Number skills. Jemma Michael. This chapter will revise your skills in working with whole numbers, fractions and decimals.

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1 Number skills Jemma and Michael are playing a game of darts. It is Jemma s turn and she has thrown her darts as shown in the photograph. Can you calculate the number of points scored? Jemma and Michael continue to play the game. The results of their throws of darts in each round are shown in the table below. Jemma Michael double, 0, triple,, double, double, triple 0,, triple 0, double, double, 0, triple double,,, double, This chapter will revise your skills in working with whole numbers, fractions and decimals.

2 re you Maths Quest READY? for Victoria Are you ready? Try the questions below. If you have difficulty with any of them, extra help can be obtained by completing the matching. Either click on the icon next to the question on the Maths Quest CD-ROM or ask your teacher for a copy. Can you complete the following questions without a calculator? Calculate each of the following. a + b 0 + c d 0 Calculate each of the following. a b Calculate each of the following, rounding the answer to decimal places where appropriate. a b Evaluate each of the following. a + of b ( ) Find all the factors of: a 0 b List the first multiples of: a b Round each number. a to the nearest ten b to the nearest 00 Calculate each of the following, writing your answer as a mixed numeral if appropriate.. a + b.0 Calculate each of the following. a b.. 0 Calculate each of the following. a. +. b.. Calculate each of the following. a.. b.

3 Chapter Number skills Basic operations: non-calculator arithmetic In this chapter we review basic arithmetic as it applies to several topics. You are encouraged to attempt this chapter without a calculator. The following exercise revises the four basic operations, + and. See how many questions you can do without a calculator. A Basic operations: non-calculator arithmetic Calculate each of the following. a + b + c + d + e 0 + f + g h i j Calculate each of the following. a b c d e f g 0 h 0 i 0 j k 0 l Calculate each of the following. a b c d e f g h i Calculate each of the following. a b c 0 d 0 e f Calculate each of the following, rounding the answer to decimal places where appropriate. a b c d 0 e f g h i j 0 Calculate each of the following, rounding the answer to decimal places where appropriate. a b + c The four operations d e f g + + h i j k l The classrooms at Straight Line High School have rows of desks with desks in each row. How many desks are there in each classroom?. Basic operations GC EXCEL Tangle tables GCprogram Tables Tables EXCEL EXCEL The four operations (DIY) Mathcad Spreadsheet program Casio TI.. Spreadsheet Spreadsheet

4 Maths Quest for New South Wales Stephen was organising a Guess the number of Lollies competition for his school fete. He put lollies in the jar, but when he wasn t looking, his little brother and his friends ate of the lollies. How many were left? For their outstanding results in a recent Science project, six students were given a bag containing 0 smarties. If they were divided up evenly, how many would each student receive? 0 If each member of a class of students brings in $ as a donation to a charity, how much money would the class have raised? In a particular year level there are students. If are boys, how many are girls? Order of operations Evaluate +. In the previous exercise, you revised the four basic operations of addition, subtraction, multiplication and division. Mathematics, like music, is an international language so a few rules are needed to ensure that mathematicians find the same answer to a given question. Mathematicians have agreed on some rules about the order in which to do the four operations. Any part in grouping symbols must be calculated first. After that, division and multiplication must be done in the order that they appear in the question from left to right, and finally addition and subtraction must be worked from left to right. Write the question. + Use the order of operations to decide = + which part to calculate first and work it. (Multiplication) Complete the question. (Addition) = Evaluate + ( ) ( ). Write the question. + ( ) ( ) Use the order of operations to decide = + which part to calculate first and work it. (Grouping symbols) Work the next part. (Multiplication) = + Work the last part. (Addition and = Subtraction)

