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Notes on arithmetic, rounding, and the strange economics of calculator apps.
How do you divide fractions?
Keep, change, flip: 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8 = 1 7/8. Why the flip is really multiplication, mixed numbers done properly, and why dividing can make the answer bigger.
How do you multiply fractions?
Straight across, no common denominator: 2/3 × 3/4 = 6/12 = 1/2. Cancelling before you multiply, mixed numbers done properly, and why 0.333 × 3 gives 0.999.
How do you convert a repeating decimal to a fraction?
The block goes over that many nines: 0.363636... is 36/99 = 4/11. The algebra behind the rule, repeats that start late, and why 0.999... is exactly 1.
How do you calculate an average percentage?
Not by averaging the percentages: 80% of 20 students and 40% of 5 is 18 of 25, so 72% and not 60%. Parts over wholes, weighting by group size, and when the plain average is safe.
How do you convert a fraction to a decimal?
The fraction bar is a division sign: 3/4 is 3 ÷ 4 = 0.75. Long division by hand, the power of ten shortcut, and why a denominator of 2s and 5s stops while 1/3 never does.
How do you calculate a weighted average?
Value times weight, summed, divided by the total weight: 90, 78 and 85 at 20, 30 and 50 percent give 83.9. GPA by credits, portfolio returns, and the score you need on the final.
How do you calculate an average?
Sum divided by count: 4, 8, 9, 15 gives 36 ÷ 4 = 9. Mean, median and mode, and the five salaries where four people earn under half the average.
How do you convert a decimal to a fraction?
Digits over the matching power of ten, then reduce: 0.75 = 75/100 = 3/4. Repeating decimals go over nines, and 0.33 is not 1/3.
How do you calculate percentage increase?
New minus old, over old, so 1,450 to 1,595 is 10%. The multiplier both ways, increases past 100%, and why three years of raises do not average 8.3333%.
What makes a good fraction calculator app?
Mixed number entry, exact arithmetic instead of decimals underneath, automatic simplifying, and a toggle between 53/12 and 4 5/12. Plus the three second test.
What is the best calculator app for iPhone?
Four questions that decide it: history, whether the math is free, one time price versus weekly, and tracking. With live App Store prices and ratings read on 19 August 2026.
How do you calculate percentage change?
New minus old, divided by old. Increases, decreases, the multiplier shortcut, percentage points, and why down 50% then up 50% leaves you 25% short.
What is scientific notation on a calculator?
A coefficient between 1 and 10, times a power of ten, printed as 6.42E6. Converting both ways, multiplying by adding exponents, the EE key, and engineering notation in threes.
How do you calculate markup?
Profit divided by cost, where margin divides the same profit by the price. The conversion table, keystone pricing, and why marking up 40% leaves you a 28.57% margin.
How do you convert km to miles?
Divide by 1.609344, or multiply by 5 and divide by 8 when there is no calculator to hand. The Fibonacci trick, a table, speed limits, and why the marathon is 42.194988 km.
What does E mean on a calculator?
It is shorthand for a power of ten, so 1.2E8 is 120,000,000. How to read it, how to type one with the EE key, the unrelated lowercase e, and the digits the display quietly drops.
How to calculate a discount percentage
One multiplier does the whole job. The mental route through 10%, how to read the percent off from two prices, why 20% then 10% is 28% and not 30%, and where the cents go missing.
What is the percent error formula?
Subtract, drop the sign, divide by the accepted value, multiply by 100. Worked lab examples, when percent error goes negative, and why it is not percent difference.
How to calculate a tip
Move the decimal one place left, then scale. The mental method for 15, 18 and 20 percent, a rate table, and the cent that binary floating point loses on a 41.30 bill.
How to add fractions
Match the denominators, add the numerators, carry the whole. The cross-multiply shortcut, mixed numbers like 2 3/4 + 1 2/3, and why converting to decimals bakes an error in before you start.
Why does 0.1 + 0.2 = 0.30000000000000004?
Because 0.1 has no exact form in binary, the same way 1/3 has none in decimal. What the machine really stores, why almost every calculator does this, and the arithmetic that does not.
Which calculator apps have no subscription?
Real prices from the live App Store listings. Also the finding we did not expect: the calculator with no ads at all is rated 3.02, and one full of them is rated 4.87.
How to split a bill with tip
An 84.50 bill, 18%, three people. The arithmetic, the mental shortcut, and the direction you have to round so the table does not come up two cents short.