Add and subtract decimals up to two decimal places

What you will learn

• Add and subtract decimals up to two decimal places

Models used: number sentences, stories, tables.

Before you start

• Round decimals to a whole number, one or two decimal places

Connect the action to the maths

A ribbon is 0.35 m long. We join another 0.27 m. How can hundredths help us find the new length?

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Represent the first ribbon as 35 hundredths of one metre. Every little square stands for the same length: 0.01 m.

   0.35 m = 35 hundredths of a metre

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   35/100 = 0.35 = 35%

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Add 27 more of those same units. We now have 62 hundredths, which fill six rows and two extra squares.

   35 hundredths + 27 hundredths = 62 hundredths

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   62/100 = 0.62 = 62%

3. Keep tenths with tenths and hundredths with hundredths. Read each value with the heading above its column.

   In columns, five hundredths plus seven hundredths gives twelve hundredths. Exchange ten of them for one tenth. Keep two hundredths.

   0.35 + 0.27 = 0.62

   Keep tenths with tenths and hundredths with hundredths.

   Tenths	Hundredths
   3	5
   + 2	+ 7
   5 + 1 exchanged	2

4. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Subtraction undoes the join. Take the added 27 hundredths away from 62. The original 35 hundredths remain.

   0.62 − 0.27 = 0.35

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   35/100 = 0.35 = 35%

Worked example: An exchange when taking away

A 0.62 m ribbon is shortened by 0.27 m. How much remains?

1. Read the place heading before the digit. A counter in a different column has a different value.

   Start with six tenths and two hundredths. We need to take away two tenths and seven hundredths.

   Ones0

   Tenths6

   Hundredths2

   Thousandths0

   0.62 = 6 tenths + 2 hundredths

2. Keep tenths with tenths and hundredths with hundredths. Read each value with the heading above its column.

   Two hundredths are not enough to remove seven. Exchange one tenth for ten hundredths. The amount stays 0.62.

   Keep tenths with tenths and hundredths with hundredths.

   Tenths	Hundredths
   6	2
   5	12

   After the exchange, how many hundredths are available?

   12

3. Keep tenths with tenths and hundredths with hundredths. Read each value with the heading above its column.

   Remove seven of the twelve hundredths, then two of the five tenths. Read what remains.

   Keep tenths with tenths and hundredths with hundredths.

   Tenths	Hundredths
   5 − 2	12 − 7

   A 0.62 m ribbon is shortened by 0.27 m. How much remains?

   0.35

4. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   The answer is 0.35 m. Join 0.27 m back on to check the original length.

   0.35 + 0.27 = 0.62

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   35/100 = 0.35 = 35%

Common mistakes to discuss

• Lining up the right-hand ends. Align the decimal points, not the last digits. 5.4 + 3.47 is 8.87: the 4 is 4 tenths and must sit above the 4 tenths.

Check your understanding

• Add and subtract decimals by combining or exchanging equal-sized units.
• explain decimal addition and subtraction using like units
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.