5 Chapter Number skills The order to work operations is: grouping symbols, division and multiplication from left to right, addition and subtraction from left to right. B Order of operations Evaluate the following. a + b + c ( + ) d ( ) e + f ( + ) g ( of 0) h + i 00 0 j + k + l Evaluate the following. a + ( of ) b ( + ) c ( ) d + e + ( ) ( ) f ( ) + g + + h + + i + ( of 0) j (- of 0) ( ) + multiple choice a is equal to: A 0 B C D b ( ) + 0 is equal to: A B C D State whether the use of grouping symbols makes a difference to the answer in each of the pairs of questions below. a + ( + ) b ( ) c of 0 ( of 0) d + ( + ) e + ( ) + f ( ) g + ( + ) h + ( ) + 0 Order of operations. Mathcad MATHS MATHS QUEST C H A L LL E N G G E E Find the number which is as much less than as it is more than 0. Using five s and no other numbers, combine them using addition, subtraction, multiplication, division and grouping symbols as needed, to produce each of the following values:,,,,,,,,. (Hint: = ) Show a quick way to find the value of ( ) without using a calculator. A snail is climbing the stem of a plant which is 0 cm tall. Each day from am to pm it climbs 0 cm and each night from pm to am it slides down 0 cm. Starting from ground level, how many hours will it take for the snail to reach the top?

6 Maths Quest for New South Wales The New York Museum of Modern Art discovered ed this after studying the Matisse painting Le Bateau for days! Answer the whole number questions to find the puzzle answer code A A D D G ( ) + = = 0 G H = I I ( + ) = 0 = N N = + = N O P = + S T U W = = E I S W

7 Chapter Number skills Factors, multiples, prime and composite numbers In order to understand the theory of numbers, we studied factors, multiples, prime numbers and so on, in chapter of Maths Quest. Here we revise a few of these terms. Factors A factor is a whole number that divides exactly into another whole number, with no remainder. A pair of numbers can have a highest common factor (HCF) or a lowest common factor (LCF). Multiples A multiple of a whole number is found when that number is multiplied by another whole number. A pair of numbers can have a lowest common multiple (LCM). Two numbers can t have a highest common multiple. Why not? Prime numbers A prime number is a number that has exactly two different factors, and the number itself. The number is not a prime number. Why? Are there any even prime numbers? Composite numbers A composite number is any number other than, which is not a prime number. A composite number has more than two different factors. The number is not a composite number. Find all the factors of. Find the factor pairs of the number. Remember that and the number itself are both factors. List the factors in order from smallest to largest.,,,,,,,,,,,, Find the highest common factor (HCF) of and. List the factors of.,,,,, List the factors of.,,, Compare the lists to find the highest factor which is in both lists. The HCF of and is.

8 Maths Quest for New South Wales Find the lowest common multiple (LCM) of and. List the first few multiples of.,,,, 0 List the first few multiples of.,,,, Find the lowest common multiple or the The lowest common multiple is. lowest multiple which is in both lists. One way of finding a common multiple is to multiply the two numbers together but this does not always give the lowest common multiple. List the numbers from to 0 inclusive which are prime numbers. List all of the numbers from to 0.,,,,,,,,, 0 Cross out all of the even numbers,,,,,,,,, 0 because they have a factor of. List the factors of the remaining numbers. List the numbers that have only two factors.,,,,,,, The prime numbers from to 0 are,, and.. A factor is a whole number that divides exactly into another whole number, with no remainder.. A multiple of a whole number is found when that number is multiplied by another whole number.. A prime number is a number that has exactly two different factors, and the number itself. The number is not a prime number.. A composite number is any number other than, which is not a prime number. A composite number has more than two factors.. The number is the exception. It is neither composite nor prime.

