What is 5/42 plus 4/21? (Answer: 13/42)

Exact Answer

==================================================
Problem: What is 5/42 plus 4/21?
Formula / Expression: 5/42 + 4/21
Final Answer: 13/42
==================================================

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 5/42 by 1, and multiply the numerator and denominator of 4/21 by 2 so both fractions share the common base 42.
Working: 5 × 1/42 × 1 = 5/42 and 4 × 2/21 × 2 = 8/42

Step 3: Add the Numerators
Now add the numerators (5 + 8 = 13) and keep the common denominator 42 unchanged.
Working: 5 + 8/42 = 13/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 42 is 1, confirming that 13/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).
Working: 13 ÷ 42 = 0.309524 (30.9524%)

Key Values:
- Simplified Fraction: 13/42
- Mixed Number Form: 13/42
- Decimal Value: 0.309524
- Percentage: 30.9524%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-42-plus-4-21/
==================================================

5/42 + 4/21 = 13/42

Simplified Fraction

13/42

Mixed Number

Proper (13/42)

Decimal Value

0.309524

Percentage

30.9524%

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: 5/42 + 4/21

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 5/42 by 1, and multiply the numerator and denominator of 4/21 by 2 so both fractions share the common base 42.

5 × 1/42 × 1 = 5/42 and 4 × 2/21 × 2 = 8/42

Step 3

Add the Numerators

Now add the numerators (5 + 8 = 13) and keep the common denominator 42 unchanged.

5 + 8/42 = 13/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 42 is 1, confirming that 13/42 cannot be reduced further—it is already in its simplest irreducible form.

13/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).

13 ÷ 42 = 0.309524 (30.9524%)

Visual Representation

The diagram below illustrates 5/42 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/42`
Mixed Number Form	`13/42`
Decimal Form	`0.309524`
Percentage	`30.9524%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/42 plus 4/21 as a fraction?

5/42 + 4/21 in simplest fraction form is 13/42.

What is 5/42 plus 4/21 as a decimal?

5/42 + 4/21 converted to a decimal is 0.309524.

What is 5/42 plus 4/21 as a percentage?

5/42 + 4/21 expressed as a percentage is 30.9524%.

Does 5/42 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.309524...) because the denominator contains prime factors other than 2 and 5.