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is 14. 3x-1=14 X=15 because (15-1=14) 3x5 is 15. A really good way to solve equations is by using baliking (2X + 3 = 14). The idea is to get x on by using inverse operations, Imagine 2x + 3 is on the left.If we subtract. 1 and 11 on the other. something from one sidem We have to subtract the same frang the other side. We can amount only use the equals sign when the equations are balanced. Now to get. to x, we need to divide 2. And divide the other side by 2. Solve: 7x + 4-25 Get x by itself using Operations. inverse 7x +4=25 write the equation 7x+4-4=25-4 Subtract 4 from both sister 7x=21 Simplify 7x=7=21=7 dinde both sides by I X=3 simplify the soulution 1² X=3 Solve the equation -2x +3=1. • its own set of scales Gut x by itself using riverse In sect pager -2x +3=4 write the equation. -2x +3-3=7-3 Subtract 3 from both sides. -2x - 2x=4 simplity vade both sides by -2 XA-2 simplify The Solution is x==2 Questions - 22/4/20 Q1: The cost to upgrade from a Standard seat to a seat with more legroom is £35. The standard seat casts 5 and the upgraded seat costs £357. F Complete the equation that describes. this £357 = 5 + £35 How much does the standard steat cost (s)? S= £322 Questions - 23/4/20= 01: The number of photos a memory Stick holds is the memory stick capsestry capachy (a) divided by the size of each photo The size of each photo is 5MB and the stick holds 1884 photos. Complete the equation that describes this, 1884 = C÷ 5 mb What is the memory sticks capacity (J? C=9420 MB' Papimeter-24/4/20 The perimeter is the total lenghth the edge of a shape. How can we calculate the perimeter of the shape? Well first we nenil to know need the munserments of the rectangle NEXT PAGE lenghth around hem GEM This rectangle is bcm long; and it's 4cm. wide. To calculate the perimeter, we need to add 6cm up the edges of the shape + встриставет ти ст. There is quicker way the perinater of e 2 sides of the length of the rectangle are the same. The 2 sides of the are also the width of the rectangle Same. to calculate rectangle, the 2x6cm = 12 m 2x 4 cm=8CM 12-cm +8cm = 20cm M = 4 10 y= 6m+4=28 3g-15=15 8m² -25=55 m = 10 9-6*6=13 19=42 +=148 6-3-5=11 92-14=76 $=10² Noah Says: I am thinking of a number (S). When I multiply it by 7 and add 23, the answer us 107. What is Noahs number? S=12✓ Simplify fractions. • Simplify the practions into its simplised form (0) c) ²/2 = 3 6 ) ² = = = = 2 ²8= 30 d) 1² = ² LO 욥. b) 122= RES A parallelogram is any quadrilateral with two pairs of parallel lines! Reclangles & Squares also have two pairs of paralled lines so they are a hype of parallelogram. The area of a parullatogram is the same as the area of the rectangle that shares its base and height. . area of parallelogram = base x height abxh height base It is important to use the perpendicular height not the slant height. arch / area = base x height What is the base? the base is gcm What is the height? The height is the measurement perpendicur Cat right-angles) to base. the height What is the area? 15 3cm. The base is 9cm The height is 3cm So areas аст бароит вст = 27cm² What is Volume? Volume is a meausurement of Space there is inside is inside a 3D object. Volume can and meter cubes, m3, There is a quiber of be measured in centermetere cubes, cm³ To fiord Volumes than by Counting subes. Start by couding the number of cubes in quicher way The Each first cow has the same number of cubes. row. so multiply VOLUME= number 다 195 by the amount the Question Q1 A refrigerater his volume 849.22.5 cm³ -has dy 65cm نہیں ہے ۔ Work out the depth d CM What springs to mind when you think of the word 'avacage? think usual, most common or You may perhaps. typical Did you know.ee the average length of a ginaffe's neck. Is 1.8cm 50% - ÷2 25% 74 10% - 10 1% - 7000 Are the widths and height in proption to the -percentages? prophon. It seems This widths and height are in that using the TV screens to represent the proportains should be ok. So why is it misleading? doen't see the width as the desilo Your еде factor of size. It lootks at the area of Soutlation's Image image books much aure than double the size of Weston's image. Here are the area's of the images. the area of the Southton image is four times