9 Chapter Number skills C Factors, multiples, prime and composite numbers Find all the factors of. Complete the following table, listing all of the factors for each of the numbers.. Number Factors Number Factors Find the highest common factor (HCF) of and 0. Using the table in question or otherwise, find the highest common factor (HCF) for each of the following pairs of numbers. a and b and 0 c 0 and 00 d and e and f and g and 0 h and List the first six multiples of each of the following. a b c d 0 e f g h Find the lowest common multiple of and. List the numbers from 0 to 0 inclusive which are prime numbers. Copy the table below into your workbook. Factors, multiples, prime and composite numbers GCprogram HCF and LCM GC HCF and LCM Mathcad program Casio TI. a b c Circle all of the prime numbers. Mark all of the composite numbers green. How many prime numbers are there between and 0 inclusively? EXCEL Sieve of Eratosthenes Spreadsheet

10 0 Maths Quest for New South Wales List the numbers in the table from question which are prime numbers. 0 Find the lowest common multiple of and. List all the multiples of from 0 to 0 inclusive. Find the highest common factor of 0 and 0. List the first 0 multiples of. What pattern do you notice? With the exception of, prime numbers can end in only one of five digits. What are they and why? Find the highest common factor of and. MATHS MATHS QUEST H C A L LL E N G G E E I have only four factors, two of which are and. I am less than 0. What number am I? I am a multiple of. I have and as two of my factors and I am between 0 and 0. What number am I? I have both and as factors and I am a multiple of. I am less than 0. What number am I? Squares and square roots Squaring a number means multiplying the number by itself. One way to this is to think about drawing the number as a square shape. = = squared can be written as. = can be written as =. = = squared can be written as. can be written as =. The opposite or inverse of squaring a number is to find its square root. The square root of a number is the number that, when multiplied by itself, gives the original number. The square root of is because = or =. If a square number is drawn as a square shape, as shown above, the square root is the side length of the square. The symbol for finding the square root is. For larger square roots use a calculator as it has a square root key on it.

11 Chapter Number skills Evaluate. A number squared means multiply the number by = itself. Evaluate, either mentally or using a calculator. = Evaluate: a b (round to decimal places). a Either use a calculator or compute in your head to find what number multiplied by itself equals. a = so = b Use a calculator to find what number multiplied b. by itself equals. Write one more decimal place than required. Round to the required number of decimal places.. ( decimal places) The answer to worked example can be checked. The answer to should be bigger than because = and it should be less than because =. The answer. is between and.. When a number is multiplied by itself, the answer is a square number.. The square root of a number is the number which multiplies by itself to give the original number. D Squares and square roots Rewrite the following using the shorthand method. a b c d 0 0 e f Evaluate the following squares. a b c d e f g h Squares and square roots EXCEL Squares and square roots (DIY) Mathcad Spreadsheet

12 Maths Quest for New South Wales WorkSHEET. Evaluate the following. a a b c d e f g 00 h 00 i 00 j 00 k 00 l 00 Evaluate the following, rounding the answer to decimal places. b a b c 0 d Evaluate the following. a + b c + 00 d + 00 e f + Darts competition Have you played darts before? Different regions on the dartboard score a different number of points. The diagram shows the regions where you can score double points or triple points. There are a number of different games you can play with various rules for scoring. Jemma and Michael are playing a game where you must throw a double before you can start scoring. Each player takes turns to throw darts in each round. A player starts with a score of 0 and subtracts their score obtained in each round until they reach 0. The winner is the person who reaches 0 first. The only condition is that the last throw must land on a double score. What is the highest score that can be obtained on the throw of one dart? If Jemma s first throw hit a double, the second hit 0 and the third hit triple, what is her overall score at the end of round? (Remember to start from 0.) Michael s darts hit, and double. What is his overall score at the end of round? Use the table on page to calculate each person s overall score at the end of each round. For Jemma to win in the next round, she needs to finish with a double. List three different sets of positions on the board that her darts must hit for her to win in this round. Repeat question for Michael. If you were playing and your overall score was, list possible scenarios for how you could win in the next round. 0 double points (0) 0 triple points (0) 0 0 (bullseye)

