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Multiplying Fractions

Units and Fractions Multiplying Fractions

Table Of Contents

🎬 Math Angel Video: How to Multiply Fractions

How to Multiply Fractions (General Method)?

$Explanation of how to multiply fractions using the general method and cross-cancelling method, showing steps and simplification.$

⏩️ (0:01)

🛎️ The general method for multiplying fractions follows these 3 steps:

$$\frac{4}{7} \times \frac{3}{8} = ?$$

Step 1: Multiply the numerators:
$$4 \times 3 = 12$$
Step 2: Multiply the denominators:
$$7 \times 8 = 56$$
Step 3: Simplify the fraction if possible:
$$\frac{12}{56} = \frac{3}{14}$$

Cross-Cancelling for Multiplying Fractions

$Cross-cancelling method for multiplying fractions 1/2 and 3/5, showing the simplified result as 3/10.$

⏩️ (0:23)

🛎️ What is Cross-Cancelling?

Cross-cancelling (or cross-cancellation) is a useful trick that simplifies fraction multiplication before multiplying, making calculations easier.

🛎️ An Example of Cross-Cancellation:

$$\frac{11}{24} \times \frac{36}{55} = ?$$

Step 1: Identify Common Factors
Check if the numerator of one fraction and the denominator of the other have a common factor.
- 11 and 55 share a factor of 11
- 36 and 24 share a factor of 12
Step 2: Divide by the Common Factors
Reduce those numbers by dividing both by their common factor.
- 11 and 55 become 1 and 5
- 36 and 24 become 3 and 2
Step 3: Multiply the Simplified Numerators and Denominators
$$\frac{1}{2} \times \frac{3}{5} = \frac{1 \times 3}{2 \times 5} = \frac{3}{10}$$
Step 4: Double-check for Further Simplification
Since 3 and 10 have no common factors other than 1, the fraction is already in its simplest form.

How to Multiply Fractions by Whole Numbers?

$Multiplication of 88 piano keys by the fraction 13/22 to find the number of black keys, resulting in 52.$

⏩️ (1:30)

To multiply a fraction by a whole number, rewrite the whole number as a fraction with a denominator of 1.

For example: A piano has 88 keys, and $\large \frac{13}{22}$ of them are black. To find the number of black keys, we multiply:

$$ 88 \times \frac{13}{22} = ? $$

Step 1: Rewrite the Whole Number as a Fraction

$$ \frac{88}{1} \times \frac{13}{22} $$

Step 2: Simplify Using Cross-Canceling
- The greatest common factor (GCF) between 88 and 22 is 22.
- So 88 and 22 become 4 and 1.
Step 3: Multiply the Simplified Fractions

$$ \frac{4}{1} \times \frac{13}{1} = \frac{52}{1} = 52 $$

❇️ The answer: There are 52 black keys on the piano.

How to Multiply Mixed Numbers?

$Explanation of handling mixed fractions by converting them into improper fractions, with the correct answer highlighted as 17.$

⏩️ (2:18)

🛎️ What is A Mixed Number?

A mixed number consists of a whole number and a fraction.

To multiply mixed numbers with fractions, you must convert them into improper fractions first.

For example,
$$ 3 \frac{2}{5} \times 5 = ? $$

Step 1: Convert the Mixed Number
$$ 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $$

Step 2: Multiply the Fractions and Simplify
$$ \frac{17}{5} \times 5 = 17 $$

❇️ Thus, the final answer is 17.

🍪 Quiz: Practice Multiplying Fractions by Whole Numbers and Mixed Numbers

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Multiplying Fractions

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Q: What is $\frac{3}{5} \times \frac{2}{7}$?

$\frac{15}{35}$

$\frac{5}{14}$

$\frac{6}{12}$

$\frac{6}{35}$

Feedback: Not quite! Multiply the numerators: 3 × 2 = 6. Then, multiply the denominators: 5 × 7 = 35. The result is $\frac{6}{35}$, which cannot be simplified further.

Feedback: Well done! Multiply the numerators: 3 × 2 = 6. Then, multiply the denominators: 5 × 7 = 35. The result is $\frac{6}{35}$, which cannot be simplified further.

