What are fractions and how are they used in IB MYP Mathematics?

Fractions represent a part of a whole and are used in IB MYP Mathematics to develop a deeper understanding of numbers and their relationships. They are expressed as a ratio of two integers, with the numerator indicating the number of parts and the denominator indicating the total number of equal parts. Fractions are essential for solving problems involving division, ratios, and proportions.

How do you add and subtract fractions with different denominators?

To add or subtract fractions with different denominators, you must first find a common denominator, which is typically the least common multiple of the denominators. Once you have a common denominator, convert each fraction to an equivalent fraction with this common denominator. Then, add or subtract the numerators while keeping the denominator the same. Simplify the resulting fraction if possible.

What is the process for multiplying and dividing fractions in Mathematics?

To multiply fractions, multiply the numerators together to get the new numerator and the denominators together to get the new denominator. Simplify the resulting fraction if necessary. For dividing fractions, multiply by the reciprocal of the divisor. This means flipping the second fraction and then multiplying as usual. Simplify the result to its simplest form.

How can I convert a fraction to a decimal in the IB MYP curriculum?

To convert a fraction to a decimal, divide the numerator by the denominator using long division. The result is the decimal equivalent of the fraction. This skill is important in the IB MYP curriculum as it helps students understand the relationship between different number forms and enhances their problem-solving abilities.

What strategies can be used to compare and order fractions?

To compare and order fractions, you can convert them to have a common denominator and then compare the numerators. Alternatively, convert the fractions to decimals and compare the decimal values. Visual models, such as number lines or pie charts, can also help in understanding the relative sizes of fractions. These strategies are emphasized in the IB MYP Mathematics curriculum to build a strong foundation in number sense.

Why is "Writing $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{2}{5}$." a common mistake in Fractions?

Why it happens: Adding numerators AND denominators. How to avoid it: Only add numerators AFTER making a common denominator. 3/6 + 2/6 = 5/6.

Why is "Flipping the FIRST fraction when dividing." a common mistake in Fractions?

Why it happens: Confusion about which to invert. How to avoid it: Always flip the SECOND fraction (the divisor). a/b ÷ c/d = a/b × d/c.

Why is "Leaving the answer unsimplified." a common mistake in Fractions?

Why it happens: Rush to write down the numbers. How to avoid it: Always check HCF = 1 on your final answer. Mark schemes typically deduct for an unsimplified final form.

IB MYP Mathematics (MYP - M)

Fractions

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Short Notes - Fractions

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Detailed Study Notes

Detailed notes on Number for IB MYP Mathematics, covering key concepts, explanations, examples, and exam-focused revision points.

Fractions — IB MYP Mathematics (Extended): the four operations on rational numbers

Fractions are the next step beyond integers. This MYP Mathematics Extended note covers simplification, the four operations, mixed numbers, and converting to decimals — building the toolkit for algebra.

At a glance

A FRACTION $\dfrac{a}{b}$ is a quotient. $a$ = numerator, $b$ = denominator $(b \ne 0)$ .
Simplify by dividing top and bottom by the HCF.
Adding/subtracting: COMMON DENOMINATOR first.
Multiplying: $\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}$ .
Dividing: 'flip the second' $\to \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}$ .
Mixed numbers $\leftrightarrow$ improper fractions: $3\tfrac{2}{5} = \tfrac{17}{5}$ .

What you’ll learn

Mapped to the IB MYP Mathematics subject guide (2026 onwards).

MYP Mathematics A — Simplify, add, subtract, multiply and divide fractions.
MYP Mathematics A — Convert between fractions, mixed numbers and decimals.
MYP Mathematics C — Show clear working with consistent fraction notation.
MYP Mathematics D — Use fractions in real contexts (recipes, sharing, percentages).

Equivalent fractions and simplification

The same value can be written in infinitely many ways.

A fraction's value doesn't change when you multiply (or divide) BOTH the top and bottom by the same non-zero number: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{50}{100}.$

A fraction is in simplest form (or lowest terms) when the HCF of numerator and denominator is 1.

Worked example. Simplify $\dfrac{36}{84}$ .

$\text{HCF}(36, 84) = 12$ .
$\dfrac{36 \div 12}{84 \div 12} = \dfrac{3}{7}$ .

Equivalent fractions represent the same amount even when the number of pieces (and the piece size) differ.

Multiply/divide top AND bottom by the same number to find equivalents.
Simplest form: HCF = 1.
Always simplify your final answer.

Adding and subtracting fractions

Common denominator → combine numerators.

To add or subtract fractions you need a common denominator — most efficiently the LCM of the existing denominators.

Worked example. Compute $\dfrac{2}{3} + \dfrac{1}{4}$ .

$\text{LCM}(3, 4) = 12$ .
$\dfrac{2}{3} = \dfrac{8}{12}$ , $\dfrac{1}{4} = \dfrac{3}{12}$ .
Add the numerators: $\dfrac{8 + 3}{12} = \dfrac{11}{12}$ .
Check for simplification: $\text{HCF}(11, 12) = 1$ , already in simplest form.