13 Chapter Number skills Calculate The result of 0 is. Is the following statement true or false? =. List all the prime numbers from 0 to 0 inclusive. List all the factors of. Use the order of operations to calculate 0 +. Evaluate of ( ). Write down the highest common factor of and 0. Write down the lowest common multiple of and. 0 Evaluate of, rounding the answer to decimal places. Estimation Sometimes it is convenient to be able to make calculations without a calculator: an estimation of the answer is enough. Rounding to the first digit means that many calculations can be done mentally and with very little effort. Estimation works in the same way, whichever of the four basic operations are being used. Find an estimate for. Write the question. Round each number to the first digit Calculate the answer in your head if = 0 possible. Otherwise do it on paper. The estimate can be checked by using a calculator. However, that is not the purpose of a quick estimation. An estimation is a way of checking a calculation. For example, if the worked answer to is., then an estimation of 0 is reasonably close and suggests that the working is correct. It is not necessary to round numbers from to, because it is easy enough to multiply or divide by these numbers.

14 Maths Quest for New South Wales 0 A total of people have accepted the Mad Hatter s invitation to a tea party. He expects that each of the guests will drink about cups of tea. Estimate how many cups of tea the Mad Hatter needs to be ready to pour. Decide which operation is required, and use it to write a mathematical expression. Round to the first digit. (Don t round numbers less than.) 0 Multiply. = 0 Write a sentence. The Mad Hatter needs to be ready to pour approximately 0 cups of tea. Note: If the people each drank cups of tea, 0 would not be enough because has been rounded down to 0. Three people, or if the Mad Hatter is counted, have not been included. Estimation is also a good way to make sure that the answer to a question worked on a calculator looks right and makes sense.. To estimate, round to the first digit and work out the answer to the simplified problem.. Estimating is a way of checking calculations.. An estimation is an approximate answer. E Estimation. Find an estimate for each of the following. a b + c d e f g h 0 i j 0 k l 0 m ( + 0) n o 0 p ( 0) ( + )

15 Chapter Number skills Complete the table below with the rounded question, the estimated answer and the exact answer. The first one has been worked. Question Rounded question Estimated answer Exact answer a b c + + d 0 e 0 f g h 0 + i j Estimation EXCEL The four operations Mathcad Spreadsheet 0 If people came to a school social and each paid $ admittance, find an estimate for the amount of money collected. Find an approximate answer to each of the worded problems below. Remember to write your answer in a sentence. a A company predicted that it would sell cars in a month at $ each. About how much money would they take in sales? b A tap was leaking ml of water each hour. Approximately how many millilitres of water would be lost if the tap was allowed to leak for hours? c The Year cake stall sold pieces of cake for cents each. How much money did they make? d Steven swam laps of a 0 m pool and, on average, each lap took him seconds. If he swam non-stop, for approximately how many seconds was he swimming? e An audience of people attended a silverchair concert at the Sydney Entertainment Centre and paid $ each for their tickets. How much money was taken at the door? f A shop sold articles at $.0 each. How much money was paid altogether? g On Clean Up Australia Day, people volunteered to help. If they each picked up pieces of rubbish, how many pieces of litter were collected altogether?

16 Maths Quest for New South Wales Addition and subtraction of fractions Simplify. A fraction has two parts, the top part which is called the numerator and the bottom part which is called the denominator. Numerator Denominator A proper fraction has a numerator that is less than the denominator such as. An improper fraction has a numerator that is greater than this line means divide the denominator such as. A mixed numeral contains a whole number part and a proper fraction part such as. Equivalent fractions are fractions that are equal in value =. When adding and subtracting fractions, the denominators must be the same. Write the question. Find the lowest common denominator; that is, the lowest multiple common to both. Write both fractions with the same denominator; that is, the lowest common denominator. Subtract. (Simplify if appropriate.) = = = Calculate +. When adding and subtracting mixed numerals, they can be changed to improper fractions first, then worked as shown in worked example. However, it is often better to add or subtract the whole number parts first and then the fraction parts. Write the question. + Write the fraction parts with the same denominator. = + Add the whole number parts. = + Add the fraction parts. = Convert the improper fraction part to a mixed numeral. = + Add the whole number parts. =

