It is important to understand how multiplying by works because not all numbers that we will be multiplying will be whole numbers. Here is an example of multiplying a decimal number by To multiply the decimal number 0. We move it from the hundredths column to the tens column. We must make sure that we show that the units column is worth zero by writing a zero in this space.
If there are no digits to the left of the decimal point, we always write a single zero digit in front of the decimal point to show this. When multiplying a number with more than one digit by , we need to make sure that we move every digit three places to the left. For example: We begin by moving the 3 three places to the left. We move it from the tenths column to the hundreds column. The 9 can then follow.
We move the 9 from the hundredths column to the tens column. From Dostoevsky's Crime and Punishment What does it mean to be ostensible? From Dickens's Bleak House What is behoveful?
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Wasn't it obvious? How could he be presented as a hero instead? In Romeo and Juliet , what are the different types of irony used? Um, what's irony? What is the main theme in Fahrenheit ? Why is Invisible Man considered a bildungsroman? Rank that eventually prompts him to disclose his own secret? What is a definition of short story?
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How about decimals and fractions to percents? What should I do if my teacher wants me to solve an inequality on a number line?
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Do you know where I can find help on the weekends or whenever? How do you convert metric measurements? I'm curious about converting Celsius to Fahrenheit, or Fahrenheit to Celsius. How do I convert from one to the other? In basic math, the fraction bar shows division. So why does this equation show multiplication instead of division?
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How do big rocks wear down over time? What does genetic recombination mean? Just answer these questions about them. You will check your answers later. Now do calculations A to I. Then check the answers you gave in question 5. Choose three different numbers between 3 and 11, and write them down below. Add your first number to your third number. Multiply the answer by your second number.
Multiply your first number by your second number. Also multiply your third number by your second number. Add the two answers. If you worked correctly, you should get the same answers in b and c. Do you think you will get the same result with numbers between 10 and , or any other numbers?
The fact that your answers for calculations like those in 7 b and 7 c are equal, for any numbers that you may choose, is called the distributive property of multiplication over addition. This can be described by saying that multiplication distributes over addition. Check whether the distributive property is true for the following sets of numbers:. Use the numbers in question 8 a to investigate whether multiplication also distributes over subtraction.
It is quite fortunate that multiplication distributes over addition, because it makes it easier to multiply. To add two numbers, the one may be written below the other.
Writing the numbers like this has the advantage that. This makes it possible to work with each kind of part separately. The numbers in each column can be added to get a new set of numbers:. Note that you can do the above steps in any order. Instead of starting with the units parts as shown above, you can start with the hundred thousands, or any other parts. Starting with the units parts has an advantage though: it makes it possible to do more of the work mentally and to write less, as shown below:.
To achieve this, only the units digit 4 of the 14 is written in the first step. The 10 of the 14 is remembered and added to the 30 and 80 of the tens column, to get We say the 10 is carried from the units column to the tens column.
The same is done when the tens parts are added to get only the digit "2" is written in the tens column, so it means 20 , and the is carried to the next step. A municipal manager is working on the municipal budget for a year.
He has to try to keep the total expenditure on new office equipment below R He still has to budget for new computers that are badly needed, but this is what he has written so far:. How much has the municipal manager budgeted for printers and computer screens together? How much, in total, has the municipal manager budgeted for chairs and tables? Work out the total cost of all the items the municipal manager has budgeted for. There are many ways to subtract one number from another. For example, R - R can be calculated by "filling up" from R to R The difference between R and R can now be calculated by adding up the numbers that had to be added to to get Another easy way to subtract is to round off and compensate.
The calculation can proceed as follows:. To do question 1, you may use any one of the above two methods, or any other method you may know and prefer.
Do not use a calculator, because the purpose of this work is for you to come to understand how subtraction may be done.
What you will learn here, will later help you to understand algebra. Check each of your answers in question 1 by doing addition, or by doing subtraction with a different method than the method you have already used. Another method of subtraction is to think of the numbers in expanded notation. Unfortunately, it is not possible to subtract in the columns now. However, the parts of the bigger number can be rearranged to make the subtraction in each column possible:.
