Mathematical Literacy Level 4 Module 2

Mathematical Literacy NQF 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Solving problems with time, conversions, rate, ratio and proportion Module 2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 2.1 Time, time-of-day formats, elapsed time, calendars and timetables 2.2 Measurement conversions 2.3 Solving problems involving different time zones 2.3 Performing workplace-related calculations involving ratios 2.3 Calculations involving proportion 2.3 Perform workplace-related calculations involving rates Downloaded from hlayiso.com Maths Lit NQF Level 4

Time, time-of-day formats, elapsed time, calendars and timetables Unit 2.1 Analogue time Analogue clocks use a mechanical method to keep time. Digital time Digital clocks usually show 24 hours. Downloaded from hlayiso.com Maths Lit NQF Level 4

Time, time-of-day formats, elapsed time, calendars and timetables Unit 2.1 Analogue time Analogue clocks show 12 hours on their faces and represent time by the position of hands on the dial. Digital time Digital clocks use electronic methods to keep time. Downloaded from hlayiso.com Maths Lit NQF Level 4

Time, time-of-day formats, elapsed time, calendars and timetables Unit 2.1 Analogue time The 24-hour day is divided into two periods of twelve hours: • Before noon: the morning, from 12 a.m. to 11.59 a.m. • After noon: the time from 12 p.m. to 11.59 p.m. Digital time 24-hour time does not use a.m. and p.m. • The times go from 0:00 to 23:59. • The time 24:00 is the same as 0:00 (midnight). Downloaded from hlayiso.com Maths Lit NQF Level 4

Recording times in minutes, seconds Unit 2.1 and milliseconds • Stopwatches are convenient digital handheld instruments. • Timing starts at the press of a button, and stops when the button is pressed again. The elapsed time is shown on the screen. Another press resets the stopwatch to zero. • Watches and cell phones often have stopwatches built into them. Downloaded from hlayiso.com Maths Lit NQF Level 4

Recording times in minutes, seconds Unit 2.1 and milliseconds • The stopwatch in the picture here recorded 12:38,56. • The minutes and the seconds are not decimal, because 1 minute = 60 seconds. • Milliseconds are decimal. 1 second = 1 000 milliseconds. • Example: 25 mins, 4 secs and 163 millisecs = 25 mins 4,163 secs Downloaded from hlayiso.com Maths Lit NQF Level 4

Did you know? Unit 2.1 Accurate timing of sports events is very important. The finishing times of sprint athletes can differ by only a few hundredths of a second. Downloaded from hlayiso.com Maths Lit NQF Level 4

Did you know? Unit 2.1 In international sporting events: • A loudspeaker behind each runner gives the starting signal. This is because sound takes time to travel and if an athlete is further from the starting pistol, the tiny time difference could make the difference between winning and losing the race. • A special camera detects when an athlete passes the finish line and shows the exact time. • Stopwatches are not used because the time it takes to press the stop button also makes the result inaccurate. Downloaded from hlayiso.com Maths Lit NQF Level 4

Calendars Unit 2.1 Downloaded from hlayiso.com Maths Lit NQF Level 4

Calendars Unit 2.1 • There are 365 days in a calendar year, except every fourth year, which is a leap year with 366 days. • The years 2008, 2012, 2016 and 2020 are all leap years. • There are 52 complete 7-day weeks in each calendar year, with 1 day left over (or 2 in a leap year). • The year is divided into 12 months. Each month has 30 or 31 days, except for February, which has 28 days (or 29 days in a leap year). Downloaded from hlayiso.com Maths Lit NQF Level 4