For mixed numbers (e.g. $2\tfrac{1}{3} + 1\tfrac{1}{2}$ ), convert to IMPROPER fractions first:

$2\tfrac{1}{3} = \tfrac{7}{3}$ , $1\tfrac{1}{2} = \tfrac{3}{2}$ .
Common denominator 6: $\tfrac{14}{6} + \tfrac{9}{6} = \tfrac{23}{6}$ .
Convert back: $\tfrac{23}{6} = 3\tfrac{5}{6}$ .

Common denominator BEFORE combining.
Use LCM, not just the product (smaller numbers).
Mixed numbers: convert to improper FIRST.

Multiplying and dividing fractions

Multiply straight across; divide = flip + multiply.

Multiplication: multiply numerators together and denominators together: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}.$

CANCEL common factors BEFORE multiplying to keep numbers small: $\frac{4}{9} \times \frac{3}{8} = \frac{4 \times 3}{9 \times 8} = \frac{12}{72} = \frac{1}{6}.$ Better: $\frac{\cancel{4}^1}{\cancel{9}^3} \times \frac{\cancel{3}^1}{\cancel{8}^2} = \frac{1}{6}.$

Division: to divide by a fraction, MULTIPLY by its reciprocal ('flip the second'): $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}.$

Why? Dividing by $\tfrac{c}{d}$ asks 'how many $\tfrac{c}{d}$ s fit?' which is the same as multiplying by $\tfrac{d}{c}$ .

Worked example. $\dfrac{2}{5} \div \dfrac{3}{4} = \dfrac{2}{5} \times \dfrac{4}{3} = \dfrac{8}{15}$ .

Multiply: top $\times$ top, bottom $\times$ bottom.
Cancel first to avoid large numbers.
Divide: flip the SECOND fraction and multiply.

Fractions ↔ decimals ↔ percentages

All three are different ways to write the same number.

The most useful conversions:

Fraction	Decimal	Percentage
$\tfrac{1}{2}$	$0.5$	$50\%$
$\tfrac{1}{4}$	$0.25$	$25\%$
$\tfrac{3}{4}$	$0.75$	$75\%$
$\tfrac{1}{5}$	$0.2$	$20\%$
$\tfrac{1}{8}$	$0.125$	$12.5\%$
$\tfrac{1}{3}$	$0.\overline{3}$	$33.\overline{3}\%$

To convert a fraction to a decimal: divide the numerator by the denominator.

To convert a decimal to a fraction: write it as a fraction over a power of 10, then simplify: $0.36 = \frac{36}{100} = \frac{9}{25}.$

To convert to a percentage: multiply the decimal by 100, or write the fraction with denominator 100.

For Extended Level you also need RECURRING DECIMALS like $0.\overline{3} = \tfrac{1}{3}$ . Covered in detail in the Recurring Decimals subtopic.

$\tfrac{a}{b}$ as a decimal = $a \div b$ .
Decimal $\to$ fraction: power of 10 denominator, then simplify.
Percentage = fraction with denominator 100.

Quick recap

Equivalent fractions: same value, different form.
Add/subtract: COMMON DENOMINATOR first.
Multiply: top × top, bottom × bottom. Cancel early.
Divide: flip the second, then multiply.
Always simplify the final answer.

Memorise this

Verbatim phrases and definitions MYP criterion-A markschemes credit.

$\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}$
$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}$
Mixed → improper: $a\tfrac{b}{c} = \dfrac{ac+b}{c}$
Fraction $\to$ decimal: divide top by bottom

How it’s examined

Criterion A: speedy operations + simplification. Criterion C: clearly written common-denominator step. Criterion D: recipe / sharing / percentage applications.

Sources: IB MYP Mathematics subject guide (IBO, official). Last reviewed 2026-05-25.

Take this whole topic with you

Step-by-step worked examples — Fractions

Step-by-step solutions to past-paper-style questions on fractions, written exactly the way a tutor would explain them at the board.

