Mathematical Literacy Level 2 Module 4

Mathematical Literacy NQF 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Solving problems using ratio, rates and percentages Module 4 Downloaded from hlayiso.com Maths Lit NQF Level 2

Overview 4.1 Ratio 4.2 Rates 4.3 Percentages Downloaded from hlayiso.com Maths Lit NQF Level 2

Ratio Unit 4.1 Definition A ratio is a comparison of two or more numbers. • Ratios show us how a quantity is divided up into parts. ” • The numbers are of the same type or measurement. • The parts in a ratio are each exactly the same size. • You write ratios without their units. • A ratio of 5 : 3 is not the same as a ratio of 3 : 5 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.1 page 64 Unit 4.1 b) There are 12 female students and 16 male students in a class. What is the ratio of males to females? 1. Read the question carefully. Write down the quantities. 12 females; 16 males 2. Write them in ratio form. Remove the units. Check the order 16 : 12 3. Simplify if you can. Is there a number that divides into both sides of the ratio? 16 : 12 divided by 4 4:3 Downloaded from hlayiso.com Maths Lit NQF Level 2

Comparing ratios Unit 4.1 • Compare ratios by writing both ratios in their simplest form. • Different ratios that simplify to the same ratio are called equivalent ratios. • To find equivalent ratios, multiply or divide both quantities by the same number. • For example 100 : 600 is equivalent to 25 : 150 and 1 : 6. 100 : 600 25 : 150 ÷4 ÷4 ÷25 ÷25 25 : 150 1:6 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.2 page 65 Unit 4.1 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 4.1 Unit 4.1 Complete Exercise 4.1 on page 66 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Dividing quantities in a given ratio Unit 4.1 • When you divide a quantity in a certain ratio, calculate how many parts the quantity is divided into, and the amount of each part. > Example 4.3, page 67 A survey shows that a ratio of 5 : 1 students in a college earn money by working on the weekends, or don't earn money by working on the weekends. If there are 2 088 students in the college, how many earn money and how many do not? Downloaded from hlayiso.com Maths Lit NQF Level 2

Dividing quantities in a given ratio Unit 4.1 1. Write down the ratio 5:1 Write down the quantity of the whole. 2 088 2. Write down the total number of parts. 5+1=6 3. Divide the whole by the number of parts. 2 088 ÷ 6 = 348 This is the number in each part. 4. Find each quantity in the ratio. Multiply the number of parts by the amount in one part. 5 parts x 348 = 1 740 students who earn money 1 part x 348 = 348 students who do not earn money. Downloaded from hlayiso.com Maths Lit NQF Level 2

Using ratios to find unknown quantities Unit 4.1 • Ratios show a quantity is divided up or shared. • Using the ratio, you can find quantities of one amount if you know the quantity of another amount. > Example 4.4, page 68 In a bag of red and green sweets, the ratio of red sweets to green sweets is 3 : 4. If the bag contains 120 green sweets, how many red sweets are there? Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.4 page 68 Unit 4.1 a) Identify the known ratio and the unknown ratio. Use x for the unknown number in a ratio. red : green known ratio 3:4 unknown ratio x : 120 We don't know the number of red sweets if there are 120 green sweets. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.4 page 68 Unit 4.1 • Write both ratios as fractions in the same order Red Red x 3 = = Green Green 120 4 • Cross-multiply the fractions. x 3 = 120 4 4 × x = 3 × 120 4 x = 360 • Solve for x : 4 x ÷ 4 = 360 ÷ 4 x = 90 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.4 page 68 Unit 4.1 Check: • The answer should simplify to the known ratio. • Replace x with 90 in x : 120 90 : 120 ÷ 30 ÷ 30 3:4 • There are 90 red sweets in the second bag Downloaded from hlayiso.com Maths Lit NQF Level 2

Scale ratios Unit 4.1 • A scale ratio on a drawing or map shows the ratio of the length on the drawing to the length in real life. • The wall in this plan is 4 cm long in the drawing. • In real life, it is 400 cm, which is 4 m. Downloaded from hlayiso.com Maths Lit NQF Level 2

