Chapter 1 Chemistry in Our Lives 1.4 Learning Chemistry: Key Math Skills Learning Goal Review math concepts used in chemistry: place values, positive and negative numbers, percentages, solving equations, and interpreting line graphs. © 2014 Pearson Education, Inc.

Identifying Place Values For any number we can identify a place value for each digit. 4378 Digit Place Value 4 thousand 3 hundred 7 tens 8 ones

Identifying Place Values We can identify a place value for each digit in a number with a decimal point. 8.192 Digit Place Value 8 ones 1 tenths 9 hundredths 2 thousandths

Learning Check Identify the place value for each of the digits in the following number: 45.127 Digit Place Value 4 5 1 2 7

Solution Identify the place value for each of the digits in the following number: 45.127 Digit Place Value 4 tens 5 ones 1 tenths 2 hundredths 7 thousandths

Using Positive and Negative Numbers in Calculations A positive number is any number that is greater than zero and has a positive sign, (+). The positive sign is often understood and not written. For example: + 8 is also written as 8. A negative number is any number that is less than zero and has a negative sign, (–). For example: – 8

Multiplication with (+) and (–) Numbers When two positive numbers or two negative numbers are multiplied, the answer is positive. 3 × 4 = +12 (–3) × (–4) = +12

Multiplication with (+) and (–) Numbers When a positive number, and a negative number are multiplied, the answer is negative. 3 × (–4) = –12 (–3) × 4 = –12

Division with (+) and (–) Numbers Rules for division of positive and negative numbers are the same as those for multiplication. When two positive numbers or two negative numbers are divided, the answer is positive (+).

Division with (+) and (–) Numbers When a positive number and a negative number are divided, the answer is negative (–).

Addition with (+) and (–) Numbers When positive numbers are added, the sign of the answer is positive (+). 2 + 3 = 5 The (+) sign (+5) is understood.

Addition with (+) and (–) Numbers When negative numbers are added, the sign of the answer is negative (–). (–2) + (–3) = –5

Addition with (+) and (–) Numbers When a positive number and a negative number are added, the smaller number is subtracted from the larger number. The result is the same sign as the larger number. 11 + (–15) = –4

Subtraction with (+) and (–) Numbers When two numbers are subtracted, change the sign of the number to be subtracted. 13 – (+4) = 13 – 4 = 9 13 – (–4) = 13 + 4 = 17 –13 – (–4) = –13 + 4 = –9 –13 – (+4) = –13 – 4 = –17

Calculating a Percentage To determine a percent, divide the parts by the total (whole) and multiply by 100%. Given 20 coins, if 5 are pennies, what percent of the coins are pennies?

Learning Check If you eat 2 pieces (parts) of pizza that contained 6 pieces (whole), what percent did you eat?

Solution If you eat 2 pieces (parts) of pizza that contained 6 pieces (whole), what percent did you eat?

Percentage as Decimals Given a percent such as 25%, it can be converted to a decimal. 1. Write the percent value over 100. Express this fraction as a decimal. 0.25

Solving Equations Rearrange the equation to solve for x: 2x + 8 = 14 To remove 8, subtract 8 from both sides. 2x + 8 – 8 = 14 – 8 2x = 6 To isolate the variable x, divide both sides by 2. x = 3 Check your answer; replace x with 3. (2 × 3) + 8 = 14 becomes 6 + 8 = 14.

Solving Equations To solve for a particular variable, perform the same mathematical operations on both sides of the equation. TF = 1.8 TC + 32 To obtain an equation solving for TC from TF, subtract 32 from both sides. TF – 32 = 1.8 TC + 32 – 32 TF – 32 = 1.8 TC

Solving Equations To isolate TC, divide both sides by 1.8. becomes

Learning Check Solve the following equation for R: PV = nRT

Solution Solve the following equation for R: PV = nRT 1. To isolate R, divide both sides by nT. Cancelling nT, isolates R on the right side of the equation.

Interpreting a Line Graph A line graph represents the relationship between two variables. The graph below represents the volume of a gas plotted against its temperature.

Interpreting a Line Graph The graph title, “Volume of a Balloon versus Temperature”, indicates that the volume of a gas is plotted against its temperature. The vertical (y) axis label indicates that the volume is measured in liters. The horizontal (x) axis label indicates that the temperature of the balloon is measured in Celsius.

Interpreting a Line Graph Each point on the graph represents a volume in liters that was measured at a specific temperature. The line on the graph indicates that the volume of the balloon increases as the temperature of the gas increases. This is called a direct relationship.

Learning Check Given the following graph, Does the distance increase or decrease with time? How many hours did the rider need to travel 15 km?

Solution Given the graph, Does the distance increase or decrease with time? The distance increases with time. How many hours did the rider need to travel 15 km? The rider needed 3 h to travel 15 km.

Concept Map