Introduction To Fractions

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수업 노트

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).

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연습 문제

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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

더 많은 문제

9.Nora makes a birthday cake. Nora has a packet containing 250g of cherries. She uses 7/10 of the cherries in the cake. Find the mass of cherries she has left.
Medium
- A75 g
- B175 g
- C25 g
- D100 g
10.Georgiana is travelling by train from Redtown to Teignley. The price of a ticket is $13.50. Georgiana’s ticket price is reduced by one-third because she is a student. Work out how much she pays for her ticket.
Medium
- A$9.00
- B$4.50
- C$13.50
- D$10.00
11.A fuel tank holds 52 litres when full. The tank is a quarter full. Jim fills the tank with fuel that costs $2.18 per litre. Work out how much Jim pays.
Hard
- A$85.02
- B$28.34
- C$56.68
- D$113.36
12.Saskia has $600. She spends 1/5 of the $600 on a coat and gives 1/3 of the $600 to her son. What fraction of the $600 does she have left? Give your answer in its simplest form.
Hard
- A7/15
- B8/15
- C2/5
- D1/3
13.Jeff and his friends win a prize. Jeff’s share is $160 which is 5/11 of the prize. Work out the value of the prize.
Medium
- A$352
- B$288
- C$416
- D$320
14.Find a fraction that makes this statement true: 7/9 < ? < 8/9.
Hard
- A15/18
- B5/6
- C23/27
- D17/18
15.A car park has 880 spaces. At 0600 one morning, 1/40 of the 880 spaces are filled. By 0630, no cars have left the car park but another 1/5 of the 880 spaces are filled. Work out the fraction of the 880 spaces that are empty at 0630.
Hard
- A31/40
- B33/40
- C7/8
- D3/4
16.Work out 2 1/4 ÷ 1 5/6. Give your answer as a mixed number in its simplest form.
Hard
- A1 7/22
- B1 5/22
- C2 1/4
- D1 1/2
17.What is the numerator in the fraction 3/8?
Easy
- A3
- B8
- C11
- D5
18.Shade 3/4 of a rectangle divided into 8 equal squares. How many squares should you shade?
Easy
- A6
- B4
- C3
- D2
19.Find 2/5 of $80.
Easy
- A$32
- B$16
- C$40
- D$24
20.A cake recipe uses 3/4 cup of sugar. How much sugar is needed for 8 cakes?
Medium
- A6 cups
- B4 cups
- C8 cups
- D12 cups
21.A tank is 2/3 full. It holds 120 litres when full. How many litres are in the tank?
Easy
- A80 litres
- B60 litres
- C40 litres
- D100 litres
22.Which fraction is equivalent to 1/2?
Easy
- A2/4
- B2/3
- C3/4
- D1/4
23.Simplify the fraction 18/24.
Easy
- A3/4
- B6/8
- C9/12
- D2/3
24.Convert 7/3 to a mixed number.
Easy
- A2 1/3
- B3 1/3
- C2 2/3
- D1 4/3
25.What fraction of the shape is shaded? (A circle divided into 4 equal parts, 1 part shaded)
Easy
- A1/4
- B3/4
- C1/2
- D1/3
26.There are 30 students in a class. 2/5 are girls. How many boys are there?
Medium
- A18
- B12
- C20
- D15
27.A prize of $200 is shared. Ahmed gets 3/8 of the prize. How much does Ahmed get?
Medium
- A$75
- B$60
- C$80
- D$120
28.Write 4/6 in its simplest form.
Easy
- A2/3
- B1/2
- C3/4
- D2/5
29.What is 1/3 of 2/5?
Medium
- A2/15
- B3/8
- C2/8
- D1/15
30.Convert 4 2/3 to an improper fraction.
Easy
- A14/3
- B10/3
- C12/3
- D8/3
31.Which of these fractions is the largest?
Medium
- A3/4
- B1/2
- C2/3
- D5/8
32.A piece of ribbon is 2/3 m long. You cut off 1/2 m. How much ribbon is left?
Medium
- A1/6 m
- B1/3 m
- C1/2 m
- D1/4 m
33.What is the numerator in the fraction 5/9?
Easy
- A5
- B9
- C4
- D14
34.What does the denominator in a fraction represent?
Easy
- AThe number of parts you have
- BThe total number of equal parts the whole is divided into
- CThe number of wholes
- DThe size of one part
35.Which of these fractions is equivalent to 1/2?
Easy
- A2/4
- B3/8
- C4/6
- D5/12
36.What is the numerator in the fraction 7/12?
Easy
- A7
- B12
- C19
- D5
37.What does the denominator in the fraction 3/8 represent?
Easy
- AThe number of parts you have
- BThe total number of equal parts the whole is divided into
- CThe number of parts shaded
- DThe value of the fraction
38.Which of these is an improper fraction?
Easy
- A2/3
- B5/4
- C7/8
- D1/2
39.The fraction 6/8 is equivalent to 3/4.
Easy
True or false?
40.Convert the mixed number 3 2/5 to an improper fraction.
Medium
- A17/5
- B13/5
- C15/5
- D11/5
41.Convert the improper fraction 19/4 to a mixed number.
Medium
- A4 3/4
- B3 3/4
- C4 1/4
- D5 1/4
42.Which of the following fractions is the smallest?
Medium
- A3/4
- B2/3
- C5/8
- D7/12
43.Arrange these fractions in order of size, starting with the smallest: 2/3, 5/6, 1/2, 7/12.
Hard
- 2/3
- 5/6
- 1/2
- 7/12
44.Match each improper fraction to its equivalent mixed number.
Hard
- 11/4
- 7/3
- 9/2
- 13/5
- 2 3/5
- 2 1/3
- 2 3/4
- 4 1/2
45.Which of the following fractions are equivalent to 2/3? Select all that apply.
Medium
- A4/6
- B6/9
- C8/12
- D10/15
- E3/2
46.The fraction 8/12 simplifies to 2/3.
Easy
True or false?
47.Complete the sentence.
Easy
In the fraction 5/9, the numerator is ____ and the denominator is ____.
48.What is 1/5 of 100?
Easy
49.Find 3/8 of 72.
Medium
50.Simplify the fraction 24/36 to its simplest form.
Easy
24/36 = ____
51.Write down a fraction that is equivalent to 2/5.
Easy
52.A recipe requires 2/3 cup of sugar. How much sugar is needed for 9 cakes?
Medium
53.Work out 3/8 of 64.
Medium
54.Fill in the blanks to complete the sentence.
Easy
To convert a mixed number to an improper fraction, multiply the whole number by the ____ and add the ____.
55.Explain how to find an equivalent fraction to 3/7.
Medium
56.What is 1/5 of 100?
Easy
- A20
- B24
- C22
- D18
57.Find 3/8 of 72.
Medium
- A27
- B30
- C24
- D33
58.A recipe requires 2/3 cup of sugar. How much sugar is needed for 9 cakes?
Medium
- A7 cups
- B6 cups
- C8 cups
- D5 cups
59.Work out 3/8 of 64.
Medium
- A26
- B22
- C24
- D28

복습 노트

## 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.

플래시카드

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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