L1 · Adding and subtracting decimals to solve problems

Learning goal

“I can add and subtract decimals accurately by lining up the decimal points, use estimation to check that my answer is reasonable, and solve multi-step problems with decimals in money, length and mass contexts.”

Align — to line up the decimal points (and therefore every place value) before adding or subtracting.

Estimate — a quick rough calculation with rounded numbers, used to predict and check an answer.

Sum — the result of an addition.

Difference — the result of a subtraction.

Worked example

4.86 + 2.37. Step 1 (estimate first): 4.86 is about 5 and 2.37 is about 2, so the answer should be near 7. Step 2 (align): write the numbers with decimal points in a column. Tenths under tenths, hundredths under hundredths. The decimal point is the fence post everything hangs on. Step 3 (add right to left): 6 + 7 = 13 hundredths - write 3, carry 1 tenth. 8 + 3 + 1 = 12 tenths - write 2, carry 1 one. 4 + 2 + 1 = 7 ones. Step 4: Sum = 7.23. The estimate said about 7 - reasonable. Say it plainly: lining up the decimal points is not a ritual - it is what makes tenths add to tenths and hundredths to hundredths.

Check yourself — explain it

We line up decimal points because...

Paired problem — example still visible

6.4 + 0.38 -> pad 6.4 as 6.40: 6.40 + 0.38 = 6.78

Faded completion — last step is yours

"12.9 + 3.45: estimate about 13 + 3 = 16; aligned: 12.90 + 3.45 = ___" -> 16.35

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz