What is 10/42 plus 10/21? (Answer: 5/7)

Exact Answer

==================================================
Problem: What is 10/42 plus 10/21?
Formula / Expression: 10/42 + 10/21
Final Answer: 5/7
==================================================

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 10/42 by 1, and multiply the numerator and denominator of 10/21 by 2 so both fractions share the common base 42.
Working: 10 × 1/42 × 1 = 10/42 and 10 × 2/21 × 2 = 20/42

Step 3: Add the Numerators
Now add the numerators (10 + 20 = 30) and keep the common denominator 42 unchanged.
Working: 10 + 20/42 = 30/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 42, which is 6. Divide both the numerator and denominator by 6.
Working: 30 ÷ 6/42 ÷ 6 = 5/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 7 produces a repeating decimal (approximately 0.714286, or 71.4286%).
Working: 5 ÷ 7 = 0.714286 (71.4286%)

Key Values:
- Simplified Fraction: 5/7
- Mixed Number Form: 5/7
- Decimal Value: 0.714286
- Percentage: 71.4286%

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

10/42 + 10/21 = 5/7

Simplified Fraction

5/7

Mixed Number

Proper (5/7)

Decimal Value

0.714286

Percentage

71.4286%

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

10 × 1/42 × 1 = 10/42 and 10 × 2/21 × 2 = 20/42

Step 3

Add the Numerators

Now add the numerators (10 + 20 = 30) and keep the common denominator 42 unchanged.

10 + 20/42 = 30/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 42, which is 6. Divide both the numerator and denominator by 6.

30 ÷ 6/42 ÷ 6 = 5/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 7 produces a repeating decimal (approximately 0.714286, or 71.4286%).

5 ÷ 7 = 0.714286 (71.4286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/7`
Mixed Number Form	`5/7`
Decimal Form	`0.714286`
Percentage	`71.4286%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

10/42 + 10/21 in simplest fraction form is 5/7.

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

10/42 + 10/21 converted to a decimal is 0.714286.

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

10/42 + 10/21 expressed as a percentage is 71.4286%.

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

It results in a repeating decimal (approximately 0.714286...) because the denominator contains prime factors other than 2 and 5.