Conversions Unit 2.1 1 000 milliseconds = 1 second 1 minute = 60 seconds 1 hour = 60 minutes = 3 600 seconds 1 day = 24 hours 1 week = 7 days 1 year is about 52 weeks 1 year = 365 days (for the Earth to travel once around the Sun) 10 years = 1 decade 10 decades = 1 century = 100 years 1 000 years = 1 millennium (plural of “millennium” is “millennia”) Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.1 Unit 2.1 Complete Exercise 2.1 on page 38 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Calculating duration Unit 2.1 • When you calculate how long something takes, you need to add or subtract with hours, minutes and seconds. • Calculators use the decimal system, so remember to multiply or divide by 60 to get decimal answers. > Example 2.1 page 39 1. Thabo leaves home at 05:25 and gets to his destination at 11:40. How long did his trip take? • 05:25 to 06:00 is 35 mins, 06:00 to 11:00 = 4 hrs, 11:00 to 11:40 = 40 mins • 35 + 40 = 75 mins = 1 h 15 min • 4 h + 1 h 15 min = 5 h 15 min Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.1 page 39 Unit 2.1 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.2 Unit 2.1 Complete Exercise 2.2 on page 40 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Time management tools Unit 2.1 • Timetables and schedules can be used to list tasks, allocate time to tasks and sequence tasks. • Schedules may be worked out backwards, from the expected delivered date, or forwards, working out how long each stage will take from the time when production can start. Downloaded from hlayiso.com Maths Lit NQF Level 4

Time management tools Unit 2.1 Examples: • Public information boards used for hours of operation of businesses and government offices, airline timetables, train schedules, bus schedules, television programming, concerts and sporting events • A workplace schedule to list the work hours for employees and the operating hours for the public • Project management scheduling as the first step of a project such as constructing a building, developing a product or planning an entertainment event. Downloaded from hlayiso.com Maths Lit NQF Level 4

Time management tools Unit 2.1 1. List the tasks accurately, with detail. 2. Estimate how much time is needed for each task. Rather allow more time than less. 3. Determine how much time is available. 4. Allocate time to your earliest deadlines first, but don’t neglect the later ones. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.3 Unit 2.1 Complete Exercise 2.3 on page 43 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Tide timetables Unit 2.1 Tides The daily changes in the water levels of the ocean Tides timetables ” This table shows the times when the tides will be high and low. ” Downloaded from hlayiso.com Maths Lit NQF Level 4

Tide timetables Unit 2.1 Tide timetables are useful for: Calculating when it is best to sail a boat into shallow ports or under bridges. Planning coastal construction projects. Disaster clean-ups, e.g. an oil spill disaster Recreation, e.g. swimmers, hikers crossing rivers, surfers looking for big waves. Fishermen use information about the tides to improve their catches because certain species of fish gather during periods of high or low water. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.4 Unit 2.1 Complete Exercise 2.4 on page 46 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Measurement conversions Unit 2.2 To convert from one unit of measurement to another: Decide whether you are converting to a bigger unit or a smaller unit. ÷ x Converting to a Converting to a bigger smaller unit, your unit, your measurement will be measurement will be smaller, so you will bigger, so you will divide. multiply. Downloaded from hlayiso.com Maths Lit NQF Level 4

Measurement conversions Unit 2.2 Units of length 10 mm = 1 cm 100 cm = 1 m 1 000 m = 1 km Downloaded from hlayiso.com Maths Lit NQF Level 4

Measurement conversions Unit 2.2 Units of volume or capacity 1 000 ml = 1 ℓ 1 000 ℓ in 1 kℓ Downloaded from hlayiso.com Maths Lit NQF Level 4

Measurement conversions Unit 2.2 Units of mass 1 000 mg 1 in 0001 g ml = 1 ℓ 1 000 g in 1 kg1 0001ℓ in 0001kg kℓin 1 tonne Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.5 Unit 2.2 Complete Exercise 2.5 on page 47 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Using given conversion factors and Unit 2.2 tables Cooking conversions: • 1 teaspoon (tsp) = 5 millilitres (ml) • 1 tablespoon (Tbsp) = 15 millilitres (ml) • 1 cup = 250 millilitres (ml) Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.4 page 48 Unit 2.2 Write all the measurements in this scone recipe in millilitres: • 2 cups sifted flour • ½ tsp salt • 4 tsp baking powder • 2 Tbsp margarine • ¾ cup milk • 2 cups of flour = 2 × 250 ml = 500 ml • ½ tsp salt = ½ × 5 ml = 2,5 ml • 4 tsp baking powder = 4 × 5 ml = 20 ml • 2 Tbsp margarine = 2 × 15 ml = 30 ml • ¾ cup milk = ¾ × 250 ml = 187,5 ml Downloaded from hlayiso.com Maths Lit NQF Level 4

