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Convert fractions, decimals, and percentages to each other. Calculate percentages of amounts and solve word problems involving percentages.

Mathematics

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Here are the solutions to the problems:

The first two questions involve shading shapes, which I cannot do directly. However, I can provide the numerical representations.

A half can be written...

  • As a fraction: 12\boxed{\frac{1}{2}}
  • As a decimal: 0.5\boxed{0.5}
  • As a percentage: 50%\boxed{50\%}

A quarter can be written...

  • As a fraction: 14\boxed{\frac{1}{4}}
  • As a decimal: 0.25\boxed{0.25}
  • As a percentage: 25%\boxed{25\%}

Complete the following:

  • What is 80% of R1.00? 80% of R1.00=0.80×R1.00=R0.8080\% \text{ of R}1.00 = 0.80 \times \text{R}1.00 = \boxed{\text{R}0.80}
  • What is 0.5 of R1.00? 0.5×R1.00=R0.500.5 \times \text{R}1.00 = \boxed{\text{R}0.50}
  • What is 12\frac{1}{2} of R1.00? 12×R1.00=0.5×R1.00=R0.50\frac{1}{2} \times \text{R}1.00 = 0.5 \times \text{R}1.00 = \boxed{\text{R}0.50}
  • What is 25% of R1.00? 25% of R1.00=0.25×R1.00=R0.2525\% \text{ of R}1.00 = 0.25 \times \text{R}1.00 = \boxed{\text{R}0.25}
  • What is 0.25 of R1.00? 0.25×R1.00=R0.250.25 \times \text{R}1.00 = \boxed{\text{R}0.25}
  • What is 14\frac{1}{4} of R1.00? 14×R1.00=0.25×R1.00=R0.25\frac{1}{4} \times \text{R}1.00 = 0.25 \times \text{R}1.00 = \boxed{\text{R}0.25}

Complete the following (Grade 6 children):

There are 120 children in grade 6.

  • 30% of the children are boys. How many children are boys?
  1. Convert the percentage to a decimal.

    $$
    30\% = 0.30
    $$
    
  2. Multiply the decimal by the total number of children.

    $$
    0.30 \times 120 = \boxed{36 \text{ boys}}
    $$
    
    • 25% of the children like strawberry ice cream. How many children like strawberry ice cream?
  3. Convert the percentage to a decimal.

    $$
    25\% = 0.25
    $$
    
  4. Multiply the decimal by the total number of children.

    $$
    0.25 \times 120 = \boxed{30 \text{ children}}
    $$
    
    • What percentage of children like other flavoured ice-creams? If 25% like strawberry ice cream, then the remaining percentage likes other flavours.

      100%−25%=75%100\% - 25\% = \boxed{75\%}
    • How many children like other flavoured ice-creams?

  5. Convert the percentage for other flavours to a decimal.

    $$
    75\% = 0.75
    $$
    
  6. Multiply the decimal by the total number of children.

    $$
    0.75 \times 120 = \boxed{90 \text{ children}}
    $$
    
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