What is 10/28 plus 11/21? (Answer: 37/42)

Exact Answer

==================================================
Problem: What is 10/28 plus 11/21?
Formula / Expression: 10/28 + 11/21
Final Answer: 37/42
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).
Working: LCD(28, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 10/28 by 3, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.
Working: 10 × 3/28 × 3 = 30/84 and 11 × 4/21 × 4 = 44/84

Step 3: Add the Numerators
Now add the numerators (30 + 44 = 74) and keep the common denominator 84 unchanged.
Working: 30 + 44/84 = 74/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/84 ÷ 2 = 37/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 42 produces a repeating decimal (approximately 0.880952, or 88.0952%).
Working: 37 ÷ 42 = 0.880952 (88.0952%)

Key Values:
- Simplified Fraction: 37/42
- Mixed Number Form: 37/42
- Decimal Value: 0.880952
- Percentage: 88.0952%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-28-plus-11-21/
==================================================

10/28 + 11/21 = 37/42

Simplified Fraction

37/42

Mixed Number

Proper (37/42)

Decimal Value

0.880952

Percentage

88.0952%

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: 10/28 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).

LCD(28, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 10/28 by 3, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.

10 × 3/28 × 3 = 30/84 and 11 × 4/21 × 4 = 44/84

Step 3

Add the Numerators

Now add the numerators (30 + 44 = 74) and keep the common denominator 84 unchanged.

30 + 44/84 = 74/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 84, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/84 ÷ 2 = 37/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 42 produces a repeating decimal (approximately 0.880952, or 88.0952%).

37 ÷ 42 = 0.880952 (88.0952%)

Visual Representation

The diagram below illustrates 10/28 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/42`
Mixed Number Form	`37/42`
Decimal Form	`0.880952`
Percentage	`88.0952%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/28 plus 11/21 as a fraction?

10/28 + 11/21 in simplest fraction form is 37/42.

What is 10/28 plus 11/21 as a decimal?

10/28 + 11/21 converted to a decimal is 0.880952.

What is 10/28 plus 11/21 as a percentage?

10/28 + 11/21 expressed as a percentage is 88.0952%.

Does 10/28 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.880952...) because the denominator contains prime factors other than 2 and 5.