Multiplying fractions and mixed numbers

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टीचर्स के लिए: Multiplying fractions and mixed numbers (Primary Maths, Grade 5) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके स्टूडेंट्स लाइव गेम की तरह खेलें।

लेसन नोट्स

What is Multiplication?

Multiplication is a quick way to add the same number many times. For example, 3 × 4 means 4 + 4 + 4 = 12.
The numbers you multiply are called factors. The answer is called the product.
The multiplication sign is × (like 3 × 4) or a dot (like 3 ⋅ 4). Both mean the same.
Multiplication is commutative: 3 × 4 = 4 × 3. The order does not change the product.
You can think of multiplication as counting objects in a rectangle. If a rectangle is 3 rows and 4 columns, it has 3 × 4 = 12 squares.

Multiplying a Fraction by a Whole Number

To multiply a fraction by a whole number, multiply the top number (the numerator) by the whole number. The bottom number (the denominator) stays the same.
Example: \frac{2}{5} \times 3 = \frac{2 \times 3}{5} = \frac{6}{5}.
If the product is an improper fraction (top bigger than bottom), you can write it as a mixed number: \frac{6}{5} = 1\frac{1}{5}.
Think of \frac{2}{5} \times 3 as 3 groups of \frac{2}{5}, which is \frac{2}{5} + \frac{2}{5} + \frac{2}{5} = \frac{6}{5}.

Multiplying a Fraction by a Fraction

To multiply two fractions, multiply the numerators together and multiply the denominators together.
Example: \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}.
You can simplify before multiplying if you see a common factor. For example, \frac{2}{3} \times \frac{3}{4} can be simplified to \frac{1}{1} \times \frac{1}{2} = \frac{1}{2}.
Always check if your answer can be simplified. For example, \frac{4}{8} simplifies to \frac{1}{2}.

Why Multiplying by a Fraction Less Than 1 Makes the Answer Smaller

When you multiply a number by a fraction that is less than 1, the product is smaller than the original number.
Example: 6 \times \frac{1}{2} = 3. The answer 3 is less than 6.
This is because multiplying by \frac{1}{2} is like finding half of the number.
Multiplying by \frac{3}{4} is like finding three quarters of the number, so the answer is less than the number.
This is different from multiplying by a whole number greater than 1, which makes the answer bigger.

Using Area Models for Fraction Multiplication

An area model is a rectangle divided into equal parts. It helps you see fraction multiplication.
To multiply \frac{1}{2} \times \frac{1}{3}, draw a rectangle, split it into 2 rows and 3 columns. Shade 1 row and 1 column. The overlapping part is \frac{1}{6} of the whole.
The area of a rectangle is length × width. If the sides are fractions, the area is the product of those fractions.
Area models show why \frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}.

Multiplying Mixed Numbers

A mixed number has a whole number and a fraction, like 2\frac{1}{3}.
To multiply mixed numbers, first change them to improper fractions (where the numerator is bigger than the denominator).
To change 2\frac{1}{3} to an improper fraction: multiply the whole number by the denominator (2 × 3 = 6), add the numerator (6 + 1 = 7), and keep the denominator: \frac{7}{3}.
Then multiply the improper fractions as usual.
Example: 1\frac{1}{2} \times 2\frac{1}{3} = \frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = 3\frac{1}{2}.

Dividing with Fractions (Unit Fractions)

A unit fraction has 1 as the numerator, like \frac{1}{2}, \frac{1}{3}, \frac{1}{4}.
To divide a whole number by a unit fraction, multiply by the denominator. Example: 4 \div \frac{1}{2} = 4 \times 2 = 8.
To divide a unit fraction by a whole number, multiply the denominator by the whole number. Example: \frac{1}{3} \div 2 = \frac{1}{3 \times 2} = \frac{1}{6}.
Division is the opposite of multiplication. If 3 \times 4 = 12, then 12 \div 3 = 4.

Solving Real-World Problems

You can use fraction multiplication to find a fraction of an amount. For example, \frac{2}{3} of 12 is \frac{2}{3} \times 12 = 8.
If a recipe needs \frac{3}{4} cup of sugar and you make half the recipe, you need \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} cup.
If you run \frac{2}{5} of a 10 km race, you run \frac{2}{5} \times 10 = 4 km.
When solving word problems, look for words like 'of', 'times', or 'product' to know you need to multiply.

