Mixed Numbers

7/4 is more than a whole. Four quarters make one whole, with 3 quarters left.

There is a shorter way to write it.

Mixed number is a whole number with a fraction beside it, such as 1 3/4.

From pieces to wholes

Divide the top by the bottom. 7 ÷ 4 is 1 with 3 left, giving 1 3/4.

And back again

2 1/3 is 2 wholes, each 3 thirds, plus 1 more third. That is 7 thirds.

Whole ones and pieces left over

2 3/4 means two whole ones and three quarters more. It is one number, not two, and it sits on the number line between 2 and 3. The whole-number part and the fraction part are added together, even though no plus sign is written.

Converting to an improper fraction

2 3/4 is 2 wholes, each worth 4 quarters, so 8 quarters, plus 3 more: 11/4. The shortcut is to multiply the whole number by the denominator and add the numerator. Knowing where the shortcut comes from stops you multiplying the wrong pair.

Converting back

11/4 means eleven quarters. Four quarters make a whole, so 11 ÷ 4 = 2 remainder 3, giving 2 3/4. The quotient is the whole number and the remainder is the new numerator — a genuine use for remainders just one chapter after meeting them.

Which form to use

Mixed numbers are easier to picture and to judge for size; improper fractions are easier to calculate with. Convert to improper before multiplying, and convert back at the end if the answer needs to be readable. Neither form is more correct.