AI Tutor
If two bakers read the exact same recipe card, could one end up baking a giant five-pound cake while the other bakes a tiny cookie?
Take the mixed expression 2.5+12×42.5 + \frac{1}{2} \times 4. If you add first, you get 1212, but if you multiply first, you get 4.54.5!
To keep calculations consistent, mathematicians rely on the order of operations — a set ranking that tells us which operation gets solved first.
When an expression mixes fractions and decimals, we face an extra puzzle: should we turn everything into decimals, or everything into fractions?

Choosing Team Decimal

If every fraction in your problem turns into an easy decimal like 12=0.5\frac{1}{2} = 0.5 or 34=0.75\frac{3}{4} = 0.75, switching everything to decimals is often the fastest route.
Let's solve (0.75+12)×4−1.2(0.75 + \frac{1}{2}) \times 4 - 1.2 using this decimal strategy.
Parentheses came first, so converting 12\frac{1}{2} to 0.50.5 let us add cleanly to get 1.251.25 inside the grouping.
Next, multiplication beat subtraction, giving 1.25×4=51.25 \times 4 = 5, and final subtraction yielded 3.83.8.
A common trap here is calculating 4−1.24 - 1.2 first because subtracting whole numbers looks easy, but multiplication always takes priority over subtraction.
What happens when a fraction refuses to turn into a tidy decimal, like 13\frac{1}{3} which becomes 0.333…0.333\dots forever?