LEMMA

Applied arithmetic

Mixed numbers

TEAS math

A nonnegative mixed number is a whole plus a fraction; convert to improper form before multiplying.

What this covers

acb​=ca⋅c+b​
  • To add, work the wholes and the fractions separately, then carry if the fractions pass one.
  • To multiply, convert to improper fractions first and cancel before multiplying.
  • To convert back, divide: the quotient is the whole, the remainder stays over the denominator.
  • Answer choices usually come as mixed numbers — convert your improper result back.

Worked example

Worked example

Add 2 3/4 and 1 3/4.

  1. 2+1=3The whole numbers combine on their own.
  2. 43​+43​=46​=121​The fractions pass one whole, so one carries.
  3. 3+121​=421​The carried whole joins the others.
Another worked example

Compute 2¼ − 1⅔.

  1. 241​−132​=49​−35​Convert each nonnegative mixed number to its entire improper fraction.
  2. 1227​−1220​=127​Equal denominators make equal-sized pieces; subtract their counts.

A common mistake

A mistake Lemma catches

From 43​+43​=46​=121​

3+21​3+121​

“The fractions add to 3/4 + 3/4 = 6/4, which is more than one whole: 6/4 = 1 1/2. That whole carries into the whole-number part: 3 + 1 1/2 = 4 1/2. Keeping only the 1/2 drops the carried 1.”

Try one

Sample problem

A shift used 3 3/4 boxes of gloves in the morning and 4 3/4 in the afternoon. How many boxes in total? Enter the answer as a decimal.

343​+443​

Practice mixed numbers free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

Where this fits

Before this