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Mixed vs. Improper

Overview

Top heavy or sidecar?

What is it?

Converting between '1 1/2' and '3/2'.

History

Improper fractions are easier for algebra; Mixed numbers are easier for cooking.

Key Idea

MAD: Multiply, Add, Denominator stays same.

Practice This Topic

Concept Guide

Plain English: An improper fraction is 'Top Heavy' (bigger number on top). It means you have more than one whole item. 3/2 means you have 3 halves... which is 1 whole and 1 half left over.

Real-world example: Buying lumber. You buy '2 by 4s', but often need lengths like 8 1/2 feet.

How to do it

  1. Mixed to Improper (MAD):
  2. Multiply whole number by bottom.
  3. Add the top number.
  4. Put result over original bottom.
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Common Pitfall

Forgetting to keep the denominator the same when converting.

Word Problem
"A recipe needs 1 1/2 cups of flour. How many 'half-cup' scoops is that?"
Reasoning: 1 x 2 = 2. 2 + 1 = 3. Answer: 3/2 (Three scoops).

Practice Examples

MAD Method
1 2 - -> 2x3=6 -> 6+1=7 -> 7/3 3
Seven Thirds.