2 / 6

Q: What is $\frac{7}{5}$ of 15?

15

24

21

18

Feedback: Not quite! Multiply $\frac{7}{5} \times 15$ by rewriting 15 as $\frac{15}{1}$. Cross-cancel 5 and 15 to get 1 and 3. Multiply 7 by 3 to get 21.

Feedback: Well done! Multiply $\frac{7}{5} \times 15$ by rewriting 15 as $\frac{15}{1}$. Cross-cancel 5 and 15 to get 1 and 3. Multiply 7 by 3 to get 21.

3 / 6

Q: What is $\frac{15}{35} \times \frac{5}{10}$ ?

$\frac{3}{10}$

$\frac{15}{25}$

$\frac{5}{35}$

$\frac{3}{14}$

Feedback: Not quite! Simplify $\frac{15}{35}$ to $\frac{3}{7}$ and $\frac{5}{10}$ to $\frac{1}{2}$. Multiply the numerators: $3 \times 1 = 3$. Multiply the denominators: $7 \times 2 = 14$. The result is $\frac{3}{14}$.

Feedback: Well done! Simplify $\frac{15}{35}$ to $\frac{3}{7}$ and $\frac{5}{10}$ to $\frac{1}{2}$. Multiply the numerators: $3 \times 1 = 3$. Multiply the denominators: $7 \times 2 = 14$. The result is $\frac{3}{14}$.

4 / 6

Q: What is $\frac{16}{24} \times \frac{18}{27}$ ?

$\frac{4}{9}$

$\frac{1}{4}$

$\frac{2}{3}$

$\frac{1}{2}$

Feedback: Not quite! Simplify: $16$ and $24$ divide by $8$, becoming $2$ and $3$, and $18$ and $27$ divide by $9$, becoming $2$ and $3$. Multiply: $2 \times 2 = 4$ and $3 \times 3 = 9$, giving $\frac{4}{9}$.

Feedback: Well done! Simplify: $16$ and $24$ divide by $8$, becoming $2$ and $3$, and $18$ and $27$ divide by $9$, becoming $2$ and $3$. Multiply: $2 \times 2 = 4$ and $3 \times 3 = 9$, giving $\frac{4}{9}$.

5 / 6

Q: What is $\frac{25}{40} \times \frac{32}{50}$ using the cross-cancelling method?

$\frac{2}{5}$

$\frac{8}{25}$

$\frac{5}{8}$

$\frac{4}{5}$

Feedback: Not quite! Simplify: $25$ and $50$ divide by $25$, becoming $1$ and $2$, and $40$ and $32$ divide by $8$, becoming $5$ and $4$. Multiply: $1 \times 4 = 4$ and $5 \times 2 = 10$, giving $\frac{4}{10}$, which simplifies to $\frac{2}{5}$.

Feedback: Well done! Simplify: $25$ and $50$ divide by $25$, becoming $1$ and $2$, and $40$ and $32$ divide by $8$, becoming $5$ and $4$. Multiply: $1 \times 4 = 4$ and $5 \times 2 = 10$, giving $\frac{4}{10}$, which simplifies to $\frac{2}{5}$.

6 / 6

Q: What is $2 \frac{1}{3} \times \frac{9}{4}$ using the cross-cancelling method?

$\frac{27}{12}$

$\frac{21}{4}$

$\frac{21}{8}$

$\frac{18}{12}$

Feedback: Not quite! Convert $2 \frac{1}{3}$ into an improper fraction: $2 \frac{1}{3} = \frac{7}{3}$. Cross-cancel: $9$ and $3$ divide by $3$, becoming $3$ and $1$. Multiply: $7 \times 3 = 21$ and $1 \times 4 = 4$, giving $\frac{21}{4}$.

Feedback: Well done! Convert $2 \frac{1}{3}$ into an improper fraction: $2 \frac{1}{3} = \frac{7}{3}$. Cross-cancel: $9$ and $3$ divide by $3$, becoming $3$ and $1$. Multiply: $7 \times 3 = 21$ and $1 \times 4 = 4$, giving $\frac{21}{4}$.

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