bigger than the Weston image despite the proportion only being double If the percentages is double then the area the chordd aslo be doubled. image We want the image for soution to bea Simillar to the image for Weston so need use one scale factor for both width and height. To get a scale factor of 2 for area we need to multiply width and height by √2. MYF аксга ) 3-ви аху - дн g Select the value of [1]-20-11.5 L 12 [13. Суботу у суки ук у уч хол оч уж уйкут е у ут. ду ут от в уста m=3. .:: = уз. ухухух уче ухууу Yxykyry ym утургу губ 4 Answer: Write no Tnt S discow T Q5- Find the value of c 3532 6 n (0²)5 as a single power of n 1) Which one of these grids is shaded red and blue in the ratio 1.5? A For VA 14 every P V 77 Zo 14 I red theres & blue 1) am mathswatch 2) in your homelearning hooldat 2 (at the back, of my mather book) complete question 16-400 33/4-21½ = 3/1/20 Step 1 Multicidy 3 & 4 to get 12 12+3=2x5+1 1 4 Step 2) Add 12 and 3 to get 15 15 2X5+1 u 5 5 Step 3) Mutiply 2 and 5 to get 10 15 4 10+1 5 Steph) Add 10 and I to get 11 15 द f 2 2 ( Step 5) Least common mutiply of 4 and 5 is 20. Convert 15u and "s to fractions with denominator 20 1 75-44 40 20 7.5 1 Step 6) Since 20 and ( dencernator, So Sabtract them by Subtracting their numerators. uw have the same 20 75-44 20 1 Step 1 Subtract 175 from lill to get 31 75-44 20 31 20 Ratio - Summary - School alwrite the ratio 32:24 in it's simplest forum. LO: Consolidate the different types of ratio covered. (1) ta of people in a class are left handed T write the ratio of left handed people to right banded people C Expand and Simplify 2 (5a-b/+4 (26+a)=14a+bb • Work out 4356 ÷ 66 = Work out 600000=120 5.8 liters = ml •Work 4.9x5.1 11. Round 10.025 correct b 2 decimal places. 1₂ Solve 268 x + 3) = 54 2 • Workout 30-10*5 +40 Evaluate 2 What is 15 Enter Sinn g £900 3(x+9) + 2(x+5) 2(x+5) 4 Simplifiy tais fraction. S1 Ratio S2. Simplity (Keep the units Same) -ratio 12 * write as fraction. Make sure Denominatorrs are the same remove the nominators to simplify W Dave is making cookies He mixes flour, butter and 6.4.7 Dave uses 160 grams of butter. Work out how much flour and FB Sugar +*Guo : 160:40? in the rolio of Sugar S (4 : 1)ave flour - 240grams. Sugar-ho Dave usese and greed red sweets to In a bag there are blue Sweets, red sweets Sweets. The ratio of blue sweeks to green Sweets is 5:32 Share tho in the ratio 1:4 between Tim & Sam Tim will get f Sam will get t T : not to $ S h 30 W 661 make two rec A Square of area 36cm² is cut to -tangles. A & B Area = 36cm² The ratio & area A to area B is 2:1 Work out he dimensions of rectangles. A & B Rectangle It Lengh: Width: A CM. Rectangle B Lengh- Nidth: 18411 210,30. (4) 5) C Who to draw a portrait. Step 1:0 Hind 7/2 12 } Y=40+5. 22-2-1 y-31 ↓ S 7 = 4x=2+5 = -8 +5. f y=42+5 =4x-1+5. == 4+5. y=3x+4 Ds y=3xx -4. or y=3x-2-4. 04y=-6-4 big y = -10 €3-2-1 0 1 2 3 4 1 213 ↓ y=hx+5 y=4x+5 4 =4x0+5 1045 =5. y = 3x -4. very= 3x ze=4 0² y=3x=1-4 es y=-= 42 4xx We have used tricking with discminator of 100. 100. When for demandinator is 10X the sumber tells us the Het is equivalent to the fraction. percentage Yor example: 56 100 4 100 We can also find fraction and percentage equivalents. when the denominater is not lov. Brum Mordles percentage help us express fractions. Let's Chart with an't fractions. On't fractions have a numerator of I for paremple: 11 10 Let's find the percentage equivalent for t We short by "lowing I whole bar 100% | whole → 00/--- To find 1/2 use then split the whole bar into 2 equal part 1.2 equal park or 35 -> 100% Now we shade and shade and labil Iof the 2 the 2 equal parks. equal part or ½ → 100:2 = 50% X-50% ma-unit Bar models can also help us express -omit fractions as percendiges Non-unit fractions have a pomamater grater Han lo We are now to look at ratios using arrays. In this array, each circle represunt piece of fruit gring Apple- Orange- - We want the ratio of apples in cranges to be 3:5. This I apples in every Soranges means be table We can put the results Taumber of apples number of oranges. coloured in coloured q 15 Inequalities - Intero >= granter than Key Info 7 = greater than or equal to <= less than = less than or equal to Example: x 25 means d'Ewer is any XL Examples. than or mgacher • greater than 5 Cre equal to 5 Bundy realis Represent the inequality x2-3 the number line on + --4-3-2-10 2 5-4-3-2-1 Ө The uncoloured circle tells be -3. Represent the inequally x3 on the u 234 that it can't Colowed circle Jells us that it could be -3 us Represent the inequality number line 4 --6-5-4-3 -2 -1 65-4-3 Represent the inequality on the number line -56x44 x ²5 on the 2 3 o A 456 If -24x5 -2 x is an Finlar gec Possible answers: what are whole number -101236 s in is a whole number. 