Grade Six Mathematics
Answers to last week’s exercise
Exercise 1
Albert is 10 years old. a. Ginny has done 11 pages so far. b. Ginny has to complete 4.5 pages by Thursday. a. Linda is 0.67ft taller than Estrella. b. Estrella is 0.17ft taller than Sofia.
Matt swam 8.14 miles that week.
Exercise 2
Happy Sunday, boys and girls! I’m sure your week at school was amazing. I’m certain that you are prepared to learn! Last week, we examined the fundamentals of addition and subtraction of decimals. This week, we’ll be learning about the concept of multiplying and dividing decimals. Let’s begin!
Multiplication of a Decimal by Powers of 10
What are the powers of 10?
A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times. E.g. 10, 100, 1000, 10000 etc…..
To multiply by a power of 10, simply move the decimal to the right the same number of places as the number of zeros.
Let us look at examples below:
a. Calculate 5.34 x 10
→Since
Explanation there is one zero in the number ‘10’, we move the decimal one place to the right. We get: 53.4.
Therefore, 5.34 x 10 = 53.4.
b. Calculate: 46.334 x 100
Explanation: Since there are two zeros in the number ‘100’, we move the decimal two places to the right. We get: 4633.4.
Therefore, 46.334 x 10 = 4633.4.
Exercise 1
Calculate the product of the following: a) 7.843 x 100 b) 356.4 x 10 c) 353.87 x 10 d) 665.3 x 100 e) 674.84 x 1000 f) 335.35 x 10 g) 64.84 x 100 h) 4.1311 x 1000
Great job, boys and girls!
Are you aware that we can also multiply a decimal number by a whole number? Let’s examine how!
Multiplying decimals by whole numbers
Decimals can be multiplied by whole numbers by first multiplying as though ther e were no decimal. Next, determine how many digits there are in each number following the decimal. Finally, add the corresponding quantity of digits behind the decimal in the product.
Let us examine the examples below: Example 1. Multiply 5.7 x 5.
Without taking into account the decimal places, 1.25 is treated as the whole number ‘125’ in this case and multiplied by 15. The two numbers’ product is 1875. By counting the amount of places in the decimal 1.25, the product’s decimal point is finally added. The decimal point is positioned after two places, starting from the right, in the product 1875 because there are two decimal places in 1.25 and 0 decimal places in 15. As a result, the answer is 18.75.
Let us apply our knowledge by calculating the following:
Exercise 2
Calculate the product of the following:
a) 34.5 x 3 b) 23.1 x 4 c) 62.2 x 11 d) 841. 3 x 2 e) 635. 4 x 5 f) 22.11 x 6 g) 2.3 x 12 h) 23.4 x 5
Excellent work, pupils!
Let’s now learn how to divide decimal numbers by powers of 10.
Division of Decimal numbers by powers of 10
When dividing by a power of ten, the decimal point should be shifted to the left by the number of zeros in the power of ten. In contrast to when we multiply decimals by powers of 10, we move in the opposite direction here .For example, let’s calculate: 175.321 ÷ 100.
In this example, we can see that 100 has two zeros.
Decimal point should be moved two spaces to the left. So, 175.321 ÷ 100 = 1.75321
Example 2:
227.21 ÷ 1000
Here, we observe that there are three zeros in 1000. So, move the decimal point three places to the left. So 227.21 ÷ 1000 = 0.22721
Now let’s apply what we have learned and calculate the following:
Exercise 3
Calculate the following: a) 546.2 ÷ 100 b) 433.32 ÷ 10 c) 5136.1 ÷ 100 d) 6679.12 ÷ 1000 e) 11.2 ÷ 10 f) 764.237 ÷ 100 g) 121.3 ÷ 1000 h) 651 ÷ 100
Great job! Let’s learn how to divide decimals by whole numbers, just as we did with multiplication.
Division of decimals by whole number
● Step 1: First, write the division in the standard form. Start by dividing the whole number part by the divisor.
● Step 2: Place the decimal point in the quotient above the decimal point of the dividend. Bring down the tenth digit.