1.1.1 Use of integers, fractions, decimals, and percentages

• What are integers?

  Whole numbers that can be positive, negative, or zero
• If you have 12 apples and give away 5, how many apples do you have left?

  7 apples
• What are the characteristics of integers?

  • Whole numbers
  • Can be positive, negative, or zero
  • Do not include fractions or decimals
• What are integers defined as?

  Whole numbers without fractions or decimals
• What do integers not include?

  Fractions or decimals
• What are decimals?

  Numbers that include a decimal point
• What is the part before the decimal point called?

  Whole number part
• What is the part after the decimal point called?

  Fractional part
• In the decimal $3.14$, what is the whole number part?


  3
• How can you use the numerator and denominator to determine the value of a fraction?

  • The value of the fraction is the numerator divided by the denominator
  • For example, if the numerator is 5 and the denominator is 6, the value of the fraction is 5/6
• What is the relationship between the numerator and denominator in a fraction?

  • The numerator represents the number of parts we have
  • The denominator represents the total number of parts in the whole
• What is the numerator in the fraction shown in the image?

  5
• How is the fraction $\frac{5}{6}$ interpreted?


  The whole is divided into 6 parts, we have 5
• What does 100% mean in the context of the pizza?

  You ate the whole pizza
• What does the decimal point in decimals indicate?

  It shows parts of a whole
• What does eating 50 slices of pizza represent?

  You ate 50 percent (50%) of the pizza
• What does the numerator in a fraction indicate?

  How many parts we have
• In the fraction $\frac{5}{6}$, how many parts do we have?


  5 parts
• What does the denominator in a fraction represent?

  Total number of equal parts the whole is divided into
• How do you convert a fraction to a decimal?

  Divide the numerator by the denominator
• What is the result of dividing $\frac{1}{2}$ by $\frac{1}{3}$?


  $1 \frac{1}{2}$
• What does it mean when a toy car is 25% off?

  You pay less money for the toy car
• What is the result of multiplying $\frac{1}{2}$ by $\frac{1}{3}$?


  $\frac{1}{6}$
• Can you have half a toy in integers?

  No, integers are always whole
• How does a percentage relate to sales, according to the study material?

  A percentage off means you pay less money
• What does the symbol % represent?

  "Out of 100"
• What is the result of subtracting $\frac{1}{4}$ from $\frac{3}{4}$?


  $\frac{1}{2}$
• What is the result of converting the decimal 0.25 to a percentage?

  Multiply 0.25 by 100
• What is the result of adding $\frac{1}{4}$ and $\frac{1}{4}$?


  $\frac{1}{2}$
• What is the denominator in the fraction shown in the image?

  6
• What does a fraction represent?

  Parts of a whole divided into equal parts
• What are the four types of arithmetic operations mentioned?

  Integers, fractions, decimals, percentages
• What is 50% as a decimal?

  0.5
• What does the decimal $3.14$ represent in terms of wholes and parts?


  3 wholes plus 14 out of 100 parts
• What are the steps for converting between fractions, decimals, and percentages?

  1. Fraction to Decimal: Divide numerator by denominator
  2. Decimal to Fraction: Write over 10, 100, or 1000 and simplify
  3. Percentage to Decimal: Divide by 100
  4. Decimal to Percentage: Multiply by 100
  5. Fraction to Percentage: Multiply by 100
  6. Percentage to Fraction: Divide by 100 and simplify
• What does it mean that integers can't have half a toy?

  It means integers are always whole numbers
• How does a shopping discount of 20% on a £50 shirt affect the price?

  You pay £40
• What are the arithmetic operations performed with fractions?

  • Addition: $\frac{1}{4} +$$\frac{1}{4} =$$\frac{2}{4} =$$\frac{1}{2}$
  • Subtraction: $\frac{3}{4} - \frac{1}{4} =$$\frac{2}{4} =$$\frac{1}{2}$
  • Multiplication: $\frac{1}{2} \times \frac{1}{3} =$$\frac{1}{6}$
  • Division: $\frac{1}{2} \div \frac{1}{3} =$$\frac{3}{2} =$$1 \frac{1}{2}$
• How do you convert a percentage to a decimal?

  Divide by 100
• What are the equivalent forms of percentages?

  • Fraction: Write over 100 and simplify
  • Decimal: Divide by 100