17 Chapter Number skills A rough estimate can be found by adding or subtracting the whole number. For example, + =, so + >. If the first fraction part is smaller than the second fraction part when subtracting fractions, there is more than one way of finding the answer. One way is to convert the numbers to improper fractions first. Another is to use the method of equal addition, as shown in Maths Quest. Both methods are shown in the following worked example. Calculate. Method : Converting to improper fractions Write the question. Notice that is bigger than, so convert both = - fractions to improper fractions. Write both fractions as equivalent fractions with the = - 0 same denominator. Subtract the fractions. = Convert to a mixed numeral. = Method : Using the method of equal addition Write the question. Write both fraction parts with the same denominator. = - Add the appropriate fraction to both fractions to make = ( ) ( ) the second mixed number equal to a whole number. = - (Add - in this example.) 0 0 Subtract. = To add or subtract fractions with the same denominator, add or subtract the numerators.. To add or subtract fractions with different denominators, make the denominators the same by using equivalent fractions, then add or subtract.. To add or subtract mixed numerals, either: (a) change the mixed numerals to improper fractions then add or subtract, or (b) add or subtract the whole numbers, then the fraction parts.

18 Maths Quest for New South Wales EXCEL Spreadsheet Mathcad Adding and subtracting fractions Adding and subtracting fractions.. F Addition and subtraction of fractions Simplify the following fractions, working from left to right. a b - - c d Simplify the following fractions, writing the answer as a mixed numeral if appropriate. a + b + c + + d Simplify the following. a + b + c - d e + f - g - + h Simplify and evaluate. (Remember to write your answers as mixed numerals.) a + b - c d - e f g + - h - i + j - k - + l m n Calculate the following. a + b c d e + f + g + h + i j + Calculate the following. a - b c 0 d 0 If Mary eats of a block of chocolate for afternoon tea, and after dinner, how much of the block has she eaten altogether? Seven bottles of soft drink were put out onto the table at a birthday party. How much soft drink was left over after bottles were consumed? Frank has a part-time job at the local newsagency. If he spends of his pay on comic books, and on lollies, what fraction of his pay does he have left over? 0 In my class, of the students ride their bikes to school, catch the bus and the rest get a lift. What fraction of my class get a lift to school? A Year class organised a cake stall to raise some money. If they had 0 whole cakes to start with, and sold cakes at recess and then at lunch time, how much cake was left over?

19 Chapter Number skills Multiplication and division of fractions To multiply fractions, multiply the numerators and multiply the denominators. It does not matter if the denominators are different. Change the mixed numerals to improper fractions before multiplying. Simplify. Write the question. Change the mixed numerals to improper fractions and cancel if possible. Multiply the numerators and multiply the denominators. = = - - Change to a mixed numeral and simplify if appropriate. = Find. Division is the same as multiplying by the second fraction turned upside down. Write the question. Change mixed numerals to improper fractions. = Change to and tip the second fraction, = ( and tip), and cancel if appropriate. Multiply numerators and denominators. = Simplify if appropriate. =. To multiply fractions: (a) change mixed numerals to improper fractions (b) cancel if appropriate (c) multiply numerators and multiply denominators (d) change the answer to a mixed numeral if appropriate and simplify.. To divide fractions: (a) change mixed numerals to improper fractions (b) change the to and tip or invert the second fraction ( and tip) (c) cancel if appropriate (d) multiply numerators and multiply denominators (e) change the answer to a mixed numeral and simplify if appropriate.

