What is 17/42 plus 10/21?
17/42 plus 10/21 equals 37/42 (or 0.880952 in decimal form). Learn the step-by-step solution to add 17/42 and 10/21 using Least Common Denominator and simplification.
Exact Answer
17/42 + 10/21 = 37/42
Simplified Fraction
37/42
Mixed Number
Proper (37/42)
Decimal Value
0.880952
Percentage
88.0952%
Step-by-Step Solution: 17/42 + 10/21
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 17/42 by 1, and multiply the numerator and denominator of 10/21 by 2 so both fractions share the common base 42.
17 × 1/42 × 1 = 17/42 and 10 × 2/21 × 2 = 20/42
Step 3
Add the Numerators
Now add the numerators (17 + 20 = 37) and keep the common denominator 42 unchanged.
17 + 20/42 = 37/42
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 42 is 1, confirming that 37/42 cannot be reduced further—it is already in its simplest irreducible form.
37/42
Step 5
Decimal & Percentage Representation
Dividing the numerator 37 by denominator 42 produces a repeating decimal (approximately 0.880952, or 88.0952%).
37 ÷ 42 = 0.880952 (88.0952%)
Visual Representation
The diagram below illustrates 17/42 plus 10/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 37/42 |
| Mixed Number Form | 37/42 |
| Decimal Form | 0.880952 |
| Percentage | 88.0952% |
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Frequently Asked Questions
What is 17/42 plus 10/21 as a fraction?
17/42 + 10/21 in simplest fraction form is 37/42.
What is 17/42 plus 10/21 as a decimal?
17/42 + 10/21 converted to a decimal is 0.880952.
What is 17/42 plus 10/21 as a percentage?
17/42 + 10/21 expressed as a percentage is 88.0952%.
Does 17/42 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.880952...) because the denominator contains prime factors other than 2 and 5.