The Foundation Drill: Master Fractions, Percentages & Geometry

Hi! I'm Teacher Amara. Let's get these math fundamentals so solid you could do them in your sleep. These three topics are the 'big wins' of middle school math—master them, and everything else gets easier.

1. Fractions: The Common Denominator #

You can't add apples and oranges, and you can't add thirds and quarters. To add or subtract, the bottom numbers (denominators) must match. We find a number both denominators go into (the LCM).

Worked Example Solve: \frac{2}{3} + rac{1}{4}

  • 1.
    Find the common ground: Both 33 and 44 go into 1212.
  • 2.
    Adjust the tops: To get 1212, multiply 23\frac{2}{3} by 44 (top and bottom) to get 812\frac{8}{12}. Multiply 14\frac{1}{4} by 33 to get 312\frac{3}{12}.
  • 3.
    Combine:812+312=1112\frac{8}{12} + \frac{3}{12} = \frac{11}{12}.
  • Quick Quiz #

    What is 25+13\frac{2}{5} + \frac{1}{3}?

    Single choice

    2. Percentages: The 10% Shortcut #

    Instead of scary decimals, start with 10%. To find 10% of any number, just move the decimal point one spot to the left. Once you have 10%, you can find 5% (half it) or 20% (double it).

    Worked Example Find 15%15\% of 8080.

  • 1.
    Find 10%:80÷10=880 \div 10 = 8.
  • 2.
    Find 5%: Half of 88 is 44.
  • 3.
    Add them up:8+4=128 + 4 = 12.
  • Quick Quiz #

    What is 20%20\% of 150150?

    Single choice

    3. Geometry: Fence vs. Grass #

    Confusing Area and Perimeter is the #1 mistake students make.

    • Perimeter: The 'Fence.' The distance around the outside edge.
    • Area: The 'Grass.' The flat space inside the shape.

    Worked Example Find the area and perimeter of a 44m ×\times99m garden.

    • Perimeter:4+9+4+9=264 + 9 + 4 + 9 = 26m.
    • Area:4×9=364 \times 9 = 36m².

    Quick Quiz #

    A rectangular desk is 66cm wide and 1212cm long. What is its Area?

    Single choice