Math practice, built for the classroom
How many digits the first number has.
How many digits the second number has.
The basics, the vocabulary, and a worked example for everything in Calc Quest.
Whole number places (right to left): ones → tens → hundreds → thousands → ten thousands …
In 4,325: the 5 is in the ones place, 2 is in the tens place, 3 is in the hundreds place, 4 is in the thousands place.
Decimal places (right after the decimal point): tenths → hundredths → thousandths …
In 4.325: the 3 is in the tenths place, 2 is in the hundredths place, 5 is in the thousandths place.
Zeros in front of a whole number mean nothing. 007 = 7 — leading zeros don't add any value, they're just padding.
Zeros at the end of a decimal mean nothing changes. 4.5 = 4.50 = 4.500 — adding zeros after the last decimal digit doesn't change the value.
A zero in the middle is a placeholder, and it matters. In 105, the 0 holds the tens place — without it, 105 would become 15, a completely different number.
The numbers being added are called addends; the answer is the sum.
Line up digits by place value and add each column right to left. If a column totals 10 or more, write the last digit and carry the 1 into the next column.
Line up the decimal points so tenths sit under tenths, hundredths under hundredths — then add exactly like whole numbers.
The number you start with is the minuend; the number being taken away is the subtrahend; the answer is the difference.
Line up by place value, subtract right to left. If the top digit is smaller than the bottom digit, borrow 1 from the column to its left.
Line up the decimal points (pad with trailing zeros if one number has fewer decimal digits — remember, trailing zeros don't change the value), then subtract as usual.
If you're subtracting a bigger number from a smaller one (like 7 − 20), the answer is negative. Find the difference the normal way using the bigger number minus the smaller one, then put a minus sign in front.
The numbers being multiplied are factors; the answer is the product.
Multiply the top number by each digit of the bottom number, shifting one place left per digit, then add the partial results.
Multiply as if there were no decimal points at all, then count the total decimal digits in both original numbers and place the decimal point that many digits from the right.
Zero multiplied by any number is always zero — it doesn't matter how big the other number is.
The number being divided is the dividend; the number you divide by is the divisor; the answer is the quotient; what's left over (if anything) is the remainder.
Long division repeats: divide, multiply, subtract, bring down the next digit.
If the divisor has a decimal point, multiply both dividend and divisor by the same power of 10 to make the divisor a whole number first — this doesn't change the answer, it's the same as multiplying a fraction's top and bottom by the same thing.
If numbers don't divide evenly, keep going by adding a decimal point and zeros to the dividend (remember — adding zeros there doesn't change its value). Round the final answer to 2 decimal places if it doesn't end cleanly.
Zero divided by any non-zero number is always zero — you're sharing nothing between however many groups, so each group gets nothing.
Any number divided by zero is undefined — it isn't a number at all, not even zero. There's no way to split something into "zero groups," so the question doesn't have an answer.
Infinity (symbol: ∞) isn't a number you can count to — it's an idea for something that has no end or limit, going on forever. As you divide a number by smaller and smaller positive numbers, the answer keeps growing without ever stopping, which is why some people say it "approaches infinity" — but infinity itself is never actually reached, and it's not a valid answer to a division problem.
Tells you what order to solve a mixed expression in: Brackets → Orders (powers, like squares/cubes) → Division & Multiplication (left to right, whichever comes first) → Addition & Subtraction (left to right, whichever comes first).
Same rule, American naming: Parentheses → Exponents → Multiplication & Division (left to right, whichever comes first) → Addition & Subtraction (left to right, whichever comes first).