5 50% 9 1/2 3 33% NUMBER – Part 2 3.14 ¾ 0.001 Year 9 1.25 2345 99 %
Note 1: Adding and Subtracting Decimals Decimals are added and subtracted in the same way as whole numbers e.g. Sometimes we need to add extra zeros to show how decimals line up vertically
Note 1: Adding and Subtracting Decimals The reading on a cars odometer at the start of a trip is shown below. What will the reading be at the end of a 196.3 km journey? + 1 9 6 . 3 1 4 3 2 9 2 ALPHA IWB Ex2.03-2.04 pg 37-38 Ex 2.05-2.06 pg 40-42
Starter What fraction of a whole does 1 column represent? _______ 1/10 The shape below, outlined in green is 1 whole unit What fraction of a whole does 1 row represent? __________ 1/10 What decimal fraction of a whole does 1 square represent? __________ 0.01 How many small squares have both kinds of shading (purple)? __________ Write this as a decimal fraction of the whole square __________
Starter What fraction of a whole does 1 column represent? _______ 1/10 The shape below, outlined in green is 1 whole unit What fraction of a whole does 1 row represent? __________ 1/10 What decimal fraction of a whole does 1 square represent? __________ 0.01 How many small squares have both kinds of shading (purple)? __________ 42 Write this as a decimal fraction of the whole square __________ 0.42
Today we are learning to multiply decimals Multiplying decimals follows the same rules as multiplying whole numbers e.g. Multiply 4.1 x 2.9 4 x 3 = 12
MY CALCULATOR IS BROKEN!! Write the number in the display column as it should appear with the decimal in the correct position 2.73 1.408 1.89 21.6 36.04 12.093 16 Remember to estimate first! 0.9702 7.14 1.44 24.867 0 28.50
Note 2: Multiplying Decimals • Multiplying decimals follows the same rules as multiplying whole numbers e.g. 0.3 x 0.22 = 0.066 You might need to add an extra zero 1 dp + 2 dp ALPHA IWB Ex 2.08 pg 47 no calc Ex2.09-2.10 pg 48-49 = 3 dp
Fill the 1 litre jug. Pour out 0.3 litres into the small jug 3 times. There is now ___ L left in the large jug. 0.1 Add 1 small jug (0.3 L) to the large jug.
Starter If 5 rabbits eat 12.5 carrots in 5 days, how many carrots will 10 rabbits eat in 10 days? 50
Dividing Decimals by a whole number 7 .7 4 2 .42 20 10 1.25 125 Estimate first!
Try these! = 0.52 = 7.75 = 0.0068 = 0.655 = 0.071 = 0.01937
Dividing Decimals by a whole number Sometimes you need to add extra zeros to make division easier . 34 e.g. 0 .0 0
Note 3: Dividing Decimals e.g. Sometimes you need to add extra zeros to make division easier e.g.
Note 3: Dividing Decimals by decimals We can make the question simpler by dividing by a whole number instead. In order to do this we must move the decimal point in both number by the same amount e.g. has the same answer as has the same answer as ALPHA IWB Ex 2.14 pg 54 - 55 Ex2.16 pg 57 Ex 2.17 pg 58
Starter 0.22222222222 0.142857142.. 1 dp 0.5 Terminating Decimals 0.125 0.8 3 dp Recurring Decimals 0.09 2 dp
Note 4: Recurring Decimals Recurring decimals go on forever in a particular pattern. e.g. Sometimes a group of several digits repeat. e.g.
Note 4: Recurring Decimals _ . We use dots or a line to show a repeating pattern = 0.8 or 0.8 e.g. . . __ = 0.18 or 0.18 e.g.
