Discover Mathematics P5: Term 1, Unit 1, Lessons 10–13
GoalSubtract decimals using models and regrouping, and check by adding.
New words
difference · the answer to a subtractionregroup · to trade 1 of a place for 10 of the next place on the rightinverse operation · an operation that undoes another one: adding undoes subtracting
Explanation
Subtraction takes a part away from a whole and finds what is left. A bar model helps: the whole is the long bar, the part we know is one piece and the missing part is the other piece. To subtract decimals, line up the decimal points and subtract place by place from the right. If the digit on top is smaller than the digit below, regroup: take 1 from the next place on the left and write it as 10 in the place you are working on. Add zeros at the end of the top number if you need them: 5.2 becomes 5.20. Check every answer by adding: the difference plus the part taken away must give back the whole.
Worked examples
A bar of 0.8 m of cloth has 0.35 m cut off. What is left? 0.8 is 8 tenths = 80 hundredths, so 80 − 35 = 45 hundredths: 0.8 − 0.35 = 0.45 m. Check: 0.45 + 0.35 = 0.8.
Ones
Tenths
Hundredths
after regrouping
4
11
10
−
1
7
5
=
3
4
5
Subtract 5.2 − 1.75. Write 5.20 − 1.75. Hundredths: 0 is less than 5, so regroup 1 tenth as 10 hundredths: 10 − 5 = 5. Tenths: now 1 is less than 7, so regroup 1 one as 10 tenths: 11 − 7 = 4. Ones: 4 − 1 = 3. So 5.2 − 1.75 = 3.45. Check: 3.45 + 1.75 = 5.2.
A bottle holds 1.5 L of water and Jana drinks 0.65 L. 1.50 − 0.65 = 0.85, so 0.85 L is left. Check by adding: 0.85 + 0.65 = 1.50.
Class activity
Bottle subtraction. Fill a bottle marked in 0.1 L steps (or use a measuring jug). Say how much water is in it, for example 0.8 L. Pour some out and measure what you poured, such as 0.3 L. Write the subtraction, say the answer and check by measuring what is left. Then check by adding the poured part to the part left.
Practice
1
Subtract 0.7 − 0.25.
0.70 − 0.25 = 0.45.
2
Subtract 6.4 − 2.8.
6.4 − 2.8 = 3.6. Check: 3.6 + 2.8 = 6.4.
3
Subtract 10 − 3.65.
10.00 − 3.65 = 6.35.
4
Mina says 9.5 − 4.75 = 5.25. Check her answer by adding. What is the right answer?
5.25 + 4.75 = 10, not 9.5, so she is wrong. The right answer is 9.50 − 4.75 = 4.75, and 4.75 + 4.75 = 9.5.
5
A jug holds 2 L. Then 0.75 L is poured out. How much is left in the jug?
