Introduction To Fractions

Học bằng cách chơi

Trả lời những câu hỏi này để kiếm năng lượng, rồi câu cá và khám phá. Không cần tài khoản.

Dành cho giáo viên: slide bài học, ghi chú ôn tập, sơ đồ sẵn dùng cho Introduction To Fractions (Maths [CIE], Core) — dùng trong bài giảng của bạn, hoặc chạy chủ đề như một hoạt động lớp học tương tác để học sinh chơi như một trò chơi trực tiếp.

Ghi chú bài học

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).

Slide

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 59 câu hỏi. Đăng ký để xem tất cả.

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

Thêm câu hỏi

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

Ghi chú ôn tập

## 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.

Thẻ ghi nhớ

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.

Unlock all 59 questions, flashcards & more

Tạo tài khoản miễn phí để xem mọi câu hỏi, slide, thẻ ghi nhớ và ghi chú ôn tập cho chủ đề này.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Đề thi cũ

Luyện đề thi cũ cho chủ đề này sắp ra mắt.

Sắp ra mắt