Note 4: Recurring Decimals e.g. The dot is where the repeating pattern begins ALPHA IWB Ex 2.18 pg 60 Ex2.19 pg 61 These numbers have an infinite number of decimal places
Note 5: Rounding Decimals Finding an approximate answer is called rounding
Decide how many decimal places you will round to. This is the last digit of your answer. Rules for rounding • Look at the next digit (to the right of that place) • If the digit is 5, 6, 7, 8 or 9, round up. • If the digit is 0, 1, 2, 3 or 4, leave the digit unchanged • (round down) e.g. Round the following to 3 dp 0.1841 = 0.0128 = 0.4555 = 0.456 0.184 0.013
e.g. Nearest whole # 1 dp 214 21 cm 21.4 cm = _____ mm
In mathematics, we often get an answer more accurate than we need, therefore we must learn to round sensibly. TIP – don’t give answers that are more accurate than the question. e.g. ALPHA IWB Ex 2.20 pg 63 Ex2.21 pg 65-66 A sensible answer would be 34.7 m
Starter Write down the fraction shown in each of these diagrams Write these fractions in order, smallest to largest. 19/20 1/10 3/4 1/5 Draw a diagram to represent 2/5
Note 6: Sharing & Fractions We can compare measurements and numbers of objects using fractions 3 The total length of the post is ____ m
Note 6: Fractions on Number Lines Any number line can be split up into equal lengths to show fractions What fraction of a centimetre is one mm? Where is on this ruler ? ALPHA IWB Ex 7.02 pg 165-166 Ex7.03 pg 169 MATHLETICS ! Where is on this ruler ?
Note 7: Equivalent Fractions & Simplifying Fractions Sometimes two fractions can be represented by the same point on a number line. These two fractions are equivalent. x 2 = x 2 We can find equivalent fractions by multiplying (or dividing) the top and bottom by the same number.
Note 7: Equivalent Fractions & Simplifying Fractions (scaling up) Other possibilities are: x 2 = x 2 x 4 x 5 x 3
Note 7: Equivalent Fractions & Simplifying Fractions In math, we always want to give our answers in simplest form. We often need to change fractions to their equivalent simplest form. The fraction can be simplified to
Note 7: Equivalent Fractions & Simplifying Fractions What is the highest common factor of the numerator and denominator? 5 The fraction can be simplified to ALPHA IWB Ex 7.04 pg 173 Ex7.05 pg 176-177 MATHLETICS ! Simplify = = =
Note 8: Adding and Subtracting Fractions + = = + = = =
Note 8: Adding and Subtracting Fractions (add) (add) − = = = − = = =
Note 8: Adding and Subtracting Fractions with different denominators − − = = ALPHA IWB Ex 7.06 pg 179 Ex 7.07,7.08 pg 182 Ex7.09 pg 184-185 Puzzle pg 183 + + = =
Starter Each half could be cut into 3 equal pieces What fraction of the pizza is each slice? x x = x
Note 9: Multiplying Fractions This circle is split into 20 equal parts e.g. simplify
Try These! Simplify if possible = = = = = = = = = =
Multiplying a fraction by a whole number ALPHA IWB Ex 8.01 pg 189 #1 k-o, #2-4 Ex 8.02 pg 190-191 x 3 = e.g. Extension x 4 = x x = = =
Note 10: Reciprocals of Fractions Dividing by fractions To get the reciprocal of a fraction, just turn it upside down What do you get when you multiply a fraction by its reciprocal? e.g. x = = 1 (always)
Note 10: Reciprocals of Fractions Dividing by fractions To divide by a fraction, we multiply it by its reciprocal e.g. x = 20 slices of apples = 20 ALPHA IWB Ex 8.03 pg 192 Ex 8.04 pg 194 PUZZLE pg 195 e.g. x = =
Note 11: Mixed Numbers A mixed number is a combination of a counting number and a fraction smaller than a whole. e.g. What this really means is 4+
Note 11: Mixed Numbers An improper fraction is when our numerator is larger than our denominator. We can also write this using mixed numbers. x = e.g. (improper fraction) is the same as + + = 2 or (mixed number)
Note 11: Mixed Numbers Change to a mixed number e.g.
Try these – Change to Mixed Numbers = = = = = = = = = =
Note 11: Mixed Numbers e.g. Change to an improper fraction You try! = 4 + = + =
Note 11: Mixed Numbers In problems involving mixed numbers – change to an improper fraction first, then solve. At the end, turn the answer into a mixed fraction. e.g. ALPHA IWB Ex 8.05 pg 197-198 #2-8 Ex 8.06 pg 199 Ex 8.07-08 pg 202
Try These! Using mixed numbers = 8 - = - = = = = x = =
Note 12: Tenths, hundredth, thousandths e.g. Write as a decimal = 0.007 0.7 = 0.22 = = 1.1 = 4.01 = 75.42