What is 5/42 plus 8/21? (Answer: 1/2)

Exact Answer

==================================================
Problem: What is 5/42 plus 8/21?
Formula / Expression: 5/42 + 8/21
Final Answer: 1/2
==================================================

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 8/21 by 2 so both fractions share the common base 42.
Working: 5 × 1/42 × 1 = 5/42 and 8 × 2/21 × 2 = 16/42

Step 3: Add the Numerators
Now add the numerators (5 + 16 = 21) and keep the common denominator 42 unchanged.
Working: 5 + 16/42 = 21/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 42, which is 21. Divide both the numerator and denominator by 21.
Working: 21 ÷ 21/42 ÷ 21 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-42-plus-8-21/
==================================================

5/42 + 8/21 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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 + 8/21

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 8/21 by 2 so both fractions share the common base 42.

5 × 1/42 × 1 = 5/42 and 8 × 2/21 × 2 = 16/42

Step 3

Add the Numerators

Now add the numerators (5 + 16 = 21) and keep the common denominator 42 unchanged.

5 + 16/42 = 21/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 21 and 42, which is 21. Divide both the numerator and denominator by 21.

21 ÷ 21/42 ÷ 21 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 5/42 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/42 plus 8/21 as a fraction?

5/42 + 8/21 in simplest fraction form is 1/2.

What is 5/42 plus 8/21 as a decimal?

5/42 + 8/21 converted to a decimal is 0.5.

What is 5/42 plus 8/21 as a percentage?

5/42 + 8/21 expressed as a percentage is 50%.

Does 5/42 plus 8/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.