21 is greater than 20 5 is less time 60 What is the value of n? the values of Percentage Uez lafe LOB - How to calculate percentages of Numbers and quantites mentally! - one number aas a calculator of another without -How to write one number as of another with calculator. write one waye 36% 0 should the means Know 36 700 • Percentage whole. A percentage denominator of 100, but written in a diffrent can be used to show parks of a fraction with a percentage ST percentage thinky - six per cent of Per Cent means out of 100. So 36% is read as Hi hundred thirty six out of Here are some ways to calculat percentage exentally's to find 50% - halve the number To find 25% - halve the number and then halve the answer for just divide by W to find 20% - divide de by (double) 10 and Jinnes by 2 To find 60% - divide by 10 and links. u by To find 70% -divide by 10 and knives by 7 To find 90%-divide by 10 and linies by 9 To find 1'7- Just divide the number by 100] To find 10% - Just divide the munasher by 10. To find 75% - halve the number and balue the ancier and add the love answers logether More on the next page. To find 30%-divde by 10 and times by 3) To find 60% -divide by 10 and lives by To fud 80%-dwide by 10 and lives by 8. To find 5% -divide by 10 and halve the ansitier taba they like * Many percentages of account for be calcubled in your head, using some of the strategies. *For example, if you need to find 15% of number, fist fud By & 5% and add the tun Logela Heres how to find 612 To fid 60% duuride 120=10=12²x6 = 72 10 times by Next paye 176%% of 40 91762 70%857817 40 = 10=4x7=28 40=10=6=2=2 12 40-100=0-4 Answer: 28+2+0+4=750. Ŕ To write a number, such as a percentage of another halle fraction and then change the fraction to a percentage. Remember that a percentage is à fraction, with a denominator of 100. ."| scored 42 out of 50 34 = 84% 42x2 So 100 Test Scorer a -1 scored 6' out of lo 190 -425 out of 500 S 425 500 75 85-854 5 *If the denominator of the fraction cannot be multiplied / divided easily to make, 100, divide the numerator denominator on a calculator and multiply by the sto 100/ # Because a pe percondage can be written an decimal, there are diffrent fraction of a calculating percentages on a calculatoays of To The Fraction Wars Remember that a lout of lour of 32% of Hub 32 146 policarbage can be written 'divided by loo' 2. The Decimal Way Another Key into the calculator - 32 = 100 and think 146 = £40.72 is to write each percentage way 32 of 4146 0.32x+148 as a fraction as a decinate Mey into calculator - 0.32 x 146 = Answer Hose questions using on calculador! a) 38 of 1160 15.2 Fraction way b)45% of 22 Decimal 9.9 way 82% out of 58 Fraction way = 47.56 Decimal ung= 47.56 d) 21% of 26 kg 7600 A-5.46 e) Bk of za Ug hason! 23. Ully Decimal Way To increase an account by a percentage - first find the percentage of the aurouard •Hen add this to the original amount Iuercase £350 by 84%% • First End 8ls of £350. • Then add this te your original content. Kg in 84-100×350 = £294 £350+ £29h - Holly to decrease mot by a percentage: • First find the percentage ex of as the Then Subtract this from the original amount amount Decirace £3.50 by 84%. • First find 84% of £350? •Then subtract from the original amount 84400x350 = = 294 350-294756 -294 Ratio LO -the relationship between rotor and proportion -how to selve simple problems about rako in formal stratigies using Chow chich's to davide a quantity into two parts in ratio given Ratio is the relationship between two or more qualities. It compares "port with part numbers of LOOK AT THIS ROD: KA Radio - 3:2 If we compare the black parks and the white parts we may say '3 bbarll Squares for every 2 white squaress so the ratio of black to 312. 3 to 2 which is written