Mathematical Literacy Level 3 Module 2

Mathematical Literacy NQF 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Use an appropriate calculator to perform calculations and solve problems in a workplace context Module 2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Overview 2.1 Recognise and practise the use of functions and characters on an appropriate calculator 2.2 Adding and subtracting integers on a calculator 2.3 Use a calculator to perform calculations on fractions 2.4 Use a calculator to perform calculations on decimals 2.5 Use a calculator to perform calculations on percentages Downloaded from hlayiso.com Maths Lit NQF Level 3

Recognise and practise the use of functions and characters on an appropriate calculator Unit 2.1 Downloaded from hlayiso.com Maths Lit NQF Level 3

Recognise and practise the use of functions and characters on an appropriate calculator Unit 2.1 Get to know how your calculator works. Identify and find: • the numbers (usually in the middle, with zero at the bottom). • basic maths symbols (usually on the right). • the percentage key • the square root key • the equals key Downloaded from hlayiso.com Maths Lit NQF Level 3

Recognise and practise the use of functions and characters on an appropriate calculator Unit 2.1 Get to know how your calculator works. • To add, subtract, multiply or divide, press a number key, an operation key and another number key. • Press equals for the answer. • Basic calculators do the operations in the same order that you press the keys. • Scientific calculators follow the BODMAS order of operations. Downloaded from hlayiso.com Maths Lit NQF Level 3

Squares, square roots, cubes, cube roots Unit 2.1 3 2 Exponent Base Power Squares • The number that is being raised to the power is called the base. • The number that the base is raised to is called the exponent. • 3 squared is written 32 and means 3 × 3. • On a calculator, press the number key, followed by key. • For example, 16 gives an answer of 256 (without pressing the equals key) Downloaded from hlayiso.com Maths Lit NQF Level 3

Squares, square roots, cubes, cube roots Unit 2.1 3 2 Square roots • The number that is squared is the square root. • So the square root of (4)2 is 4. • On a calculator, enter the number and then Downloaded from hlayiso.com Maths Lit NQF Level 3

Raising numbers to higher powers Unit 2.1 3 cubed is written 33 and means 3 × 3 × 3. On a calculator, • you can multiply the number by itself twice or • square the number and multiply the answer by the number again or • multiply the number by itself and press the equals key: Press 5 × 5 =. Your answer is 25. You have worked out 52. Press = again. The screen shows 125. You have worked out 53. Press = again. The screen shows 625. You have worked out 54. Press = again. The screen shows 3 125. You have worked out 55. Downloaded from hlayiso.com Maths Lit NQF Level 3

The memory keys Module 2.1 Memory keys allow you to keep a number in the memory and then recall it. • Use to add a number to the memory. • Use to subtract a number from a number already in the memory. • Press once to show the number stored, • Press MRC twice to clear the number from the memory. • The letter M appears at the top of the display to show that the display number has been stored in the memory. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.2 page 25 Downloaded from hlayiso.com Maths Lit NQF Level 3

Clear and clear all keys Module 2.1 Some basic calculators have a and a key. • The key (or key) clears everything on the display. • The key stands for 'clear entry' and it clears the last thing that was entered. Decimal points and separators • Type in a decimal number e.g. 10 000,99. The calculator display often shows a decimal point, not a decimal comma. • Some calculators show markings (separators) between groups of three digits to make the display number easier to read. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 2.1 Unit 2.1 Complete Exercise 2.1 on page 19 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Adding and subtracting integers on a Module 2.2 calculator Examples of negative numbers: Temperatures below Changes in position up Financial freezing point and down calculations Downloaded from hlayiso.com Maths Lit NQF Level 3