Scale ratios Unit 4.1 Solve scale problems in the same way as ratio problems. Tip: • It is convenient to use centimetres when we work with scale plans. • We usually convert real-life measurement to metres. • 100 cm = 1 m Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.5 page 70 Unit 4.1 a) The wall of a room has a length of 3,5 m. How long would this be on a scale drawing if the scale ratio is 1 : 100? b) The scale of a house plan is written as the ratio 1 : 75. What are the actual measurements of i) a wall of length 3 cm on the plan ii) a window 2 cm long on the plan iii) a passageway 5 cm long on the plan? Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.5 page 70 Unit 4.1 a) Convert all measurements to centimetres. 3,5 m is 350 cm Identify the known ratio and the unknown ratio. length on plan : length in real life known 1 : 100 unknown x : 350 • Write both ratios as fractions in an equality, keeping the same order x 1 = 350 100 • Cross-multiply 100x = 350 • Solve the equation for x. 100x ÷ 100 = 350 ÷ 100 x = 3,5 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.5 page 70 Unit 4.1 • Check the answer: 3,5 : 350 ÷ 3,5 ÷ 3,5 1 : 100 • Therefore the length of the wall on the plan is 3,5 cm. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.5 b) page 70 Unit 4.1 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 4.2 Unit 4.1 Complete Exercise 4.2 on page 71 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Rates Unit 4.2 Definition A rate is a special ratio where the two terms are in different units. ” • Rates tell us how one quantity changes in relation to another quantity. • Speed is the ratio of distance divided by time. • Speed = distance : time We represent speed in units of distance per unit of time e.g. km/h Downloaded from hlayiso.com Maths Lit NQF Level 2

Some different kinds of rates Unit 4.2 • Conversion rates: • between units of measurement e.g. 10 mm per cm • between currencies e.g. the exchange rate for the Rand • Cost rates: e.g. the unit cost of an item per kilogram • Consumption rates: litres of petrol used per 100 km travelled • Speed: units of distance per units of time e.g. km/h or m/s Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.6 page 73 Unit 4.2 a) Robert works in a warehouse packing goods for delivery. He can pack 15 crates per hour. How many hours will it take him to pack 90 crates? b) Sara is an athlete whose normal race speed is 20 km/h. If she runs at her normal race speed for 7 km, how long will it take her in minutes? Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.6 page 73 Unit 4.2 • Identify known rate and known rate: 15 crates per hour unknown rate. unknown rate: 90 crates in a hours • Write an equation with = 15 crates = 90 crates between the ratios. 1 hour a hours • Cross multiply 15 × a = 1 × 90 • Solve for the unknown a = 90 ÷ 15 = 6 hours value. • Check your answer. 90 ÷ 6 hours = 15 crates/hour Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.7 page 74 Unit 4.2 a) Store A sells potatoes at R21,95 per 3 kg bag and Store B at R90 for 15 kg. What is the unit price for each and which is the better buy? • Rates Store A: R21,95 per 3 kg Store B: R90 per 15 kg • Convert to unit rates R21,95 ÷ 3 = R7,32 per kg to the nearest cent R90 ÷ 15 kg = R6/kg • Store B has the better buy. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 4.3 Unit 4.2 Complete Exercise 4.3 on page 74 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Percentages Unit 4.3 Definition Percentages are fractions with a denominator of 100 • We write the sign % instead of using the denominator. ” • We usually calculate percentage using a fraction or a decimal. • For example, 25% of R150 can be written as 25 100 × 150 = 0,25 × 150 = R37,50 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.8 a) page 77 Unit 4.3 Downloaded from hlayiso.com Maths Lit NQF Level 2

Decrease or increase by a percentage Unit 4.3 Method 1 • New value = original value + % × original value (increase) • New value = original value - % × original value (decrease) • First add the percentage increase or decrease then add or subtract it from the original value. Downloaded from hlayiso.com Maths Lit NQF Level 2

Decrease or increase by a percentage Unit 4.3 Method 2 • New value = (100 + % increase) × original value • New value = (100 - % decrease) × original value • First work out the new percentage and multiply this by the original value. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 4.9 page 78 Unit 4.3 a) The price of a shirt costing R38 is increased by 15%. Calculate the new price. Method 1 Method 2 a) Find 15% of R38: a) Need 115% of R38: 15 115 100 × 38 = 5,7 100 × 38 = 43,7 Increase R38 by R5,70 Therefore R38 + R5,70 = R43,70 Downloaded from hlayiso.com Maths Lit NQF Level 2

Using percentages to compare numbers Unit 4.3 When you compare two fractions with different denominators, you can write them as percentages. Then you can compare them easily, since they have the same denominator of 100. > Example 4.10 page 80 A class has 26 students and 13 of them are boys. Express this as a percentage. Write a fraction with the total number 13 of students in the denominator. 26 13 1300 Multiply by 100 and simplify. × 100 = 26 26 The answer is a percentage = 50% Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 4.5 Unit 4.3 Complete Exercise 4.5 on page 80 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Further applications of percentages and rates Unit 4.3 > Example 4.11 page 81 A car park attendant is paid R42 per hour for a basic 40-hour week. Overtime is paid at time and a half. If he works 48 hours in a week, how much does he earn? Basic Pay: 40 × R42 = R1 680 Overtime page: 8 × 1,5 × R42 = R504 Total pay: R1 680 + R504 = R2 184 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 4.6 Unit 4.3 Complete Exercise 4.6 on page 81 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Module assessment Module 4 Complete Module assessment on page 83 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

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