Tools that show their working
Three free calculators. Each one keeps a record of what it did, so an answer can be checked rather than only accepted. They follow different rules for the same keys, and each card below says which rule.
Adding-machine tape for 2 + 3 × 4 = - 2
- 3
- 4
- 20
Adding machine
A calculator that prints every entry to a tape, so a long column of figures can be checked line by line after it is added.
Each operator is applied the moment it is pressed, the way a desk calculator works.
Open the adding machineScientific calculator window for 2+3×4 2+3×4
14
Scientific calculator
Trigonometry, logarithms, powers, roots, π and e. The whole expression is built in the window and read back before it is answered.
Multiplication and division are done before addition and subtraction, the way written math works.
Open the scientific calculatorSolver working for 3x + 5 = 20 3x + 5 = 20
- Start with the equation as it is written.3x + 5 = 20
- Take 5 from both sides, so the x term is on its own.3x = 15
- Divide both sides by 3.x = 5
x = 5
Equation solver
Solves an equation with one unknown in exact fractions and writes out every step, so the working can be compared with your own.
Nothing is rounded. A third stays 1/3 rather than becoming 0.333.
Open the equation solver
Why 2 + 3 × 4 gives two different answers
The adding machine works the sum out as each key is pressed: 2 + 3 is 5, then 5 × 4 is 20. The scientific calculator waits for the whole expression and multiplies first, the way written math is read: 3 × 4 is 12, then 2 + 12 is 14.
Neither is broken. They follow different rules, and both rules are in use. The written rule is the one a math class uses, and chapter 3 of the pre-algebra course explains it from the start.