58
Adding and subtracting decimal fractions
Textbook: Part 2, lesson 58, pp. 84–89
GoalAdd and subtract decimals; expansion by place values; laws of addition.
New words
column method · ustun usuliplace values · xona birliklariexpansion · yoyilmacommutative law · o‘rin almashtirish qonuni
Explanation
To add or subtract decimals, first make the number of digits after the point equal by adding zeros. Then write the numbers in a column so that point is under point. Add (subtract) as with natural numbers, ignoring the point, and put the point in the answer in the same place. A number can be expanded by place values: 5.28 = 5 + 0.2 + 0.08. For decimals the commutative law (a + b = b + a) and the associative law ((a + b) + c = a + (b + c)) also hold; they make calculation easier.
Worked examples
3.6 + 2.75: 3.60 + 2.75 = 6.35. 8.4 − 3.57: 8.40 − 3.57 = 4.83.
4.7 + 2.9 + 5.3 = (4.7 + 5.3) + 2.9 = 10 + 2.9 = 12.9. Convenient grouping makes a round number.
Class activity
“Shop receipt”: write the prices of 4 items in thousands of so‘m as decimals (for example, 3.5 thousand so‘m). Using the column method, find the total and how much more is needed to reach 20 thousand so‘m.
Practice
1
Calculate 7.45 + 2.8.
10.25
2
Calculate 15.2 − 6.75.
8.45
3
Calculate conveniently: 6.3 + 4.8 + 3.7.
14.8
4
Why must the points be under each other in the column method?
So that tenths are added to tenths and hundredths to hundredths.