Adding and subtracting integers on a calculator Module 2.2 Adding a negative is the same as subtracting. 28 + (-16) = 28 - 16 = 12 Subtracting a negative is the same as adding. 54 - (-20) = 54 + 20 = 74 • Changing the sign of numbers: • Some calculators have a key. • On others, you need to use the key before or after the number. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.3 page 21 Unit 2.2 1. Caleb enters the lift of a tall building at the ground floor (level 0). He goes up 5 floors, down 6 floors, down another 3 floors and up 17 floors. He then leaves the lift. Which floor is he on? 2. A warehouse has stock of 267 chairs and receives an order for 500 chairs. How many chairs are left in stock? 1. Use the calculation 0 + 5 - 6 - 3 + 17 = 13. He is on the 13th floor. 2. 267 - 500 = -223 chairs. The warehouse needs to find 223 chairs from somewhere else. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 2.2 Unit 2.2 Complete Exercise 2.2 on page 22 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions Types of fractions • A fraction represents part of a whole that has been divided into equal pieces. 7 • If you cut a board into 10 equal pieces and use 7, then you use 10 seven tenths of the board. • The denominator of 10 shows the whole board is divided into 10 equal parts Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change a mixed number to an improper fraction: 2 15 3 3= 3 × 5 = 15 = 15 5 5 5 1 Multiply the whole number by the denominator of the fraction. Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change a mixed number to an improper fraction: 2 15 2 3 + 5 5 5 2 Add this answer to the original numerator. Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change a mixed number to an improper fraction: 2 17 3 5 5 3 Write the new numerator over the fraction line and the original denominator. Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change a mixed number to an improper fraction: Multiply the whole number by the denominator of the 1 fraction. 2 Add this answer to the original numerator. Write the new numerator over the fraction line and the 3 original denominator. Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change an improper fraction to a mixed number: 14 14 ÷ 3 = 4 3 with a remainder of 2 1 Divide the numerator by the denominator. Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change an improper fraction to a mixed number: 14 2 4 3 3 So there are 4 whole numbers with 2 thirds left over. Write the whole number and the remainder, if any, as a 2 left over fraction. Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on fractions To change an improper fraction to a mixed number: 1 Divide the numerator by the denominator. Use the whole number answer as the whole and the 2 remainder, if any, is the left over fraction. Downloaded from hlayiso.com Maths Lit NQF Level 3

Equivalent fractions Unit 2.3 Equivalent fractions Equivalent fractions are fractions with the same value, but different numbers in the numerator and denominator. To make an equivalent fraction, multiply the ” numerator and denominator by the same number. Downloaded from hlayiso.com Maths Lit NQF Level 3

Equivalent fractions Unit 2.3 Equivalent fractions Equivalent fractions are fractions with the same value, but different numbers in the numerator and denominator. ” Multiplying by is the same as multiplying by 1, so the value of the fraction has not changed. So and are equivalent fractions. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.18 page 42 Downloaded from hlayiso.com Maths Lit NQF Level 3

Adding and subtracting fractions Unit 2.3 Method 1 1. To add and subtract fractions, you must find a common denominator first. 1 2 1 2. + + lowest common denominator (LCD) is 6 2 3 6 3 4 1 = + + 6 6 6 8 4 = = 6 3 1 =1 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Adding and subtracting fractions Unit 2.3 Method 2 (with a calculator) 1. Treat each fraction like a separate division calculation. (1 ÷ 2) = , (2 ÷ 3) = (1 ÷ 6) = , . 2. Put the answers of the calculations into the calculator's memory. 3. Add to or subtract from the memory and press MRC to find the answer. You should get 1,333... Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.6 page 25 Unit 2.3 Calculate 1 2 3 + − 2 5 7 1. Divide first fraction and store 1 2 the answer in the memory. 2. Divide second fraction and 2 5 add answer to memory. 3. Divide third fraction and subtract answer from 3 7 memory. 4. Recall answer from memory. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.9 page 27 Unit 2.5 1. A restaurant makes a fruit smoothie from 1 2 cup yoghurt 1 4 cup coconut milk, 1 5 cup apple juice 1 4 cup berry juice and 1 4 cup of crushed pineapple. How many cups will the smoothie fill? Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.9 page 27 Unit 2.5 1. 1 1 1 1 1 + + + + 2 4 5 4 4 10 5 4 5 5 Lowest common = + + + + denominator of 20 20 20 20 20 20 29 = Add numerators 20 9 Change to mixed =1 cups fraction 20 OR Using a calculator = 1,45 cups Downloaded from hlayiso.com Maths Lit NQF Level 3

Multiplying fractions Unit 2.3 Example 2.7 page 26 2 1. Find of R65 5 Without a calculator: With a calculator: 2 2 13 5 x R65 = 5 x 65 2 5 65 Cancel common factors in numerator and denominator = R26 = R26 Downloaded from hlayiso.com Maths Lit NQF Level 3

Dividing fractions Unit 2.3 Example 2.8 page 27 7 3 Calculate ÷ 5 5 Without a calculator: With a calculator: Invert the second fraction and multiply 3 5 7 5 = × 9 10 5 3 7 1 1 = =2 = 2,33 = 2 3 3 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Converting fractions to decimals Unit 2.3 27 parts out of 100 parts can be written as a: 0,27 27% Fraction Decimal Percentage • One form can be converted to another. Downloaded from hlayiso.com Maths Lit NQF Level 3

Converting fractions to decimals Unit 2.3 Divide the numerator by the denominator. The whole number in a mixed number will remain a whole number in the decimal form. Downloaded from hlayiso.com Maths Lit NQF Level 3

