Fractions: Understanding Parts of a Whole: quick revision, 15 bites

A Fraction Is a Part of a Whole

One pizza slice tells the whole story.

A fraction shows **how many equal parts** of a whole you have. The bottom number (denominator) says how many equal parts the whole is divided into; the top number (numerator) says how many you take.

Takeaway. Denominator = size of each piece; numerator = number of pieces you have.

Proper, Improper, and Mixed Fractions

Three flavours of fractions — know the difference.

Takeaway. Improper fractions can be rewritten as mixed numbers and vice versa.

Equivalent Fractions: Multiply Top and Bottom

Same value, different look.

Multiplying (or dividing) numerator and denominator by the **same non-zero number** keeps the fraction's value unchanged.

Takeaway. Equivalent fractions are different names for the same point on the number line.

Simplifying a Fraction to Lowest Terms

Shrink the fraction, keep the value.

Takeaway. A fraction is in lowest terms when numerator and denominator share no factor except 1.

Comparing Fractions: Same Denominator vs Different

Which slice is bigger? Compare smartly.

Takeaway. To compare unlike fractions, either find a common denominator or cross-multiply.

Adding and Subtracting Fractions

Same denominator? Just add the tops.

Takeaway. Find a common denominator first, then add or subtract only the numerators.

Multiplying and Dividing Fractions

Multiply straight across — divide by flipping.

Takeaway. Multiplication is direct; division becomes multiplication by the reciprocal.

The Classic Fraction Blunder

Adding tops AND bottoms? Stop right there.

Takeaway. Denominators name the size of the parts — they must match before you add.

Fractions in the Kitchen and the Wallet

Recipes and discounts run on fractions.

Takeaway. Fractions are the everyday language of portions, prices, and measurements.

Remember: Denominator = Down

D for denominator, D for down.

Takeaway. Small letter cues lock in the four core fraction rules.

Exam Habits That Save Marks

Small habits, big score jumps.

Takeaway. Simplify, show the common denominator, and convert mixed numbers before operating.

Fractions as Division and Ratios

Every fraction is a division in disguise.

The fraction $\frac{a}{b}$ is exactly the division $a \div b$. This links fractions to decimals, percentages, and ratios.

Takeaway. Fraction, decimal, percent, and ratio are four views of the same quantity.

The Word 'Fraction' Comes From Breaking

Latin roots hiding in your maths book.

The word *fraction* comes from the Latin **fractus**, meaning 'broken'. The ancient Egyptians worked mainly with unit fractions like $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ — a tradition that shaped how early mathematics handled parts of a whole.

Takeaway. Fractions literally mean 'broken parts' — a fitting name for parts of a whole.

A 3-Step Fraction Word-Problem Routine

Word problems? Follow the same three moves.

Takeaway. Find the whole, translate the words, then operate and simplify.

Picture Fractions on a Number Line

See fractions, don't just calculate them.

Draw a line from 0 to 1 and split it into equal parts. Each tick is a unit fraction. $\frac{3}{4}$ sits three ticks past 0 when the segment is split into four equal parts — this makes ordering and equivalence visually obvious.

Takeaway. The number line turns abstract fraction rules into visible positions.