1Add fractions with different denominators
Getting started• addition
Question
Calculate $\dfrac{3}{5} + \dfrac{2}{7}$ .
Step-by-step solution
1. Step 1
  $\text{LCM}(5,7) = 35$ .
2. Step 2
  Convert: $\dfrac{3}{5} = \dfrac{21}{35}$ and $\dfrac{2}{7} = \dfrac{10}{35}$ .
3. Step 3
  Add numerators: $\dfrac{21+10}{35} = \dfrac{31}{35}$ .
4. Step 4
  $\text{HCF}(31,35) = 1$ , so already simplified.
Answer
$\dfrac{31}{35}$
2Multiply mixed numbers
Building confidence• multiplication
Question
Calculate $2\dfrac{1}{4} \times 1\dfrac{2}{3}$ .
Step-by-step solution
1. Step 1
  Convert to improper: $2\tfrac{1}{4} = \tfrac{9}{4}$ and $1\tfrac{2}{3} = \tfrac{5}{3}$ .
2. Step 2
  Multiply: $\dfrac{9}{4} \times \dfrac{5}{3} = \dfrac{45}{12}$ .
3. Step 3
  Simplify: $\dfrac{45}{12} = \dfrac{15}{4}$ .
4. Step 4
  Optional: convert back to mixed number $\dfrac{15}{4} = 3\tfrac{3}{4}$ .
Answer
$3\tfrac{3}{4}$ (or $\tfrac{15}{4}$ ).
3Divide fractions
Building confidence• division
Question
Calculate $\dfrac{5}{6} \div \dfrac{10}{9}$ .
Step-by-step solution
1. Step 1
  Flip the second fraction: $\dfrac{5}{6} \times \dfrac{9}{10}$ .
2. Step 2
  Cancel: $\dfrac{\cancel{5}^1}{6} \times \dfrac{9}{\cancel{10}^2} = \dfrac{9}{12}$ .
3. Step 3
  Simplify: $\dfrac{9}{12} = \dfrac{3}{4}$ .
Answer
$\dfrac{3}{4}$
4Real context: recipe scaling
Stretch• application, criterion D
Question
A recipe needs $\tfrac{3}{4}$ cup of flour to make 6 muffins. How much flour is needed for 15 muffins?
Step-by-step solution
1. Step 1
  Flour per muffin = $\dfrac{3/4}{6} = \dfrac{3}{4} \times \dfrac{1}{6} = \dfrac{1}{8}$ cup.
2. Step 2
  For 15 muffins: $15 \times \dfrac{1}{8} = \dfrac{15}{8}$ cups.
3. Step 3
  Convert to mixed: $\dfrac{15}{8} = 1\tfrac{7}{8}$ cups.
Answer
$1\tfrac{7}{8}$ cups of flour.

Key Definitions and Keywords — Fractions

Definitions to memorise and the exact keywords mark schemes credit for fractions answers — sharpened from recent examiner reports for the 2026 IB MYP Mathematics (Extended) sitting.

Numerator
Examiner keyword
The top number in a fraction; counts how many parts.
Denominator
Examiner keyword
The bottom number; tells you how many equal parts make up a whole.
Improper fraction
Examiner keyword
A fraction where numerator $\ge$ denominator, e.g. $\tfrac{7}{4}$ .
Mixed number
An integer plus a proper fraction, e.g. $1\tfrac{3}{4}$ .
Reciprocal
Examiner keyword
The reciprocal of $\dfrac{a}{b}$ is $\dfrac{b}{a}$ . Dividing by a fraction = multiplying by its reciprocal.

Common Mistakes and Misconceptions — Fractions

The traps other students keep falling into on fractions questions — taken from recent IB MYP Mathematics (Extended) examiner reports and mark schemes — and how to avoid them.

✕Writing $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{2}{5}$ .
Why it happens
Adding numerators AND denominators.
How to avoid it
Only add numerators AFTER making a common denominator. $\dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}$ .
✕Flipping the FIRST fraction when dividing.
Why it happens
Confusion about which to invert.
How to avoid it
Always flip the SECOND fraction (the divisor). $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}$ .
✕Leaving the answer unsimplified.
Why it happens
Rush to write down the numbers.
How to avoid it
Always check $\text{HCF} = 1$ on your final answer. Mark schemes typically deduct for an unsimplified final form.

Fractions — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Multiplication: multiply numerators together and denominators together: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}.$

Division: to divide by a fraction, MULTIPLY by its reciprocal ('flip the second'): $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}.$

Why? Dividing by $\tfrac{c}{d}$ asks 'how many $\tfrac{c}{d}$ s fit?' which is the same as multiplying by $\tfrac{d}{c}$ .

Worked example. $\dfrac{2}{5} \div \dfrac{3}{4} = \dfrac{2}{5} \times \dfrac{4}{3} = \dfrac{8}{15}$ .

Fraction

Decimal

Percentage

\tfrac{1}{2}

0.5

50\%

\tfrac{1}{4}

0.25

25\%

\tfrac{3}{4}

0.75

75\%

\tfrac{1}{5}

0.2

20\%

\tfrac{1}{8}

0.125

12.5\%

\tfrac{1}{3}

0.\overline{3}

33.\overline{3}\%

Fractions

Short Notes - Fractions

Detailed Study Notes

At a glance

What you’ll learn

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Add fractions with different denominators

2Multiply mixed numbers

3Divide fractions

4Real context: recipe scaling

Numerator

Denominator

Improper fraction

Mixed number

Reciprocal

✕Writing 12+13=25\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{2}{5}21​+31​=52​.

✕Flipping the FIRST fraction when dividing.

✕Leaving the answer unsimplified.

Fractions — frequently asked questions

Fractions

Short Notes - Fractions

Detailed Study Notes

At a glance

What you’ll learn

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Add fractions with different denominators

2Multiply mixed numbers

3Divide fractions

4Real context: recipe scaling

Numerator

Denominator

Improper fraction

Mixed number

Reciprocal

✕Writing 12+13=25\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{2}{5}21​+31​=52​.

✕Flipping the FIRST fraction when dividing.

✕Leaving the answer unsimplified.

Fractions — frequently asked questions

✕Writing $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{2}{5}$ .

✕Writing $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{2}{5}$ .