Converting fractions to percentages Unit 2.3 • Percentages are fractions where the denominator is 100. or 0,7 which is 70% • One whole is 100% • A whole number is a multiple of 100% e.g. 3 is 300% = 4 ÷ 5 = 0,8 = 80% = 1 ÷ 3 = 0,33333... (round off to 0,333) = 33,3% Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 2.3 Unit 2.3 Complete Exercise 2.3 on page 29 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.3 on decimals • Decimals, like fractions, describe parts of a whole number, in units of tenths, hundredths, thousandths and so on. • The decimal comma separates the whole number from the fraction. • A decimal number has digits representing the whole number, the decimal comma and digits representing the fraction e.g. 67,05 • Decimals are used to: • show amounts of money e.g. R32,95 • show measurements e.g. 12,302 kg • in business, to show the value of stocks, averages and interest rates • to read measuring instruments • in calculations Downloaded from hlayiso.com Maths Lit NQF Level 3

Converting decimals and fractions Unit 2.3 • Any fraction can be expressed as a decimal by dividing the numerator by the denominator. Divide numerator by denominator OR • Recurring decimals have digits that keep repeating shown by a dot above the digit. Downloaded from hlayiso.com Maths Lit NQF Level 3

Adding and subtracting decimals Unit 2.4 • Work from left to right, adding or subtracting numbers of the same place value. • Keep the decimal comma in the correct place. • Without a calculator: • write the numbers underneath each other • insert zeros if the numbers do not have the same number of decimal places Example: 8 , 2 0 1 • Calculate and then check with a calculator. 0 , 9 7 0 8,201 + 0,97 + 1,34 + 1 , 3 4 0 1 0 , 5 1 1 Downloaded from hlayiso.com Maths Lit NQF Level 3

Multiplying decimals Unit 2.4 Without a calculator: • Multiply as with whole numbers, without decimal commas. • Count the number of decimal places in each number multiplied. • The answer needs that number of decimal places. Count the places from the right of the answer. Example 2.15 page 32 no 2 A plumber charges R225,75 per hour and works for 3,5 hours. What is his fee? To calculate 225,75 × 3,5: 22 575 × 35 = 790 125 There are three decimal places. The fee is R790,125 Round off to R790,13 Downloaded from hlayiso.com Maths Lit NQF Level 3

Multiplying and dividing decimals Unit 2.4 When we multiply by a power of 10, we count the number of zeros and move the decimal comma the same number of places to the right. Example 2.16 page 33 1. 41,563 × 100 = 4 156,3 2 right 2. 62,7903 × 1 000 = 62 790,3 3 right 3. 1,0045 × 100 = 100,45 2 right Downloaded from hlayiso.com Maths Lit NQF Level 3

Multiplying and dividing decimals Unit 2.4 When we divide by a power of 10, we count the number of zeros and move the decimal comma the same number of places to the left. Example 2.17 page 33 1. 41,56 ÷ 1 000 = 0,04156 3 left 2. 81,2 ÷ 10 = 8,12 1 left 3. 1 004,698 ÷ 100 = 10,04698 2 left • 64 375,86 ÷ 23,24 Multiply by 100 to get rid of = 6 437 586 ÷ 2 324 decimal in denominator = 2 770,045611... = 2 770,05 rounded to two decimal places. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 2.4 Unit 2.4 Complete Exercise 2.4 on page 33 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Use a calculator to perform calculations Unit 2.5 on percentages • 'Percent' means parts per 100. • If you divide a whole quantity into 100 equal parts, then one part is 1%. • The whole amount is 100%. Example • If your business has R14 250 in cash, then R14 250 is 100% of your cash. • In decimal numbers, 100% is 1,00 or just 1. 1% = 0,01 15% = 0,15 90% = 0,9 Downloaded from hlayiso.com Maths Lit NQF Level 3

Percentages Unit 2.5 • Percentages are fractions with a denominator of 100. • 19% means 19 parts in every 100. 19 • 19% means or 0,19 100 35 • 35% of 50 can be rewritten as × 50 = R17.50 100 72 • 0,72 can be rewritten as or 72%. 100 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.18 page 35 Unit 2.5 1. Write 48% as a fraction in its simplest form. 2. Write 37,5% as a decimal fraction. 3. Change 0,415 to a percentage. 9 4. Change to a percentage. 20 5. Calculate 25% of 200. 6. Use your calculator to calculate 31% of R2,86. 7. Calculate 27% of R18. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 2.18 page 35 continued ... Unit 2.5 48 12 1. 48% = = 100 25 2. 37,5% = 37,5 ÷ 100 = 0,375 3. 0,415 x 100 = 41,5% 9 4. × 100 = 9 × 5 = 45% 20 25 5. 25% of 200 = × 200 = 50 100 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 2.5 Unit 2.5 Complete Exercise 2.5 on page 36 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Module assessment Module 2 Complete Module assessment on page 37 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

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