What does −2 3/4 mean?

Minus two and three quarters, or −2.75. The sign belongs to the whole quantity, so the fractional part is negative too: it is −(2 + 3/4), not −2 + 3/4 = −1.25. Both readings turn up in calculators that never say which one they use, which is why this page converts to an improper fraction on screen before doing anything else.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and keep the same denominator. 2 3/4 becomes (2 × 4 + 3)/4 = 11/4. The denominator never changes, which is the part most often got wrong.

Why convert before adding instead of adding the parts?

Because the fractional parts carry. 1 3/4 + 1 1/2 is not 2 and something under one: three quarters plus a half is 1 1/4, so the answer is 3 1/4 rather than 2 1/4. Converting both to improper fractions first removes the carry as a separate thing to remember.

Is 11/4 the same as 2 3/4?

Yes, exactly — they are two ways of writing 2.75. Improper fractions are easier to compute with, mixed numbers are easier to read off a tape or a recipe, and neither is more correct than the other.

Mixed Numbers Calculator

With whole number 2, numerator 3, denominator 4, mixed numbers comes to 2 3/4 — answer. It is reached in 10 steps, the last of which is 11 / 4, and each one is printed on the page with its numbers filled in. The formula is the one published by Euclid, Elements VII.2, not an approximation fitted to it.

Convert a mixed number to an improper fraction and back, and add, subtract, multiply or divide two of them.

Formula and sources checked 17 August 2026 · How we check

What to do Convert one mixed number to improper, Whole number 2, Numerator 3, Denominator 4

2 3/4

Answer for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

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What to doWhole numberA negative mixed number takes its minus here — see the note below.NumeratorDenominator

Answer

2 3/4

First as an improper fraction: sign(2 + (0)) * (abs(2) * 4 + 3)11
Second as an improper fraction: sign(1 + (0)) * (abs(1) * 2 + 1)3
Numerator before reducing: 1 * 11 + 0 * (11 * 2 + 3 * 4) + 0 * (11 * 2 - 3 * 4) + 0 * (11 * 3) + 0 * (11 * 2)11
Denominator before reducing: 1 * 4 + (0 + 0 + 0) * (4 * 2) + 0 * (4 * 3 + (0))4
Greatest common divisor: max(1, gcd(abs(11), abs(4)))1
Numerator in lowest terms: 11 / 111
Denominator in lowest terms: abs(4 / 1)4
Whole part of the answer: sign(11) * floor(abs(11) / 4)2
Fractional part left over: abs(11) - floor(abs(11) / 4) * 43
As a decimal: 11 / 42.75

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Worked example

Two and three quarters is eleven quarters: the whole number contributes 2 × 4 = 8 quarters, and the three quarters already there make 11. Nothing reduces, since 11 and 4 share no factor.

How to work it out yourself

1.To convert, multiply the whole number by the denominator and add the numerator. Two and three quarters becomes (2 × 4 + 3) / 4 = 11/4.
2.To go back, divide: 11 ÷ 4 is 2 remainder 3, so the answer is 2 3/4. Both directions appear in the derivation.
3.For arithmetic, switch the mode and fill the second mixed number. Both are converted to improper fractions first, because adding whole numbers and fractional parts separately goes wrong the moment the fractional parts carry.
4.Put the minus sign on the whole number for a negative mixed number.

The formula

First as an improper fractionsign(2 + (0)) * (abs(2) * 4 + 3)
Second as an improper fractionsign(1 + (0)) * (abs(1) * 2 + 1)
Numerator before reducing1 * 11 + 0 * (11 * 2 + 3 * 4) + 0 * (11 * 2 - 3 * 4) + 0 * (11 * 3) + 0 * (11 * 2)
Denominator before reducing1 * 4 + (0 + 0 + 0) * (4 * 2) + 0 * (4 * 3 + (0))
Greatest common divisormax(1, gcd(abs(11), abs(4)))
Numerator in lowest terms11 / 1
Denominator in lowest termsabs(4 / 1)
Whole part of the answersign(11) * floor(abs(11) / 4)
Fractional part left overabs(11) - floor(abs(11) / 4) * 4
As a decimal11 / 4

Source: Euclid, Elements VII.2 — the algorithm for the greatest common divisor

Questions people actually ask

What does −2 3/4 mean?: Minus two and three quarters, or −2.75. The sign belongs to the whole quantity, so the fractional part is negative too: it is −(2 + 3/4), not −2 + 3/4 = −1.25. Both readings turn up in calculators that never say which one they use, which is why this page converts to an improper fraction on screen before doing anything else.
How do I convert a mixed number to an improper fraction?: Multiply the whole number by the denominator, add the numerator, and keep the same denominator. 2 3/4 becomes (2 × 4 + 3)/4 = 11/4. The denominator never changes, which is the part most often got wrong.
Why convert before adding instead of adding the parts?: Because the fractional parts carry. 1 3/4 + 1 1/2 is not 2 and something under one: three quarters plus a half is 1 1/4, so the answer is 3 1/4 rather than 2 1/4. Converting both to improper fractions first removes the carry as a separate thing to remember.
Is 11/4 the same as 2 3/4?: Yes, exactly — they are two ways of writing 2.75. Improper fractions are easier to compute with, mixed numbers are easier to read off a tape or a recipe, and neither is more correct than the other.

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