Introduction To Fractions

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Lesson notes

Introduction to Fractions

A fraction is written as a/b where a (numerator) and b (denominator) are integers.
The denominator shows how many equal parts a whole is split into; the numerator shows how many parts you have.
If numerator < denominator, the fraction is less than 1; if numerator > denominator, it is greater than 1.
To shade a fraction of a diagram: divide total parts by denominator, then multiply by numerator.

Shading 3/5 of a bar

Fractions of Amounts

Method 1: Divide by denominator, multiply by numerator – e.g., 2/5 of 60: 60 ÷ 5 = 12, 12 × 2 = 24.
Method 2: Convert fraction to decimal and multiply – e.g., 1/4 of 16 = 0.25 × 16 = 4.
Method 3: Write the amount as a fraction (e.g., 60 = 60/1) and multiply fractions – e.g., 2/3 × 60/1 = 120/3 = 40.
For fractions of fractions, multiply the two fractions directly.

Equivalent Fractions

Equivalent fractions represent the same amount but are written differently (e.g., 1/2 = 6/12).
To find an equivalent fraction, multiply numerator and denominator by the same number (e.g., 5/6 = 10/12 = 15/18).
There are infinitely many equivalent fractions for any given fraction.

Simplifying Fractions

A simplified fraction uses the smallest possible integers (e.g., 12/18 = 2/3).
Simplify by dividing numerator and denominator by a common factor (e.g., 25/45 ÷ 5/5 = 5/9).
This is also called cancelling the fraction.

Mixed Numbers & Improper Fractions

A mixed number has an integer part and a fraction part (e.g., 3 3/4 means three and three quarters).
An improper fraction (top-heavy) has numerator > denominator (e.g., 15/4).
To convert mixed to improper: multiply whole number by denominator, add numerator, write over denominator (e.g., 5 2/7 = (5×7+2)/7 = 37/7).
To convert improper to mixed: divide numerator by denominator; quotient is whole number, remainder is numerator over denominator (e.g., 22/3 = 7 1/3).

Slides

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Practice questions

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1.Write 60/105 in its simplest form.
Easy
- A4/7
- B12/21
- C6/10
- D3/5
2.Write a fraction which is equivalent to 3/5.
Easy
- A6/10
- B3/10
- C6/5
- D9/10
3.Write 28/140 as a fraction in its simplest form.
Easy
- A1/5
- B2/7
- C7/35
- D4/20
4.A rectangle is divided into 8 equal squares. How many squares should be shaded to shade five-eighths of the rectangle?
Easy
- AShade 5 squares
- BShade 3 squares
- CShade 8 squares
- DShade 5/8 of a square
5.Write down a fraction that is equivalent to 7/12.
Easy
- A14/24
- B7/24
- C14/12
- D21/36
6.Find 1/5 of $200.
Easy
- A$40
- B$50
- C$100
- D$20
7.There are 12 brass instruments in an orchestra. 1/3 are trumpets, 3 are trombones and the remainder are horns. Find the number of horns.
Medium
- A5
- B4
- C3
- D6
8.Records show that 3/14 of the population of a particular type of fish, called mullet, caught are underweight. In one day, 168 mullet are caught. Work out the expected number of mullet that are underweight.
Medium
- A36
- B24
- C42
- D48

Revision notes

## Introduction to Fractions - A fraction is written as $\frac{a}{b}$ where $a$ and $b$ are integers. - **Numerator** (top) tells how many parts you have; **denominator** (bottom) tells how many parts make one whole. - Fraction < 1 if numerator < denominator; > 1 if numerator > denominator. ### Shading Fractions - To shade $\frac{3}{5}$ of 20 squares: divide 20 by 5 = 4, multiply by 3 = 12, shade 12 squares. ### Fractions of Amounts - **Method 1**: Divide by denominator, multiply by numerator. E.g., $\frac{2}{5}$ of 60: $60 \div 5 = 12$, $12 \times 2 = 24$. - **Method 2**: Convert fraction to decimal and multiply. E.g., $\frac{1}{4}$ of 16: $0.25 \times 16 = 4$. - **Method 3**: Multiply fractions: $\frac{2}{3} \times \frac{60}{1} = \frac{120}{3} = 40$. ### Equivalent & Simplified Fractions - **Equivalent fractions**: Multiply numerator and denominator by the same number. E.g., $\frac{5}{6} = \frac{10}{12} = \frac{15}{18}$. - **Simplifying**: Divide numerator and denominator by a common factor. E.g., $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$. ### Mixed Numbers & Improper Fractions - **Mixed number**: integer part + fraction part, e.g., $3\frac{3}{4}$. - **Improper fraction**: numerator > denominator, e.g., $\frac{15}{4}$. - **Convert mixed to improper**: Multiply whole number by denominator, add numerator. E.g., $5\frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{37}{7}$. - **Convert improper to mixed**: Divide numerator by denominator; quotient is whole number, remainder over denominator. E.g., $\frac{22}{3} = 7\frac{1}{3}$. ### Key Tips - Use calculator to simplify fractions (but show division steps if required). - For "of" problems, multiply. - Always simplify final fractions where possible.