20 0 Maths Quest for New South Wales EXCEL.0 Spreadsheet Mathcad Multiplying and dividing fractions Multiplying and dividing fractions G Simplify the following. Multiplication and division of fractions a b c d e f g - h 0 0 i - j - k - l Simplify the following. a b - c d e - - f g h i Simplify the following. a b c - d e f g - h - i Find the following. a - b c 0 d e f g h 0 i Simplify the following. a b c d e f g h i j - - k l m - n o Find of. ( of has the same meaning as multiplying)

21 Chapter Number skills An assortment of lollies is to be divided evenly among children. a What fraction of the total number of lollies will each child receive? b How many lollies will each child receive? Sam has been collecting caps from all around the world. If he has a total of 0 caps and of them are from the USA, how many non-american caps does he have? In the staff room there is of a cake left over from a meeting. If members of staff would all like a piece, what fraction will they each receive? 0 Year s cake stall raised $0. If they plan to give to a children s charity, and to a charity for the prevention of cruelty to animals, how much will each group receive and how much is left over? Number skills 00 WorkSHEET GAMEtime. Evaluate the answer to 0 +. Is the following statement true or false? + ( ) (0 ) = Write all the common factors of and 0. Write down the lowest common multiple of and. Write the highest common factor of and 0. Evaluate 0. + ( 0 ), correct to decimal places. A shop sold newspapers at $.0 each. Approximately how much money was taken? 0 Simplify + -. Write fractions that, when they are multiplied together, give a result of. 0 What are the missing numbers? =??

22 Maths Quest for New South Wales Fractions to decimals, decimals to fractions It is useful to be able to convert fractions to decimals and vice versa. Divide the numerator of the fraction by the denominator and round the answer to decimal places if it is not otherwise specified. Convert the following fractions to decimals, giving exact answers or correct to decimal places where appropriate. a b a Write the question. a Rewrite the question using division. = - 0. Divide, adding zeros as required. ).0 Write the answer. = 0. b Write the question. b Convert mixed numerals to improper fractions. Rewrite the question using division. = Divide, adding three zeros so that the answer is initially to decimal places. - = -. ) Round the answer to decimal places. -. A calculator can also be used to convert fractions to decimals by entering and rounding the answer correctly. When changing a decimal to a fraction, rewrite the decimal as a fraction with the same number of zeros in the denominator as there are decimal places in the question. Simplify the fraction by cancelling. If the decimal has a whole number part it is easier to write it in expanded form.. = + 0.

23 Convert the following decimals to fractions in simplest form. a 0. b. Chapter Number skills a Write the question. a 0. Rewrite as a fraction with the same number of zeros in the denominator as there are decimal places in the question. Simplify the fraction by cancelling. Write the answer. = b Write the question. b. Rewrite the decimal in expanded form. = + 0. Write as a mixed numeral with the same number of = + - zeros in the denominator as there are decimal places in the question and cancel. Write the answer. = 00 = 00. When changing fractions to decimals, divide the numerator of the fraction by the denominator and round the answer to decimal places if it is not otherwise specified.. When changing a mixed numeral to a decimal, write it as an improper fraction before dividing.. When changing a decimal to a fraction, rewrite the decimal as a fraction with the same number of zeros in the denominator as there are decimal places in the question.. Simplify the fraction by cancelling. H Fractions to decimals, decimals to fractions a Convert the following fractions to decimals, giving exact answers or correct to decimal places where appropriate. a b c d - e - f - g h - i - j Show your answers to parts a d of question on a number line. Fractions to decimals, decimals to fractions Mathcad b Convert the following mixed numerals to decimals, correct to decimal places. a b c d e f g h - i j - 0 EXCEL Converting fractions to decimals Spreadsheet