Metric and imperial conversions Unit 2.2 Although the imperial measurement system is not used in South Africa, you will see these units as they are often used in the United States and in some other countries. Length 1 inch (in) = 2,54 cm 1 foot (ft) = 12 inches = 30,5 cm 1 yard (yd) = 36 inches = 91,5 cm 1 mile (mi) = 1 760 yards = 1,6 km Volume and capacity 1 fluid ounce = 26 ml 1 pint = 20 fluid ounces = 590 ml 1 gallon = 4,5 litres (Imperial) = 3,8 litres (USA) Mass 1 ounce (oz) = 25 grams (g) 1 pound (lb) = 16 ounces (oz) = 450 grams (g) Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.5 page 49 Unit 2.2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.6 Unit 2.2 Complete Exercise 2.6 on page 49 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Solid and liquid conversions Unit 2.2 Solid volumes are usually given in cubic units and liquid volumes in ml, ℓ or kl. • 1 g of pure water has a volume of 1 ml • 1 kg of water has a volume of 1 litre You can use this as an approximation for some other liquids. • 1 000 mm3 = 1 mℓ • 1 cm3 = 1 mℓ • 1 000 cm3 = 1 ℓ • 1 m3 = 1 kℓ Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.6 page 50 Unit 2.2 1. A container in the shape of a rectangular prism has the dimensions: 7,5 cm × 10 cm × 3 cm. How much water can it hold? 1. 7,5 × 10 × 3 = 225 cm3 It can hold 225 ml of water. Downloaded from hlayiso.com Maths Lit NQF Level 4

Area and volume conversions Unit 2.2 10 mm 10 mm = 1 cm • Area: 10 mm × 10 mm in a square of 1 cm2. So there are 100 one mm squares in 1 cm2. • The conversion factor between mm2 and cm2 is 100. Downloaded from hlayiso.com Maths Lit NQF Level 4

Area and volume conversions Unit 2.2 10 mm • Volume: 10 mm × 10 mm × 10 mm in a block of 1 cm3. So there are 1 000 one mm blocks in 1 cm3. • The conversion factor between mm3 and cm3 is 1 000. • The conversion factor between cm3 and m3 is 1 000 000. Downloaded from hlayiso.com Maths Lit NQF Level 4

Area conversions Unit 2.2 Units of area Downloaded from hlayiso.com Maths Lit NQF Level 4

Volume conversions Unit 2.2 Units of volume Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.7 page 51 Unit 2.2 1. Calculate the volume (in cm3) enclosed by a box with a base size of 5 cm by 25 cm, and a height of 10 cm. 2. Convert this measurement into millilitres (mℓ). 3. Convert this measurement into litres (ℓ). 1. 5 × 25 × 10 = 1 250 cm3 2. 1 250 mℓ 3. 1,25 ℓ Downloaded from hlayiso.com Maths Lit NQF Level 4

Temperature conversions Unit 3.2 There are two main temperature scales: • °F, the Fahrenheit scale (used in America) • °C, the Celsius scale (part of the metric system) • The boiling point of water is 100°C and 212°F. • When water freezes, it measures 0°C but 32°F. • So the difference between freezing and boiling point is 100 degrees in Celsius, but 180 degrees in Fahrenheit. • To convert, use the formulae: °C = (°F − 32°) ÷ 1,8 (to find the temperature in degrees Celsius) °F = (°C × 1,8) + 32 (to find the temperature in degrees Fahrenheit) Downloaded from hlayiso.com Maths Lit NQF Level 4

