Discover Mathematics P5: Term 1, Unit 1, Lessons 6–9
GoalAdd decimals to thousandths by lining up the decimal points, and check the sum.
New words
regroup · to trade 10 of one place for 1 of the next place on the leftline up · to write numbers so that the same places are in the same columncheck · to test an answer with an estimate or another method
Explanation
To add decimals, write the numbers one under the other with the decimal points in a straight line, so that ones sit under ones, tenths under tenths and so on. If one number has fewer digits after the point, fill the gap with a zero: 12.5 becomes 12.500. Then add from the right, place by place, just like whole numbers. When a column makes 10 or more, write the ones digit and carry the tens digit to the next place on the left. Put the decimal point in the answer straight under the other points. Finally check: estimate the sum, or add in the opposite order.
Ones
Tenths
Hundredths
carry
1
1
4
6
8
+
2
7
5
sum
7
4
3
Worked examples
Add 4.68 + 2.75. Hundredths: 8 + 5 = 13, write 3 and carry 1. Tenths: 6 + 7 + 1 = 14, write 4 and carry 1. Ones: 4 + 2 + 1 = 7. So 4.68 + 2.75 = 7.43. Check by estimating: 5 + 3 = 8, and 7.43 is close to 8.
Tens
Ones
Tenths
Hundredths
Thousandths
1
2
5
0
0
+
3
2
7
4
sum
1
5
7
7
4
Add 12.5 + 3.274. Write 12.5 as 12.500 so that both numbers have three places after the point. Thousandths: 0 + 4 = 4. Hundredths: 0 + 7 = 7. Tenths: 5 + 2 = 7. Ones: 2 + 3 = 5. Tens: 1. The sum is 15.774.
One jug holds 0.865 L of water and another jug holds 0.459 L. Together: thousandths 5 + 9 = 14 (write 4, carry 1); hundredths 6 + 5 + 1 = 12 (write 2, carry 1); tenths 8 + 4 + 1 = 13 (write 3, carry 1); ones 0 + 0 + 1 = 1. The total is 1.324 L, which is more than 1 L. Check: 0.9 + 0.5 = 1.4.
Class activity
Add and check. Pick two prices or lengths with two or three digits after the point, such as 5.68 and 3.745. Add them on squared paper with the decimal points in one line. Then add them again in the opposite order. Both sums must be the same. Finish with a rounded estimate.
Practice
1
Add 3.45 + 2.8.
3.45 + 2.80 = 6.25.
2
Add 0.7 + 0.45 + 0.035.
0.700 + 0.450 + 0.035 = 1.185.
3
Hana writes 5.6 + 2.45 = 3.01. Find her mistake and give the right sum.
She lined up the right-hand digits (56 and 245) and not the decimal points. Estimate 6 + 2 = 8. The correct sum is 5.60 + 2.45 = 8.05.
4
Two ribbons are 2.75 m and 1.9 m long. They are joined end to end. How long is the new ribbon?