24 Maths Quest for New South Wales EXCEL Converting decimals to fractions Spreadsheet Convert the following decimals to fractions in simplest form. a 0. b 0. c. d. e. f 0. g.0 h. i. j 0.0 k. l.0 m. n.0 o.0 p. q.0 r 0.00 Of the people at a school social were boys. Write this fraction as a decimal. GC GC program program Casio Converting fractions to decimals TI Converting fractions to decimals Alfonzo ordered a pizza to share with three friends, but he ate 0. of it. What fraction was left for his friends? Alison sold the greatest number of chocolates in her Scouting group. She sold of all chocolates sold by the group. Write this as a decimal, correct to decimal places. On a recent science test Katarina worked the bonus question correctly as well as everything else, and her score was. What is this as a decimal 0 value? 00 Addition and subtraction of decimals Adding and subtracting decimals is a very useful skill, particularly when working with money. When adding and subtracting decimals, be sure that the decimal points are lined up one underneath the other. Find Write the numbers one underneath the other with the decimal points lined up and fill the spaces with zeros. Then add as for whole numbers putting the decimal point in the answer directly under the decimal points in the question Find..0. Write the numbers one under the other with the larger number on top and the decimal points lined up. Add in the required zeros and subtract using one of the methods shown. Method Method

25 Chapter Number skills When adding and subtracting decimals, be sure that the decimal points are lined up one underneath the other. I Addition and subtraction of decimals Find the following. a. +. b. +. c. +. d. +. e.0 +. f. +.0 g.0 +. h i j k l m n Find the following. a.. b.. c.. d..0 e.. f 0.. g..0 h i.. j. k..0 l.. Adding and subtracting decimals EXCEL Adding decimals Mathcad Spreadsheet multiple choice a b The difference between.0 and. is: A. B. C. D. The sum of. and. is: A. B. C 0. D. EXCEL Adding decimals (DIY) Spreadsheet Calculate the following. a b c 0..0 d e..0 f. g h.. i 0.. j EXCEL Subtracting decimals Spreadsheet Round to the nearest whole number to find an approximate answer to the following. a b.. +. c.. +. d. +.. a On a recent shopping trip, Salmah spent the following amounts: $., $0., $0. and $.. How much did he spend altogether? b If Salmah started with $00.00, how much did he have left after the trip?

26 Maths Quest for New South Wales Dagmar is in training for the school athletic carnival. The first time she ran the 00 m it took her.0 seconds. After a week of intensive training she had reduced her time to. seconds. By how much had she cut her time? Kathie runs each morning before school. On Monday she ran. km, on Tuesday she ran.0 km, she rested on Wednesday and on both Thursday and Friday she ran. km. How many kilometres has she run for the week? Multiplication and division of decimals Multiplication The method for multiplying decimals is almost the same as for multiplying whole numbers. Ignore the decimal point when multiplying, count the number of digits after the decimal point in each of the multiplying numbers, then add these numbers together to find the number of decimal places in the answer. It is often a good idea to use your estimating skills with decimal multiplication to check that the answer makes sense. 0 Calculate, giving an exact answer,. 0.. Write the numbers with the larger one on top. Multiply, starting with the last digit and ignoring the decimal point. Count the number of digits after the decimal point in each of the multiplying numbers and use this total as the number of decimal places in the answer. There are decimal places in. and in 0. so there will be decimal places in the answer =.0

27 Chapter Number skills Division When dividing decimals, make sure that the divisor (the number being divided by) is a whole number. If the divisor is not a whole number, but a decimal, either:. write the question as a fraction and multiply the numerator and the denominator by an appropriate multiple of 0, or. multiply both parts of the question (dividend and divisor) by an appropriate multiple of ten. Then set out the question as for division of whole numbers and divide as for whole numbers, placing the decimal point in the answer directly in line with the decimal point in the question. Calculate: a. b Give answers correct to decimal places. a Write the question as shown, adding zeros to one more decimal place than is required. Write the decimal point in the answer directly above the decimal point in the question and divide as for short division. Write the question and answer, rounded to the required number of decimal places.. a ) ( decimal places) b Write the question. b. 0.0 Multiply both parts by an appropriate multiple of 0 so that the divisor is a whole number. (In this case 00.) = (. 00) (0.0 00) =. Divide, adding zeros to one more decimal place than required. Write the decimal point in the answer directly above the decimal point in the question and divide as for short division. Write the question and answer, rounded to the required number of decimal places.. ) ( decimal places)