Key Vocabulary

Fraction: a number that shows part of a whole, like \frac{1}{2}.
Numerator: the top number of a fraction. It tells how many parts you have.
Denominator: the bottom number of a fraction. It tells how many equal parts the whole is divided into.
Improper fraction: a fraction where the numerator is bigger than or equal to the denominator, like \frac{7}{3}.
Mixed number: a whole number plus a fraction, like 2\frac{1}{3}.
Product: the answer you get when you multiply.
Unit fraction: a fraction with numerator 1, like \frac{1}{5}.

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 62 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

1.What is the result of a multiplication operation called?
Easy
- Asum
- Bdifference
- Cproduct
- Dquotient
2.Which symbol is commonly used to denote multiplication?
Easy
- A+
- B×
- C−
- D÷
3.Multiplying a fraction less than 1 by a whole number always gives a smaller answer than the whole number.
Easy
True or false?
4.Which expression gives the same value as 5 × 2/3?
Medium
- A10/3
- B5/6
- C2/15
- D7/3
5.Which of the following are correct ways to write 2 times 3? (select all that apply)
Medium
- A2×3
- B2⋅3
- C2+3
- D23
- E2×3
6.Match each multiplication expression with its product.
Medium
- 1/2 × 1/3
- 2/5 × 3/4
- 3 × 2/9
- 1/6
- 3/10
- 2/3
7.Arrange these steps in the correct order to multiply 1 1/2 by 3.
Medium
- Convert 1 1/2 to an improper fraction: 3/2
- Multiply 3/2 by 3 to get 9/2
- Write the answer as a mixed number: 4 1/2
8.A rectangle has a length of 2/3 meter and a width of 3/4 meter. What is its area?
Medium
- A1/2 square meter
- B5/7 square meter
- C6/12 square meter
- D1/2 meter

