage is 95.119%.
Does 19/40 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.95119...) because the denominator contains prime factors other than 2 and 5.