What is 2/42 plus 2/21? (Answer: 1/7)

Exact Answer

==================================================
Problem: What is 2/42 plus 2/21?
Formula / Expression: 2/42 + 2/21
Final Answer: 1/7
==================================================

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 2/42 by 1, and multiply the numerator and denominator of 2/21 by 2 so both fractions share the common base 42.
Working: 2 × 1/42 × 1 = 2/42 and 2 × 2/21 × 2 = 4/42

Step 3: Add the Numerators
Now add the numerators (2 + 4 = 6) and keep the common denominator 42 unchanged.
Working: 2 + 4/42 = 6/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 42, which is 6. Divide both the numerator and denominator by 6.
Working: 6 ÷ 6/42 ÷ 6 = 1/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 7 produces a repeating decimal (approximately 0.142857, or 14.2857%).
Working: 1 ÷ 7 = 0.142857 (14.2857%)

Key Values:
- Simplified Fraction: 1/7
- Mixed Number Form: 1/7
- Decimal Value: 0.142857
- Percentage: 14.2857%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-42-plus-2-21/
==================================================

2/42 + 2/21 = 1/7

Simplified Fraction

1/7

Mixed Number

Proper (1/7)

Decimal Value

0.142857

Percentage

14.2857%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 2/42 + 2/21

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

2 × 1/42 × 1 = 2/42 and 2 × 2/21 × 2 = 4/42

Step 3

Add the Numerators

Now add the numerators (2 + 4 = 6) and keep the common denominator 42 unchanged.

2 + 4/42 = 6/42

Step 4

Simplify the Fraction to Lowest Terms

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

6 ÷ 6/42 ÷ 6 = 1/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 7 produces a repeating decimal (approximately 0.142857, or 14.2857%).

1 ÷ 7 = 0.142857 (14.2857%)

Visual Representation

The diagram below illustrates 2/42 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/7`
Mixed Number Form	`1/7`
Decimal Form	`0.142857`
Percentage	`14.2857%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/42 plus 2/21 as a fraction?

2/42 + 2/21 in simplest fraction form is 1/7.

What is 2/42 plus 2/21 as a decimal?

2/42 + 2/21 converted to a decimal is 0.142857.

What is 2/42 plus 2/21 as a percentage?

2/42 + 2/21 expressed as a percentage is 14.2857%.

Does 2/42 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.142857...) because the denominator contains prime factors other than 2 and 5.