और सवाल

9.Put these steps in the correct order to multiply 1 1/2 by 2/3.
Medium
- Convert 1 1/2 to an improper fraction: 3/2
- Multiply the numerators: 3 × 2 = 6
- Multiply the denominators: 2 × 3 = 6
- Simplify 6/6 to 1
10.Which of the following are correct ways to multiply 2/3 by 3/4? (select all that apply)
Medium
- A(2×3)/(3×4)
- B(2×4)/(3×3)
- C(2/3) × (3/4)
- D(2×3)/(3×4) = 6/12
- E(2/3) × (4/3)
11.When you multiply a whole number by a fraction less than 1, the product is always less than the whole number.
Easy
True or false?
12.What is 2 1/3 × 1 1/2?
Medium
- A3 1/2
- B3 1/3
- C2 1/6
- D3 5/6
13.Which of the following are true? (select all that apply)
Medium
- A3 × 2/5 = 6/5
- B2/5 × 3 = 6/5
- C3 × 2/5 = 5/6
- D2/5 × 3 = 6/15
- E3 × 2/5 = 1 1/5
14.Arrange these steps in the correct order to find the area of a rectangle with length 2/3 m and width 3/4 m.
Medium
- Write the formula: area = length × width
- Substitute the numbers: area = 2/3 × 3/4
- Multiply numerators: 2 × 3 = 6
- Multiply denominators: 3 × 4 = 12
- Simplify 6/12 to 1/2
15.The product of two fractions less than 1 is always less than 1.
Easy
True or false?
16.Match each mixed number multiplication with its product.
Medium
- 1 1/2 × 2/3
- 2 1/4 × 1/3
- 3 1/5 × 5/8
- 1
- 3/4
- 2
17.A recipe needs 3/4 cup of sugar. You want to make 1/2 of the recipe. How much sugar do you need?
Hard
- A3/8 cup
- B1 1/2 cups
- C3/2 cups
- D6/4 cups
18.What is 1 \frac{1}{2} \times 2 \frac{1}{3}?
Medium
- A2 \frac{1}{6}
- B3 \frac{1}{2}
- C3 \frac{1}{3}
- D2 \frac{5}{6}
19.Which of the following is the correct first step to multiply \frac{2}{5} \times \frac{3}{4}?
Easy
- AMultiply the numerators: 2 \times 3 = 6
- BMultiply the denominators: 5 \times 4 = 20
- CAdd the numerators: 2 + 3 = 5
- DCross-multiply: 2 \times 4 = 8
20.\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
Easy
True or false?
21.What is \frac{3}{5} \times 10?
Medium
- A6
- B5
- C15
- D30
22.Which of the following are correct ways to multiply 1 \frac{1}{2} \times 2? (select all that apply)
Medium
- A1.5 \times 2 = 3
- B\frac{3}{2} \times 2 = 3
- C1 \times 2 + \frac{1}{2} \times 2 = 3
- D\frac{1}{2} \times 2 = 1
- E1 \times 2 = 2
23.Arrange these steps in the correct order to multiply 2 \frac{1}{4} by \frac{2}{3}.
Medium
- Convert 2 \frac{1}{4} to \frac{9}{4}
- Multiply numerators: 9 \times 2 = 18
- Multiply denominators: 4 \times 3 = 12
- Simplify \frac{18}{12} to 1 \frac{1}{2}
24.A recipe calls for \frac{2}{3} cup of flour. If you want to make 1 \frac{1}{2} times the recipe, how much flour do you need?
Medium
- A1 cup
- B\frac{3}{4} cup
- C1 \frac{1}{3} cups
- D1 \frac{1}{2} cups
25.Which of the following expressions have the same value as \frac{3}{5} \times \frac{5}{6}? (select all that apply)
Medium
- A\frac{1}{2}
- B\frac{15}{30}
- C\frac{3}{6}
- D\frac{5}{10}
- E\frac{1}{3}
26.Multiplying a number by \frac{3}{4} always gives a smaller result than the original number.
Easy
True or false?
27.A jug contains \frac{3}{4} liter of juice. How much juice is in 2 \frac{2}{3} jugs?
Medium
- A2 liters
- B1 \frac{1}{2} liters
- C\frac{3}{2} liters
- D2 \frac{1}{4} liters
28.Match each expression with its simplified product.
Medium
- \frac{2}{3} \times \frac{3}{4}
- \frac{1}{2} \times \frac{4}{5}
- \frac{3}{7} \times \frac{7}{9}
- \frac{1}{2}
- \frac{2}{5}
- \frac{1}{3}
29.Arrange these steps in the correct order to find the area of a rectangle with length 2 \frac{1}{3} m and width \frac{3}{5} m.
Hard
- Convert 2 \frac{1}{3} to \frac{7}{3}.
- Multiply the numerators: 7 \times 3 = 21.
- Multiply the denominators: 3 \times 5 = 15.
- Simplify \frac{21}{15} to \frac{7}{5}.
30.A square has a side length of \frac{3}{4} meter. What is its area?
Hard
- A\frac{9}{16} square meter
- B\frac{3}{4} square meter
- C1 \frac{1}{2} square meters
- D\frac{3}{8} square meter
31.Arrange these steps in the correct order to multiply 3/4 by 2/5.
Medium
- Multiply the numerators: 3 × 2 = 6
- Multiply the denominators: 4 × 5 = 20
- Simplify 6/20 to 3/10
32.The product of a fraction and a whole number can be found by multiplying the numerator by the whole number and keeping the denominator.
Easy
True or false?
33.A rectangle has a length of 2 1/2 meters and a width of 3/4 meter. What is its area in square meters?
Medium
- A1 7/8
- B2 1/8
- C3 1/8
- D3 3/4
34.Arrange these steps in the correct order to multiply 1 1/2 by 2 1/3.
Medium
- Convert 1 1/2 to 3/2
- Convert 2 1/3 to 7/3
- Multiply: (3/2) × (7/3) = 21/6
- Simplify 21/6 to 3 1/2
35.To multiply mixed numbers, you should first convert them to improper fractions.
Easy
True or false?
36.What is \frac{2}{5} \times 3?
Easy
- A\frac{6}{5}
- B\frac{5}{6}
- C\frac{6}{15}
- D\frac{2}{15}
37.What is \frac{3}{8} \times \frac{2}{3}? Give your answer in simplest form.
Medium
- A\frac{1}{4}
- B\frac{6}{24}
- C\frac{1}{3}
- D\frac{2}{8}
38.What is 1 \frac{1}{2} \times 4?
Medium
- A6
- B4 \frac{1}{2}
- C5
- D8
39.Which of the following are correct ways to multiply \frac{2}{3} by \frac{5}{7}? (select all that apply)
Medium
- AMultiply numerators: 2 × 5, and denominators: 3 × 7
- BMultiply denominators: 3 × 7, and numerators: 2 × 5
- CAdd the numerators and add the denominators
- DSimplify before multiplying if possible
40.When you multiply a fraction by a whole number, you multiply only the numerator by the whole number and keep the denominator the same.
Easy
True or false?
41.What is 3/4 of 20?
Easy
42.Complete the sentence.
Easy
The two numbers being multiplied are called ____.
43.What is the reciprocal of 2/5?
Medium
44.A rectangle has a length of 1 1/2 meters and a width of 3/4 meter. What is its area in square meters?
Medium
45.Fill in the blank:
Easy
The product of 2/5 and 3 is ____.
46.Write the reciprocal of 3/4.
Medium
47.What is \frac{2}{3} \times 6?
Easy
48.Fill in the blank to make the statement true.
Medium
\frac{3}{4} \times \frac{2}{5} = \frac{6}{20}, which simplifies to ____.
49.A rectangle has a length of \frac{3}{4} meter and a width of \frac{2}{3} meter. What is its area in square meters?
Medium
50.What is the product of \frac{2}{7} and \frac{3}{5}?
Easy
51.What is \frac{2}{3} \times 9?
Easy
52.What is \frac{3}{4} \times \frac{2}{5}? Give your answer as a fraction in simplest form.
Medium
53.Explain why multiplying by a fraction less than 1 gives a smaller result than the original number.
Hard
54.Explain why multiplying a number by a fraction less than 1 gives a smaller result than the original number. Use an example.
Hard
55.Explain why the area of a rectangle is the same even if you multiply length × width or width × length. Use the commutative property in your explanation.
Hard
56.Explain why the product of \frac{2}{3} and \frac{4}{5} is less than both \frac{2}{3} and \frac{4}{5}.
Hard
57.What is 3/4 of 20?
Easy
- A15
- B14
- C17
- D16
58.A rectangle has a length of 1 1/2 meters and a width of 3/4 meter. What is its area in square meters?
Medium
- A2.125 m²
- B1.125 m²
- C0.125 m²
- D3.125 m²
59.What is \frac{2}{3} \times 6?
Easy
- A5
- B3
- C4
- D6
60.A rectangle has a length of \frac{3}{4} meter and a width of \frac{2}{3} meter. What is its area in square meters?
Medium
- A2.5 m²
- B0.5 m²
- C1.5 m²
- D-0.5 m²
61.What is \frac{2}{3} \times 9?
Easy
- A7
- B5
- C8
- D6
62.What is \frac{3}{4} \times \frac{2}{5}? Give your answer as a fraction in simplest form.
Medium
- A0.3
- B1.3
- C-0.7
- D2.3