Temperature conversions Unit 3.2 There are two main temperature scales: • °F, the Fahrenheit scale (used in America) • °C, the Celsius scale (part of the metric system) • The boiling point of water is 100°C and 212°F. • When water freezes, it measures 0°C but 32°F. • So the difference between freezing and boiling point is 100 degrees in Celsius, but 180 degrees in Fahrenheit. To convert, use the formulae: °C = (°F − 32°) ÷ 1,8 (to find the temperature in degrees Celsius) °F = (°C × 1,8) + 32 (to find the temperature in degrees Fahrenheit) Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.8 page 52 Unit 2.2 When Bongi leaves New York, it is 104°F. It is 8°C when she arrives early the next morning in South Africa. a) What was the New York temperature in degrees Celsius? b) What was the temperature in South Africa in degrees Fahrenheit? a) Use the formula °C = (°F − 32) ÷ 1,8 °C = (104 – 32) ÷ 1,8 = 72 ÷ 1,8 = 40°C Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.8 page 52 Unit 2.2 When Bongi leaves New York, it is 104°F. It is 8°C when she arrives early the next morning in South Africa. a) What was the New York temperature in degrees Celsius? b) What was the temperature in South Africa in degrees Fahrenheit? b) Use the formula °F = (°C × 1,8) + 32 °F = (8 × 1,8) + 32 = 14,4 + 32 = 46,4°F Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.7 Unit 2.2 Complete Exercise 2.7 on page 52 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Solving problems involving different Unit 2.3 time zones • When the sun is high in the sky in one part of the world, it is completely dark on the other side. • The Earth rotates so that the sun appears to move from the east to the west, rising in the east and setting in the west. • The world is divided into time zones, so that the sun will be at its highest point at approximately twelve noon wherever you are in the world. Downloaded from hlayiso.com Maths Lit NQF Level 4

Solving problems involving different Unit 2.3 time zones • Countries choose their time zones, so the zones often follow the borders of countries rather than following a strict vertical line. Some countries, such as South Africa, India and China, have chosen a single time zone, while others have multiple time zones. • In the past, time zones used Greenwich Mean Time as a reference time. The system is now called Coordinated Universal Time (UTC). Downloaded from hlayiso.com Maths Lit NQF Level 4

Solving problems involving different Unit 2.3 time zones • The times to the west are calculated by subtracting hours from UTC time. • The times to the east are calculated by adding hours to UTC time. • South Africa is at UTC +2, so the time is always 2 hours later than UTC. • India is UTC +5½, so it is 5½ hours later than UTC. • Argentina is UTC –3, so the time is three hours earlier than UTC. • There are 24 hours in a day, so there are 24 time zones. • Any place in the same time zone has the same clock time. • When you move from one time zone to the next one in an easterly direction, you need to change your clock one hour forwards. • If you move in a westerly direction you move it one hour backwards. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.9 page 53 Unit 2.3 Use the map showing the time zones on the next slide. 1. If it is midnight at UTC, what time will it be at: a) UTC +2 b) UTC –5 c) UTC +9 2. How many time zones are there in: a) South America b) Africa? 3. Why do you think most of Europe is on one time zone? 1. a) 2 o’ clock (in the early morning) b) 7 o’clock (in the evening) c) 9 o’clock (in the morning) 2. a) 3 time zones b) 4 time zones 3. Most of Europe is in the European Union (EU) and one time zone makes business and travel easier. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.9 page 53 Unit 2.3 Downloaded from hlayiso.com Maths Lit NQF Level 4

Daylight saving time Unit 2.3 • Many countries use daylight saving time. • In summer, they officially set their clocks one hour ahead of local standard time. This allows people to do all their activities an hour earlier, which gives more daylight in the evenings. • South Africa does not do this. • Countries including USA, Great Britain and Europe use daylight saving. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.10 page 55 Unit 2.3 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.8 Unit 2.3 Complete Exercise 2.8 on page 55 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Performing workplace-related calculations Unit 2.4 involving ratios • Ratios and proportions are used in activities such as mixing ingredients and using scale drawings and maps. • Ratio, proportion, rate and percentage all describe the relationship between two quantities, but don’t give you the actual numbers involved. • The statement ‘20% of the residents have been victims of crime’ tells you the percentage of residents, but does not give you the actual number of people. • Percentages tell you a fixed relationship between numbers, which can help you to solve problems. Downloaded from hlayiso.com Maths Lit NQF Level 4

