What is 29/42 plus 15/21?
29/42 plus 15/21 equals 59/42 (or 1 17/42 as a mixed number) (or 1.404762 in decimal form). Learn the step-by-step solution to add 29/42 and 15/21 using Least Common Denominator and simplification.
Exact Answer
29/42 + 15/21 = 59/42
Simplified Fraction
59/42
Mixed Number
1 17/42
Decimal Value
1.404762
Percentage
140.4762%
Step-by-Step Solution: 29/42 + 15/21
Step 1
Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
LCD(42, 21) = 42
Step 2
Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 29/42 by 1, and multiply the numerator and denominator of 15/21 by 2 so both fractions share the common base 42.
29 × 1/42 × 1 = 29/42 and 15 × 2/21 × 2 = 30/42
Step 3
Add the Numerators
Now add the numerators (29 + 30 = 59) and keep the common denominator 42 unchanged.
29 + 30/42 = 59/42
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 42 is 1, confirming that 59/42 cannot be reduced further—it is already in its simplest irreducible form.
59/42
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (42), divide 59 by 42: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/42.
59/42 = 117/42
Step 6
Decimal & Percentage Representation
Dividing the numerator 59 by denominator 42 produces a repeating decimal (approximately 1.404762, or 140.4762%).
59 ÷ 42 = 1.404762 (140.4762%)
Visual Representation
The diagram below illustrates 29/42 plus 15/21 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 59/42 |
| Mixed Number Form | 1 17/42 |
| Decimal Form | 1.404762 |
| Percentage | 140.4762% |
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Frequently Asked Questions
What is 29/42 plus 15/21 as a fraction?
29/42 + 15/21 in simplest fraction form is 59/42 (or 1 17/42 as a mixed number).
What is 29/42 plus 15/21 as a decimal?
29/42 + 15/21 converted to a decimal is 1.404762.
What is 29/42 plus 15/21 as a percentage?
29/42 + 15/21 expressed as a percentage is 140.4762%.
How do you write 29/42 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 59/42 can be written as the mixed number 1 17/42.
Does 29/42 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.404762...) because the denominator contains prime factors other than 2 and 5.