Fraction: A number written as a/b where a and b are integers; a is the numerator, b is the denominator.
Numerator: The top number of a fraction; indicates how many parts are taken.
Denominator: The bottom number of a fraction; indicates how many equal parts the whole is divided into.
Equivalent fractions: Fractions that represent the same value, obtained by multiplying numerator and denominator by the same number.
Simplified fraction: A fraction written with the smallest possible integers by dividing numerator and denominator by a common factor.
Mixed number: A number consisting of an integer part and a fraction part, e.g., 3 3/4.
Improper fraction: A fraction where the numerator is greater than the denominator, e.g., 15/4.

Flashcards

What is a fraction? Write the general form and label the numerator and denominator.

A fraction is written as a/b where a and b are integers. The top number (a) is the numerator, the bottom number (b) is the denominator.

How do you shade 3/5 of a grid of 20 squares?

Divide 20 by 5 to get 4, then multiply by 3 to get 12. Shade 12 squares.

Find 1/5 of $200.

Divide $200 by 5: $200 ÷ 5 = $40.

Write 60/105 in its simplest form.

Divide numerator and denominator by 15: 60÷15=4, 105÷15=7, so 4/7.

Write a fraction equivalent to 3/5.

Multiply numerator and denominator by the same number, e.g., 3/5 = 6/10.

Write 28/140 as a fraction in its simplest form.

Divide numerator and denominator by 28: 28÷28=1, 140÷28=5, so 1/5.

How do you find a fraction of an amount?

Divide by the denominator and multiply by the numerator. For example, 2/5 of 60: 60÷5=12, then 12×2=24.

Find 1/3 of 90.

Divide 90 by 3: 90 ÷ 3 = 30.

What are equivalent fractions?

Equivalent fractions are two fractions that represent the same amount, e.g., 1/2 and 6/12.

How do you find an equivalent fraction?

Multiply the numerator and denominator by the same number. For example, 5/6 = 10/12 (multiply by 2).

What is a simplified fraction?

A simplified fraction uses the smallest possible integer values. It is found by dividing numerator and denominator by a common factor.

Simplify 12/18.

Divide numerator and denominator by 6: 12÷6=2, 18÷6=3, so 2/3.

What is a mixed number? Give an example.

A mixed number has an integer part and a fraction part, e.g., 3 3/4 means three and three quarters.

What is an improper fraction?

An improper fraction has a numerator larger than the denominator, e.g., 15/4.

Convert 5 2/7 into an improper fraction.

5 wholes = 5×7=35 sevenths, plus 2 sevenths = 37 sevenths, so 37/7.

Convert 22/3 into a mixed number.

22 ÷ 3 = 7 remainder 1, so 7 1/3.

Write 5 3/4 as an improper fraction.

5 wholes = 5×4=20 quarters, plus 3 quarters = 23 quarters, so 23/4.

Write 17/5 as a mixed number.

17 ÷ 5 = 3 remainder 2, so 3 2/5.

There are 12 brass instruments. 1/3 are trumpets, 3 are trombones, the rest are horns. Find the number of horns.

Trumpets: 12×1/3=4. Trombones: 3. Horns: 12−4−3=5.

3/14 of caught mullet are underweight. If 168 mullet are caught, how many are expected underweight?

168 × 3/14 = (168÷14)×3 = 12×3 = 36.

Nora uses 7/10 of 250g cherries. Find the mass left.

Used: 250×7/10 = 175g. Left: 250−175 = 75g.

A ticket costs $13.50. A student gets a one-third reduction. How much does she pay?

Reduction: 13.50×1/3 = $4.50. Pay: 13.50−4.50 = $9.00.

A fuel tank holds 52 litres. It is a quarter full. Jim fills it at $2.18 per litre. How much does he pay?

Amount to fill: 52×(3/4)=39 litres. Cost: 39×2.18 = $85.02.

Saskia has $600. She spends 1/5 on a coat and gives 1/3 to her son. What fraction of $600 does she have left? (Give simplest form)

Spent: 1/5+1/3 = 3/15+5/15=8/15. Left: 1−8/15=7/15.

Jeff's share is $160, which is 5/11 of the prize. Find the value of the prize.

Prize = 160 ÷ (5/11) = 160 × 11/5 = 160×11÷5 = 1760÷5 = $352.

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