Performing workplace-related calculations Unit 2.4 involving ratios Example ‘20% of the residents have been victims of crime’ • If there are 3 000 residents, then there are 20% × 3 000 = 600 people who have been victims of crime in that area. • If there are 10 000 residents, then 20% × 10 000 = 2 000 people have been victims of crime. Downloaded from hlayiso.com Maths Lit NQF Level 4

Ratios and different forms of ratio Unit 2.4 Ratio A ratio is a comparison of two or more numbers. We write the numbers with a colon (:) between them. ” Downloaded from hlayiso.com Maths Lit NQF Level 4

Ratios and different forms of ratio Unit 2.4 Example • If there are 8 students who travel by bus and 12 students who travel by taxi in one class, then we say we have a ratio of 8 to 12. • We can write this as 8 : 12. • Note that 8 : 12 is not the same as 12 : 8. • Ratios are written without units because the units on both sides are exactly the same. • A scale ratio on a map refers to measurement units. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.12 on page 58 Unit 2.4 Jabulani is a baker. He knows that biscuits always have the ratio of 3 : 2 : 1 for flour to butter to sugar. He needs to make as many biscuits as possible, and he has 4 cups of butter available. How much will he need of the other two ingredients? Downloaded from hlayiso.com Maths Lit NQF Level 4

Find missing numbers in a ratio Unit 2.4 Example We need to use two red tiles for every five blue tiles to make a certain mosaic pattern. This is a ratio of 2 : 5. We have 300 red tiles. How many blue tiles do we need? Solution: • We need to find the unknown part of the ratio: 2 red tiles : 5 blue tiles 300 red tiles : ? blue tiles Downloaded from hlayiso.com Maths Lit NQF Level 4

Find missing numbers in a ratio Unit 2.4 Example • Step 1: Find the total number of parts. The ratio 2 : 5 has 7 parts. • Step 2: How many in one part. 300 ÷ 2 = 150, so 1 part has 150 tiles. • Step 3: Multiply the answer by the ratio parts. 150 × 2 = 300 (already known) 150 × 5 = 750 • Step 4: Write down the answer. The answer is 750 blue tiles. Downloaded from hlayiso.com Maths Lit NQF Level 4

Simplifying and comparing ratios Unit 2.4 1. Can both numbers be divided by a common factor? 2. As with fractions, whatever you do to one number, you must also do to the other number so that the value remains the same. 3. To compare ratios, we write them as fractions. If the fractions are equivalent, then the ratios are equal. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.13 page 58 Unit 2.4 1. b) Write the following ratios in simplest form: 20 : 35 2. a) Are the ratios 2 : 5 and 12 : 16 equal? 1. b) 20 : 35 Divide both sides by 5. 4:7 1. a) 2 : 5 and 12 : 16 Write both ratios in their 2 : 5 and 3 : 4 simplest form. No, these ratios are not equal. Downloaded from hlayiso.com Maths Lit NQF Level 4

Share an amount in a given ratio Unit 2.4 Example Share 1 500 bricks in the ratio 1 : 2. • Number of parts is 3. • Divide total amount by number of parts 1 500 ÷ 3 = 500. • Multiply the answer by the ratio parts: 500 × 1 = 500 500 × 2 = 1 000 • The answer is 500 bricks and 1 000 bricks. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.14 page 59 Unit 2.4 • How many millilitres of herbal extracts and syrup will a pharmacist need to make 300 ml of a cough mixture if she mixes herbal extracts and syrup in a ratio of 1 : 5? • There are 1 + 5 = 6 parts altogether. • Divide 300 ml by 6 = 50 ml. • Multiply to find each part: 1 × 50 ml = 100 ml of herbal extracts 5 × 50 ml = 250 ml of syrup. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.9 Unit 2.4 Complete Exercise 2.9 on page 59 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Calculations involving proportion Unit 2.5 Proportion Proportion is an equation of two ratios or a statement that two ratios are equal. Examples: • Chefs need to scale recipes up or scale down using proportion. ” • Cleaners may dilute a cleaning fluid in a 1 : 8 ratio and use proportion to make the correct volume. • The number of builders needed to complete a job is inversely proportional to the length of time the job takes. • It is also possible to have two ratios that are in inverse proportion or indirect proportion to each other. Downloaded from hlayiso.com Maths Lit NQF Level 4

