Adding, subtracting, multiplying and dividing decimals, with the number of decimal places under your control and divisions that come out exactly.
Grade 4–Grade 7 · every refresh draws a new set · answer key included
Decimal operations worksheets
Work out each answer. Line up the decimal points.
Decimal operations worksheets — answer key
Work out each answer. Line up the decimal points.
20 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview
Decimals are place value continued to the right of the point, and every rule pupils need follows from that — which is why the instruction on this page is “line up the decimal points" rather than anything about counting digits. Divisions here are built by multiplying first, so each one comes out exactly rather than running into a recurring tail, and multiplication is by a whole number, because decimal-by-decimal multiplication is a separate idea that deserves its own lesson.
Grade 4 to Grade 7, ages nine to thirteen. Adding and subtracting tenths and hundredths is Grade 4 and 5 work; multiplying and dividing by a whole number follows in Grade 5 and 6; three decimal places belong with measurement and money in Grade 6 and beyond.
Set the number of decimal places to match the topic — two places is money, three is measurement in metres. Keep the whole part small while the method is new: a pupil lining up 3.45 + 1.09 is learning the same thing as one lining up 73.45 + 21.09, with a third of the arithmetic. Add working space for column layout, because the whole difficulty of decimal addition is keeping the columns straight.
Right-aligning the digits instead of aligning the points is the classic fault, and it produces answers that are wrong by a factor of ten. The second is dropping the point in the answer to multiplication — the digits are right, the size is not. The third is treating 0.5 as smaller than 0.45 because it has fewer digits, which is a place value problem rather than an arithmetic one.