1.3 Numerical Skills

• What are percentages and fractions used to represent?

  Parts of a whole
• Understanding percentages and fractions is crucial in geography for interpreting data and calculating rates of change.


  True
• Steps to convert a percentage to a fraction

  1️⃣ Divide the percentage by 100

  2️⃣ Express as a ratio
• To convert a fraction to a percentage, multiply by 100
• When calculating a percentage of a value, the part is divided by the total
• If a town has a population of 50,000 and 12,500 people are under 18, what is the percentage of the population under 18?

  25%
• To convert a percentage to a decimal, divide by 100
• 25% can be expressed as the decimal 0.25
• Percentages are useful in geography for representing parts of a whole, such as urban population or land use.


  True
• If a map has a scale of 1:100,000 and the distance between two towns on the map is 3 cm, what is the actual distance in kilometers?

  3 km
• Steps to solve a proportion using cross-multiplication

  1️⃣ Set up the proportion

  2️⃣ Cross-multiply

  3️⃣ Simplify the equation

  4️⃣ Solve for the unknown
• Percentages, fractions, and decimals are all ways to represent parts of a whole
• To convert a fraction to a decimal, you must divide the numerator by the denominator
• Steps to calculate a percentage of a value

  1️⃣ Identify the total value

  2️⃣ Identify the part of the total

  3️⃣ Divide the part by the total

  4️⃣ Multiply the result by 100
• What method is used to solve a proportion?

  Cross-multiplication
• How are ratios written?

  a/b
• A rural village with a population of 500 and a land area of 25 sq km has a population density of 20 people per sq km.
• A pie chart is best used to show the proportions of a whole.
• Match the chart type with its best use:

  Bar graph ↔️ Compares discrete categories

  Pie chart ↔️ Shows proportions of a whole
• A percentage expresses a part of a whole as a hundredth
• What is 25% expressed as a decimal?

  0.25
• If a town has a population of 50,000 and 12,500 people are under 18, what is the percentage of the population under 18?

  25%
• Match the measure of spread with its definition:

  Range ↔️ Maximum value - Minimum value

  IQR ↔️ 75th percentile - 25th percentile

  Standard Deviation ↔️ Average distance from the mean
• A percentage expresses a part of a whole as a hundredth
• What three concepts are used to represent parts of a whole in mathematics?

  Percentages, fractions, decimals
• How do you convert a fraction to a percentage?

  Multiply by 100
• Converting between percentages, fractions, and decimals is essential for working with geographical data.


  True
• Multiplying the result of dividing the part by the total by 100 gives the percentage value.


  True
• Percentages are useful in geography for representing the proportion of land used for agriculture or the urban population.


  True
• A fraction can be converted to a percentage by multiplying by 100.


  True
• Steps to calculate a percentage of a value

  1️⃣ Identify the total value

  2️⃣ Identify the part of the total

  3️⃣ Divide the part by the total

  4️⃣ Multiply the result by 100
• A proportion is an equation that states that two ratios are equal
• Proportions are used in geography to solve problems involving map scales and distances.

  True
• If a map has a scale of 1:100,000 and the distance between two towns on the map is 3 cm, what is the actual distance in kilometers?

  3 km
• What are three ways to represent parts of a whole in geography?

  Percentages, fractions, decimals
• What must you multiply a decimal by to convert it to a percentage?

  100
• What is the percentage of a town's population under 18 if 12,500 out of 50,000 people are under 18?

  25%
• In the proportion 3/5 = x/15, the value of x is 9.


  True
• Cross-multiplication is used to solve proportions.


  True
• What is the population density of an urban city with a population of 1,500,000 and a land area of 500 sq km?

  3,000 people/sq km