What is 10/42 plus 7/21? (Answer: 4/7)

Exact Answer

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Problem: What is 10/42 plus 7/21?
Formula / Expression: 10/42 + 7/21
Final Answer: 4/7
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Step-by-Step Solution:

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.
Working: LCD(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 10/42 by 1, and multiply the numerator and denominator of 7/21 by 2 so both fractions share the common base 42.
Working: 10 × 1/42 × 1 = 10/42 and 7 × 2/21 × 2 = 14/42

Step 3: Add the Numerators
Now add the numerators (10 + 14 = 24) and keep the common denominator 42 unchanged.
Working: 10 + 14/42 = 24/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 42, which is 6. Divide both the numerator and denominator by 6.
Working: 24 ÷ 6/42 ÷ 6 = 4/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).
Working: 4 ÷ 7 = 0.571429 (57.1429%)

Key Values:
- Simplified Fraction: 4/7
- Mixed Number Form: 4/7
- Decimal Value: 0.571429
- Percentage: 57.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-42-plus-7-21/
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10/42 + 7/21 = 4/7

Simplified Fraction

4/7

Mixed Number

Proper (4/7)

Decimal Value

0.571429

Percentage

57.1429%

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Step-by-Step Solution: 10/42 + 7/21

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 10/42 by 1, and multiply the numerator and denominator of 7/21 by 2 so both fractions share the common base 42.

10 × 1/42 × 1 = 10/42 and 7 × 2/21 × 2 = 14/42

Step 3

Add the Numerators

Now add the numerators (10 + 14 = 24) and keep the common denominator 42 unchanged.

10 + 14/42 = 24/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 42, which is 6. Divide both the numerator and denominator by 6.

24 ÷ 6/42 ÷ 6 = 4/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).

4 ÷ 7 = 0.571429 (57.1429%)

Visual Representation

The diagram below illustrates 10/42 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/7`
Mixed Number Form	`4/7`
Decimal Form	`0.571429`
Percentage	`57.1429%`

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Frequently Asked Questions

What is 10/42 plus 7/21 as a fraction?

10/42 + 7/21 in simplest fraction form is 4/7.

What is 10/42 plus 7/21 as a decimal?

10/42 + 7/21 converted to a decimal is 0.571429.

What is 10/42 plus 7/21 as a percentage?

10/42 + 7/21 expressed as a percentage is 57.1429%.

Does 10/42 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.571429...) because the denominator contains prime factors other than 2 and 5.