These questions ask you to combine decimal quantities, find a difference, calculate a missing amount or carry out a short sequence of changes. The central check is always the same: tenths combine with tenths, hundredths with hundredths and thousandths with thousandths.
Line up the decimal points
Write the numbers vertically with their decimal points in one column. Add trailing zeros so every place you need is visible, then calculate from right to left. For addition, 6.4 + 0.23 becomes 6.40 + 0.23 = 6.63. For subtraction, 9 − 2.46 becomes 9.00 − 2.46 = 6.54; borrow across the zeros rather than subtracting only the visible whole-number digits. Keep the decimal point in the result directly below the aligned points.
| Question signal | Set-up |
|---|---|
| Combined, total or receives | Add the quantities after aligning their decimal points. |
| Left, change, falls by or removed | Subtract the part from the starting amount after padding both numbers to matching places. |
| What must be added to reach a total | Subtract the known addend from the total, then add your result back as a check. |
| Several changes | Perform them in the stated order and retain aligned places at every step. |
Before finalising the calculation, estimate its size. A sum should exceed each positive addend, while removing a positive amount should make the starting value smaller. This quick check catches a reversed operation or a decimal point placed in the wrong column without replacing the exact calculation.
Avoid these alignment traps
| Tempting route | How to reject it |
|---|---|
| Right-align the final written digits | That can place tenths under hundredths. Align decimal points first, then append zeros on the right where needed. |
| Treat a decimal part as whole units | A quantity of several tenths is still less than one whole. Rewrite the whole number with a decimal point and zeros before subtracting. |
| Subtract whole parts and attach the old decimal digits | Borrowing can cross the decimal point, so each place must be recalculated in its aligned column. |
| Choose addition whenever both quantities appear | Read the relationship: a remaining amount or change is a difference, while a combined amount is a sum. Check whether the result should grow or shrink. |
Try it
A recipe uses 3.7 cups of one mixture and 0.25 cups of another. Enter the total number of cups.
A runner's time falls from 12.8 seconds by 0.37 second. Enter the new time in seconds.
An account starts at 24.6 dollars, receives 7.85 dollars, then pays 3.2 dollars. Enter the final amount in dollars.