To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, then place the result over the original denominator. For example, 2¾ becomes (2 × 4 + 3) ⁄ 4 = 11⁄4. Use the free converter below for instant results with step-by-step solutions.
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Convert a Mixed Number to an Improper Fraction
How to Convert a Mixed Number to an Improper Fraction (Multiply & Add Method)
A mixed number is a number made up of a whole number and a proper fraction written together, such as 3½ or 7¾. An improper fraction is a fraction where the numerator is equal to or larger than the denominator, such as 7/2 or 9/4. Converting between the two forms is a foundational fraction skill used throughout algebra, everyday measurement, and standardized tests. The Common Core State Standards (CCSS 4.NF.B.3) include working with mixed numbers and improper fractions as a key Grade 4 numeracy objective.
The Formula
(Whole × Denominator + Numerator) ⁄ Denominator
The process follows three simple steps:
Step 1 — Multiply the whole number by the denominator of the fraction part. This tells you how many equal parts are contained in the whole-number portion alone.
Step 2 — Add that product to the existing numerator. The sum represents the total number of equal parts in the entire mixed number.
Step 3 — Keep the denominator unchanged. Write the sum from Step 2 over the original denominator, and you have your improper fraction.
This table shows common mixed numbers and their improper fraction equivalents for quick lookup. Every value was calculated using the multiply-and-add formula.
Mixed Number
Working
Improper Fraction
Decimal
1½
(1×2+1)⁄2
3⁄2
1.5
2⅓
(2×3+1)⁄3
7⁄3
2.333…
2¾
(2×4+3)⁄4
11⁄4
2.75
3½
(3×2+1)⁄2
7⁄2
3.5
4⅖
(4×5+2)⁄5
22⁄5
4.4
5⅔
(5×3+2)⁄3
17⁄3
5.666…
7⅜
(7×8+3)⁄8
59⁄8
7.375
10⅗
(10×5+3)⁄5
53⁄5
10.6
What Are Some Mixed Number to Improper Fraction Examples?
Example 1: Convert 3½ to an improper fraction
Multiply the whole by the denominator: 3 × 2 = 6
Add the numerator: 6 + 1 = 7
Place over the original denominator
3½ = 7 / 2
Example 2: Convert 5⅔ to an improper fraction
Multiply the whole by the denominator: 5 × 3 = 15
Add the numerator: 15 + 2 = 17
Place over the original denominator
5⅔ = 17 / 3
Example 3: Convert 1⅞ to an improper fraction
Multiply the whole by the denominator: 1 × 8 = 8
Add the numerator: 8 + 7 = 15
Place over the original denominator
1⅞ = 15 / 8
Example 4: Convert 10⅗ to an improper fraction
Multiply the whole by the denominator: 10 × 5 = 50
Add the numerator: 50 + 3 = 53
Place over the original denominator
10⅗ = 53 / 5
Once you have your improper fraction, you can use it directly in operations like addition or subtraction, or simplify it with the Simplify Fractions Calculator. For more complex calculations involving mixed numbers, try the Mixed Number Calculator which handles all four operations.
Mixed Number to Improper Fraction — Common Questions
Multiply the whole number by the denominator, add the numerator, and place that total over the original denominator. In formula form: (Whole × Denominator + Numerator) ⁄ Denominator. For example, 4⅖ becomes (4 × 5 + 2) ⁄ 5 = 22 ⁄ 5.
Converting to improper fractions makes arithmetic operations like addition, subtraction, multiplication, and division much easier. It expresses the quantity as a single fraction rather than two separate parts, which simplifies calculations and reduces the chance of errors.
Yes. Convert the absolute value of the mixed number using the standard multiply-and-add method, then apply the negative sign to the result. For example, −2¾ becomes −(2 × 4 + 3) ⁄ 4 = −11 ⁄ 4. This converter supports negative numbers with the checkbox toggle above.
Yes. An improper fraction is any fraction where the numerator is greater than or equal to the denominator. Since 7 is greater than 3, 7⁄3 is an improper fraction. It is equivalent to the mixed number 2⅓.
Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same. For example, 11 ⁄ 4 = 11 ÷ 4 = 2 remainder 3, giving the mixed number 2¾. Try our Improper Fraction to Mixed Number Converter for instant results.
A mixed number is a number made up of a whole number and a proper fraction written together, such as 3½ or 7¾. It represents a value greater than the whole number but less than the next whole number. Mixed numbers are commonly used in everyday measurements, cooking recipes, and construction.
An improper fraction is a fraction where the numerator is equal to or larger than the denominator, such as 7⁄4 or 11⁄3. It represents a value equal to or greater than one whole. Improper fractions are preferred for mathematical operations because they are easier to multiply, divide, add, and subtract than mixed numbers.
A mixed number like 2¾ separates the whole part from the fractional part, making it easier to read and visualize. An improper fraction like 11⁄4 expresses the same value as a single fraction, making it easier to use in arithmetic. Both forms represent exactly the same quantity — they are simply written differently.
If the whole number is 0, the mixed number is just a proper fraction. Applying the formula gives (0 × denominator + numerator) ⁄ denominator, which equals the original fraction unchanged. For example, 0⅗ simply equals 3⁄5 — no conversion is needed.
Mixed numbers appear in cooking recipes (2½ cups of flour), construction measurements (5¾ inches), time tracking (1⅓ hours), and distance markers (mile 3¼). Converting them to improper fractions is essential when you need to add, subtract, or compare these measurements accurately in calculations.