The rearrangement, also called "borrowing", was done like this: 10 was taken from the 30 in the tens column, and added to the 4 in the units column. Describe the other rearrangements that were made in the above work. It is not practical to write the expanded notation and the rearrangements each time you do a subtraction.
However, with some practice you can learn to do it all in your mind without writing it down. Some people make small marks above the digits of the bigger number, or even change the digits, to keep track of the rearrangements they make in their minds. Calculate the difference between the two car prices in each case.
In each case, first estimate the answer to the nearest , then calculate. In each case, first estimate the answer to the nearest 10 , then calculate. Look again at the municipal budget on page How much money does the municipal manager have left to buy new computers? The four partial products can now be added to get the answer, which is R19 It is convenient to write the work in vertical columns for units, tens, hundreds and so on, as shown on the right above. In fact, if you are willing to do some hard thinking you can produce the answer with even less writing.
You can achieve this by working from right to left to calculate the partial products, and by "carrying" parts of the partial answers to the next column, as you can do when working from right to left in columns. It works like this:. The "4" that represents 40 is not written. It is kept "on hold" in your mind.
Again, only the "4" that represents 40 is written. The is kept on hold or "carried" to add to the answer of the next step. The work continues like this. You may use a calculator to check your answers for question 1.
Repeat the work if your answers are not correct, so that you can learn where you make mistakes. Then put your calculator away again. You may try to do the calculations in question 6 in this way. If you find it difficult, you may first write some of them up completely, and then try again to write less when you multiply. Use a calculator to check your answers for question 7. Redo the questions that you had wrong, so that you can learn to work correctly.
Use your correct answers for question 7 to give the answers to the following, without doing any calculations:. You want to buy some live chickens at R37 each and you have R available. How many live chickens can you buy in total? R is to be shared equally among 34 learners? How many full rands can each learner get? You want to buy live chickens at R47 each. You have R1 available. How many live chickens can you buy?
How much does one bag weigh? The number 26 was multiplied by a secret number and the answer was 2 What was the secret number?
This is an accurate sketch of the back of a house. The red line on the sketch is 70 mm long and it shows the width of the house. The blue line on the sketch indicates the height of the chimney. Do not measure the blue line now.
The width of the actual house is 5 mm, and the height of the chimney is 3 mm. In question 1 you knew that the amount is split into equal parts. You had to find out how many parts there are how many chickens. This is called grouping. In question 2 you knew that the amount was split into 34 equal parts. You needed to find out how big each part is how much money each learner will get. This is called sharing. In question 6 division was done for a different purpose than sharing or grouping.
Put your calculator away now. It is very important to be able to solve division problems by using your own mind. The activities that follow will help you to do this better than before. While you work on these activities, you will often have to estimate the product of two numbers. If you can estimate products well, division becomes easier to do. Hence, to start, do question 8, which will provide you with opportunities to practise your product estimation skills.
By what multiple of 10 should you multiply 27 to get as close to 6 as possible? A principal wants to buy T-shirts for the Grade 7 learners in the school. The T-shirts cost R67 each, and an amount of R8 is available. Do you think there is enough money to buy T-shirts for all the learners?
Explain your answer. How much money will be left if 20 more T-shirts are bought? The principal wants to work out exactly how many T-shirts, at R67 each, she can buy with R8 Her thinking and writing are described below.
Step 3 She has to rub out the one "0" of the on top, to make space. Step 4 She rubs out another "0". A polynomial of degree zero is a constant term. The grouping method of factoring can still be used when only some of the terms share a common factor A True B False. The sum or difference of p and q is the of the x-term in the trinomial.
A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials. J's study guide 1 card. What is the name of Steve on minecraft's name. Steel Tip Darts Out Chart 96 cards. More answers.
Q: What do thousandths add up to? Write your answer Related questions. What Does 28 And 25 Thousandths? What is. How do you add decimals to thousandths? What is the value of 4 in the number
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