Lesson 8: Fractions and Percents

New Concept

Fractions and percents are commonly used to name parts of a whole or parts of a group.

A common fraction is written with two numbers and a division bar. The number below the bar is the denominator and shows how many equal parts are in the whole. The number above the bar is the numerator and shows how many of the parts have been selected.

A percent describes a whole as though there were 100 parts, even though the whole may not actually contain 100 parts. Thus the "denominator" of a percent is always 100.

What’s next

This is just the foundation. Next, you’ll apply these ideas through worked examples involving shaded figures, number lines, and inch rulers.

Property

A fraction uses a numerator and a denominator to show parts of a whole (like $\frac{2}{5}$). A percent is a special kind of fraction where the denominator is always 100.

Examples

• $\frac{1}{4}$ of a group is the same as $100\% \div 4 = 25\%$.
• A test score of $\frac{4}{5}$ is equal to $80\%$.
• The mixed number $2\frac{3}{4}$ can be written as $275\%$.

Explanation

Think of them as two languages for the same idea! Percents make comparing things easy because everything is on the same scale of 100. It helps you quickly see who got more of the pizza!

Property

An inch ruler is a practical number line where units are divided into halves, quarters, eighths, and sixteenths for precise measurements.

Examples

• If a ruler is marked in eighths of an inch, the greatest possible error is $\frac{1}{16}$ of an inch.
• To find a length of $2\frac{1}{2}$ inches, you look for the mark exactly halfway between 2 and 3.

Explanation

The more tiny lines a ruler has, the more accurate your measurement can be! The biggest possible error from the tool is always half of the smallest unit marked.

Property

A permutation is one of the possible ways to order a set of items, like digits or letters. In a permutation, the order always matters.

Examples

• The digits 2, 3, and 5 have six permutations: $235, 253, 325, 352, 523, 532$.
• The letters C, A, T have six permutations, including CAT, ACT, and TAC.

Explanation

Think of it as shuffling! Each different arrangement is a new permutation. Making an organized list from smallest to largest is a great strategy to find every single combination without missing any.