64
Multiplying decimal fractions
Textbook: Part 2, lesson 64, pp. 110–115
GoalMultiply a decimal by a decimal; laws of multiplication.
New words
multiplication rule · ko‘paytirish qoidasidistributive law · taqsimot qonuniassociative law · guruhlash qonunicommutative law · o‘rin almashtirish qonuni
Explanation
To multiply two decimals, multiply them as natural numbers ignoring the points. In the product, separate from the right as many digits as there are digits after the point in both factors together. If there are not enough digits, write zeros on the left: 0.05 · 0.3: 5 · 3 = 15, 3 digits in all, so 0.015. For decimals the laws a · b = b · a, (a · b) · c = a · (b · c) and (a + b) · c = a · c + b · c also hold. They make calculation easier: 7.5 · 3.2 + 7.5 · 6.8 = 7.5 · (3.2 + 6.8) = 75.
Worked examples
2.4 · 1.5: 24 · 15 = 360; 2 digits in total: 3.60 = 3.6. A rectangle 4.5 cm by 2.2 cm has area 45 · 22 = 990 → 9.90 = 9.9 cm².
0.08 · 0.07: 8 · 7 = 56, 4 digits in all: 0.0056 (two zeros written on the left). Convenient calculation: 0.25 · 9.6 · 4 = 9.6 · (0.25 · 4) = 9.6 · 1 = 9.6.
Class activity
“Finding the area”: measure the width and length of a notebook page with a ruler (for example, 20.9 cm and 14.8 cm), write them as decimals, multiply to find the area and round it to tenths.
Practice
1
Calculate 1.6 · 0.4.
0.64
2
Calculate 12.5 · 0.08.
1
3
Calculate conveniently: 6.8 · 2.5 + 6.8 · 7.5.
68
4
Why is 0.2 · 0.3 = 0.06 and not 0.6?
2 · 3 = 6, and there are 2 digits in the two factors together, so 0.06.