28 Maths Quest for New South Wales. When multiplying decimals, count the number of digits after the decimal point in each of the numbers being multiplied and add these together to find the total number of decimal points in the answer.. When dividing, make sure that the divisor is a whole number.. When the divisor is a decimal, make it a whole number either by: (a) writing the question as a fraction and multiplying the numerator and denominator by a multiple of 0, or (b) multiplying both dividend and divisor by an appropriate multiple of ten.. When dividing decimals by a whole number, place the decimal point in the answer directly in line with the decimal point in the question. EXCEL EXCEL. Spreadsheet. Spreadsheet Mathcad GAMEtime WorkSHEET Dividing decimals Multiplying and dividing decimals 0 Multiplying decimals a Number skills 00. b Multiplication and division of decimals Calculate the following giving an exact answer. a. 0. b.. c.. d 0.. e.0 0. f.. g.. h. i.. j 0.. k.. l m.00 n. 0.0 o. 0.0 Calculate the following. Give answers correct to decimal places. a. b. c.0 d. e. f.0 Calculate the following. Give answers correct to decimal places, where appropriate. a. 0. b c d e. 0.0 f g h i j k l Evaluate the following, giving the answer correct to decimal place. a b.... c d... + J multiple choice a (. +..) is equal to: A. B. C. D.0 b Rounded to decimal places, (0...) is equal to: A.0 B. C 0. D. Round each of the following to the nearest whole number to find an estimate. a.. +. b.. 0. c d. 0.. A group of Year students were going on an excursion to the Planetarium. If the total cost is $.0, how much would each student have to pay?

29 Chapter Number skills summary Copy and complete the sentences below using words from the word list that follows. There are four basic mathematical operations. These are addition, subtraction, and. The correct order in which operations should be completed is: grouping symbols division and multiplication and. A number has only two factors, one and itself. A number that divides exactly into another number is a. If a number isn t a prime, then it must be or a number. A of a number is one in which that number has been multiplied by another whole number. Multiplying a number by itself is known as the number. The inverse of squaring a number is to find its. can be used to find an approximate answer. 0 In a fraction, the is the top number and the is the bottom number. A fraction that also has a whole number part is called a. A fraction is one in which the numerator is less than the denominator. In an improper fraction the numerator is than the denominator. Fractions that are equal in value are known as fractions. When adding and subtracting decimals, the must be lined up underneath one another. W ORD LIST multiple greater addition mixed numeral squaring factor multiplication composite subtraction decimal points prime estimation numerator square root denominator equivalent division proper

30 0 Maths Quest for New South Wales CHAPTER review A Calculate the following. a b c d 0 e f 0 B C D E F Use the order of operations to calculate the following. a + b ( of 0) + c 0 ( + ) d + e 0 + f + + a List all prime numbers from 0 to 0 inclusive. b List all the factors of: i ii iii 0. c Find the HCF of the following pairs of numbers: i and ii and 0 iii and. d List the first four multiples of: i ii iii 0. Evaluate the following. a b c d e f g h i. j 0.0 k. l. Use your estimation skills to find approximate answers for the following. a 0 b c 0 d Simplify the following. a + b + c G H H I J test yourself CHAPTER d e + f + Simplify the following. a b c - d e - f Convert the following fractions to decimals (correct to decimal places). a b c d e f Convert the following decimals to fractions in simplest form. a 0. b 0. c. d.0 e. f.0 0 Evaluate the following. a. +. b.. c.0 +. d. 0.0 e..00 f Evaluate the following, correct to decimal places where appropriate. a. b.0. c. 0. d.. e f