Direct proportion Unit 2.5 Definition Two variables are directly proportional to each other if, as one variable increases, the other increases in the same proportion. • If one value doubles, the other one also doubles • If one variable increases by 3 times, the other one also increases by 3 times. • If one variable decreases, the other variable also decreases in the same proportion. ” Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.15 on page 61 Unit 2.5 The cost of petrol is directly proportional to the amount of petrol purchased. If Bontle fills her car’s tank by purchasing 40 ℓ of petrol for R582, we can use this to calculate the cost of any other amount of petrol. Set up a proportion and calculate the cost of: a) 100 litres of petrol Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.15 on page 61 Unit 2.5 Downloaded from hlayiso.com Maths Lit NQF Level 4

Inverse proportion Unit 2.5 Definition When two values are inversely proportional to each other, as one value increases, the other decreases in the same proportion. • If one value doubles, the other value halves. • It takes 10 students 4 hours to carry boxes of books into the college, but it takes 20 students only 2 hours. • The number of students and the time taken are in inverse proportion to each other. • Since the ratio is ‘the other way round’, the fraction is written ‘the other way round’, or inverted. Downloaded from hlayiso.com ” Maths Lit NQF Level 4

Example 2.16 page 62 Unit 2.5 1. A farmer ploughs his land in 6 days using 5 tractors. How many days will it take to plough the same area with 3 tractors? • Write a proportion using x as the unknown: 5 tractors x days = 3 tractors 6 days • Note: the second fraction is inverted. • Solve the equation by cross-multiplying: 5×6=3×x x = 30 ÷ 3 = 10 days If he uses 3 tractors, it will take 10 days. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.10 Unit 2.5 Complete Exercise 2.10 on page 62 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Perform workplace-related calculations Unit 2.6 involving rates Rate A rate is a type of ratio, used in everyday situations. • Speed in km per hour ” • Cost per unit in rands per kilogram • Amount of medicine per millilitre • Cost rates of water and electricity services in rands per unit Downloaded from hlayiso.com Maths Lit NQF Level 4

Perform workplace-related calculations Unit 2.6 involving rates • The word ‘per’ shows that you are dealing with a rate. We can also write R15 per litre as R15/ℓ. • When you solve a rate problem you set up a formula to relate the quantities. Example Downloaded from hlayiso.com Maths Lit NQF Level 4

Steps to solve a rate problem Unit 2.6 Step 1: There are always three quantities in a rates problem, so there are three different formulae that you could use. Write them all down. Step 2: Read the problem carefully and choose the correct formula. Step 3: Substitute into the formula, making sure that you are using the correct units. Do the calculation. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.17 on page 63 Unit 2.6 1. Ayanda runs a race at a speed of 12 km/h. a) How long will it take her to run 15 km, if she keeps running at this speed? Write the time in hours and minutes. b) How long will she take to run 20 km at this speed? Write the time in hours and minutes. c) If she runs for 30 min, how many kilometres will she run? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.17 on page 63 Unit 2.5 Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.17 on page 63 Unit 2.5 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.11 Unit 2.6 Complete Exercise 2.11 on page 64 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Finding the best value for money Unit 2.6 • You can compare different food items to make sure you are getting the best deal. • To find out which size is better value for money, calculate the unit price for the product, e.g. the price per kilogram. • Then you can compare which is cheaper for the unit price, and thus better value for money. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 2.18 page 66 Unit 2.6 1. A shop advertises two different types of minced meat. Brand A of minced meat costs R55,95 for 4 kg. Brand B costs R66,80 for 5 kg. Which is better value for money? 1. Find the unit price (for one kilogram) for each brand of mince meat. Brand A: R55,95 ÷ 4 kg = R13,99/kg Brand B: R66,80 ÷ 5 kg = R13,36/kg Brand B mince meat is slightly cheaper per kilogram. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 2.12 Unit 2.6 Complete Exercise 2.12 on page 66 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

VIDEO: Application in the Workplace Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 2 Complete Module assessment on page 69 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

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