The Foundation Three: Fractions, Triangles, & Percentages

Hi everyone, it's Teacher Amara! Today we're tackling the 'Big Three' basics that show up in almost every middle-school exam. This drill isn't just about formulas; it's about spotting the patterns so you don't get stuck on test day.

1. Fractions: The Common Denominator Hack #

You can't add apples and oranges, and you can't add fifths and thirds. To make them 'speak the same language,' we find the Least Common Multiple (LCM) of the denominators.

Example: $\frac{1}{4} + \frac{2}{3}$

The Target: The LCM of 4 and 3 is 12.

The Shift:

\frac{1 \times 3}{4 \times 3} = \frac{3}{12}

and

\frac{2 \times 4}{3 \times 4} = \frac{8}{12}

The Result:

\frac{3 + 8}{12} = \frac{11}{12}

Warning

Teacher Tip: A common mistake is adding the bottom numbers (denominators). Never do this. The denominator is just the "label" for the size of the slice; only the number of slices (numerators) changes.

Single choice

2. Geometry: Why we "Divide by 2" #

To find the area of a triangle, remember it’s essentially half of a rectangle. That’s why the formula is $A = \frac{1}{2} \times \text{base} \times \text{height}$ .

Example: Find the area of a triangle with a base of $4\text{ cm}$ and a height of $5\text{ cm}$ .

$A = 0.5 \times 4 \times 5$
$A = 10\text{ cm}^2$

Info

Pro Tip: In right-angled triangles, the two sides meeting at the L-shape are your base and height. Ignore the long diagonal side (the hypotenuse) when calculating area!

Single choice

3. Percentages: The 10% Mental Method #

While you can always multiply by a decimal, the fastest way to find percentages is the 10% Rule.

To find 10%, move the decimal one spot left.
To find 5%, halve your 10% result.

Example: Find $15\%$ of $60$ .

Find 10%:

60 \div 10 = 6

Find 5%:

6 \div 2 = 3

Add them:

6 + 3 = 9

Single choice

Great job! Mastering these three pivots will make your algebra and geometry lessons much smoother. Keep practicing!

Created by

amara.math.helpTeacher Amara