रिवीज़न नोट्स

## Multiplying Fractions and Mixed Numbers ### Multiplying a Fraction by a Whole Number - **Multiply the numerator (top number) by the whole number.** Keep the denominator (bottom number) the same. - Example: \(\frac{2}{5} \times 3 = \frac{2 \times 3}{5} = \frac{6}{5}\). - If you can, simplify the answer. \(\frac{6}{5}\) is an improper fraction (top bigger than bottom). You can write it as a mixed number: \(1\frac{1}{5}\). ### Multiplying a Fraction by a Fraction - **Multiply the numerators together, and multiply the denominators together.** - Example: \(\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}\). - **Why is the answer smaller?** When you multiply by a fraction less than 1, you are taking a part of something. For example, \(\frac{1}{2} \times \frac{3}{4}\) means half of three-quarters, which is less than three-quarters. ### Area Models - You can draw a rectangle and split it into parts to show fraction multiplication. - Example: To show \(\frac{1}{2} \times \frac{3}{4}\), draw a rectangle, split it into 4 equal columns and shade 3 columns (that's \(\frac{3}{4}\)). Then split it into 2 equal rows and shade 1 row (that's \(\frac{1}{2}\)). The double-shaded part is \(\frac{3}{8}\) of the whole rectangle. ### Multiplying Mixed Numbers - **Convert each mixed number to an improper fraction first.** - A mixed number has a whole number and a fraction, like \(2\frac{1}{3}\). - To convert: multiply the whole number by the denominator, then add the numerator. Put that over the denominator. - Example: \(2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}\). - Then multiply the improper fractions as usual. - Example: \(1\frac{1}{2} \times 2\frac{1}{3} = \frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = 3\frac{1}{2}\). ### Dividing with Unit Fractions - A **unit fraction** has 1 as the numerator, like \(\frac{1}{2}\), \(\frac{1}{3}\), \(\frac{1}{4}\). - **Dividing a unit fraction by a whole number:** Multiply the denominator by the whole number. - Example: \(\frac{1}{3} \div 2 = \frac{1}{3 \times 2} = \frac{1}{6}\). - **Dividing a whole number by a unit fraction:** Multiply the whole number by the denominator. - Example: \(2 \div \frac{1}{3} = 2 \times 3 = 6\). ### Real-World Problems - **Finding a fraction of an amount:** Multiply the amount by the fraction. - Example: Find \(\frac{2}{3}\) of 12. \(\frac{2}{3} \times 12 = \frac{2 \times 12}{3} = \frac{24}{3} = 8\). - Always check if your answer makes sense. If you multiply by a fraction less than 1, the answer is smaller than the original number. ### Key Tips - **Simplify** your answers when possible. - **Convert mixed numbers** to improper fractions before multiplying. - Use **area models** to see what is happening. - Practice with real-life examples like recipes, sharing, and measuring.

