042. Adding and Subtracting Decimals

Learning Intentions

• To understand that to add or subtract decimals, additional zeros might need to be entered for some decimal places
• add decimals
• subtract decimals

Pre-requisite Summary

• Understand the meaning of the decimal point
• Know the place value of tenths, hundredths and thousandths
• Be able to align numbers by place value in vertical calculations
• Understand that adding trailing zeros does not change the value of a decimal, for example $4.5=4.50$
• Recall basic addition and subtraction facts with whole numbers
• Understand regrouping in addition and subtraction

Worked Examples

Worked Example 1

a) Explain why $3.4$ can be written as $3.40$.
b) Rewrite $5.2+3.47$ so the decimal places line up.
c) Find the sum.

Worked Example 2

Add the decimals:
a) $4.6+2.35$
b) $12.48+3.7$

Worked Example 3

Add the decimals:
a) $0.75+1.206$
b) $8.09+0.4$

Worked Example 4

Subtract the decimals:
a) $7.5-2.34$
b) $15.08-6.7$

Worked Example 5

Subtract the decimals:
a) $3.200-1.48$
b) $10.05-0.678$

Worked Example 6

a) Calculate $4.7+2.38-1.05$.
b) Show how adding zeros helps line up the decimals.
c) State the final answer.

Problems

Problem 1

a) Explain why $6.3$ can be written as $6.30$.
b) Rewrite $2.8+4.56$ so the decimal places line up.
c) Find the sum.

Problem 2

Add the decimals:
a) $5.7+1.26$
b) $14.35+2.8$

Problem 3

Add the decimals:
a) $0.68+2.154$
b) $9.07+0.6$

Problem 4

Subtract the decimals:
a) $8.4-3.25$
b) $16.09-7.8$

Problem 5

Subtract the decimals:
a) $4.500-2.37$
b) $11.04-0.586$

Problem 6

a) Calculate $5.8+1.47-0.92$.
b) Show how adding zeros helps line up the decimals.
c) State the final answer.

Exercises

Understanding and Fluency

1. Rewrite each decimal with extra zeros so both numbers have the same number of decimal places:
   a) $3.4$ and $2.56$
   b) $7.09$ and $1.3$
   c) $0.8$ and $4.125$

2. Add the decimals:
   a) $2.5+1.4$
   b) $3.7+4.26$
   c) $5.08+2.3$

3. Add the decimals:
   a) $0.45+1.2$
   b) $6.34+0.58$
   c) $12.007+3.4$

4. Subtract the decimals:
   a) $5.8-2.1$
   b) $9.6-3.45$
   c) $14.02-7.3$

5. Subtract the decimals:
   a) $3.700-1.28$
   b) $8.05-0.679$
   c) $20.4-6.08$

6. Add or subtract as required:
   a) $4.6+3.27$
   b) $7.25-2.9$
   c) $0.906+1.04$

7. Add or subtract as required:
   a) $15.08+2.7$
   b) $6.3-1.456$
   c) $9.99+0.01$

8. Calculate:
   a) $3.5+2.48-1.2$
   b) $7.04-2.3+0.56$
   c) $10.5-4.75-1.2$

Reasoning

9. Explain why $4.7$ and $4.70$ have the same value.

10. A student writes
    [
    \begin{array}{r}
    3.4 \
    +2.56 \
    \hline
    2.90
    \end{array}
    ]
    Explain the mistake.

11. Explain why decimal points must line up when adding or subtracting decimals.

12. A student says $5.2-1.85=4.65$. Explain the error.

Problem-solving

13. A bottle contains $1.75$ L of juice and another contains $2.4$ L. How much juice is there altogether?

14. A runner completes $3.6$ km in the morning and $4.25$ km in the afternoon. What total distance does the runner complete?

15. A rope is $8.5$ m long. A piece of length $2.75$ m is cut off. How much rope remains?

16. A tank contains $12.08$ L of water. If $3.6$ L is used, how much water remains?

17. A shop sale totals $14.75, and a customer returns an item costing $2.80. What is the new total?

18. A packet weighs $0.85$ kg and another weighs $1.275$ kg. What is the combined mass?

Potential Misunderstandings

• Students may line up digits instead of lining up decimal points
• Students may think adding zeros to the end of a decimal changes its value
• Students may ignore place value and add tenths to hundredths incorrectly
• Students may forget to regroup when adding or subtracting decimals
• Students may drop the decimal point in the answer
• Students may subtract the smaller digit from the larger digit in each column instead of regrouping correctly
• Students may think the answer must have the same number of decimal places as the first number only
• Students may make errors when one decimal has fewer decimal places and needs trailing zeros added

Next: 043. Multiplying and Dividing Decimals by Powers of Ten