fraction: A number that shows part of a whole. It has a top number (numerator) and a bottom number (denominator).
numerator: The top number of a fraction. It tells how many parts you have.
denominator: The bottom number of a fraction. It tells how many equal parts the whole is divided into.
mixed number: A number made of a whole number and a fraction, like 2 1/3.
improper fraction: A fraction where the numerator is bigger than or equal to the denominator, like 7/3.
unit fraction: A fraction with 1 as the numerator, like 1/2 or 1/4.
product: The answer you get when you multiply two numbers.
area model: A drawing that uses a rectangle split into parts to show multiplication of fractions.
simplify: To make a fraction smaller by dividing the top and bottom by the same number. For example, 2/4 simplifies to 1/2.
commutative property: The rule that says you can multiply numbers in any order and get the same answer. For example, 2 × 3 = 3 × 2.

फ्लैशकार्ड

What does 3 × 4 mean as repeated addition?

3 × 4 means 4 + 4 + 4, which is 12. It is like having 3 groups of 4.

What is the result of a multiplication called?

The result is called the product. For example, in 3 × 4 = 12, 12 is the product.

What are the two numbers you multiply together called?

They are called factors. In 3 × 4, both 3 and 4 are factors.

How do you multiply a fraction by a whole number? Give an example.

Multiply the numerator by the whole number and keep the denominator the same. For example, 3 × 1/4 = 3/4.

What is 2 × 3/5?

2 × 3/5 = 6/5, which is 1 1/5.

How do you multiply two fractions? Give an example.

Multiply the numerators together and the denominators together. For example, 1/2 × 3/4 = 3/8.

What is 2/3 × 4/5?

2/3 × 4/5 = 8/15.

When you multiply a number by a fraction less than 1, is the product larger or smaller than the original number?

Smaller. For example, 6 × 1/2 = 3, which is less than 6.

Why is 8 × 1/4 less than 8?

Because 1/4 is less than 1, so you are taking only a part of 8. 8 × 1/4 = 2, which is less than 8.

What is 5 × 2/3? Is the product greater or less than 5?

5 × 2/3 = 10/3 = 3 1/3, which is less than 5 because 2/3 is less than 1.

How can you use an area model to show 1/2 × 1/3?

Draw a rectangle, divide it into 2 equal parts vertically and 3 equal parts horizontally. Shade 1/2 and 1/3. The overlapping part is 1/6 of the whole, so 1/2 × 1/3 = 1/6.

What is 1/4 × 1/2? Use an area model idea.

1/4 × 1/2 = 1/8. The overlapping part of 1/4 and 1/2 is 1/8 of the whole.

How do you multiply mixed numbers? Give the first step.

First, change each mixed number to an improper fraction. For example, 1 1/2 becomes 3/2.

What is 1 1/2 × 2 1/3?

Change to improper fractions: 3/2 × 7/3 = 21/6 = 3 1/2.

What is 2 1/4 × 1 1/3?

2 1/4 = 9/4, 1 1/3 = 4/3, so 9/4 × 4/3 = 36/12 = 3.

How do you divide a unit fraction by a whole number? Give an example.

Keep the numerator 1 and multiply the denominator by the whole number. For example, 1/3 ÷ 2 = 1/6.

What is 1/4 ÷ 3?

1/4 ÷ 3 = 1/12.

How do you divide a whole number by a unit fraction? Give an example.

Multiply the whole number by the denominator of the fraction. For example, 2 ÷ 1/3 = 2 × 3 = 6.

What is 5 ÷ 1/2?

5 ÷ 1/2 = 5 × 2 = 10.

A recipe needs 2/3 cup of sugar. You make 1/2 of the recipe. How much sugar do you need?

You need 2/3 × 1/2 = 2/6 = 1/3 cup of sugar.

A rectangle is 3/4 m long and 2/5 m wide. What is its area?

Area = 3/4 × 2/5 = 6/20 = 3/10 square meters.

What is the product of 7 and 3/5?

7 × 3/5 = 21/5 = 4 1/5.

What is 3/8 × 4/9? Simplify if possible.

3/8 × 4/9 = 12/72 = 1/6.

What is 2 1/2 × 3/4?

2 1/2 = 5/2, so 5/2 × 3/4 = 15/8 = 1 7/8.

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