How to Multiply Fractions (General Method)? [pptime time="0:01"](0:01) [/pptime]

The general method for multiplying fractions follows these 3 steps: For example: $$\frac{4}{7} \times \frac{3}{8} = ?$$ 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-Canceling for Multiplying Fractions [pptime time="0:23"](0:23) [/pptime]

Cross-canceling is a useful trick that simplifies fraction multiplication before multiplying, making calculations easier. For example: $$\frac{11}{24} \times \frac{36}{55} = ?$$ 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? [pptime time="1:30"](1:30) [/pptime]

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.

Multiplying Fractions - Methods, Examples, Practice

Q: How to Multiply Mixed Numbers? [pptime time="2:18"](2:18) [/pptime]

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.

🎬 Video: How to Multiply Fractions

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How to Multiply Fractions (General Method)? (0:01)

The general method for multiplying fractions follows these 3 steps:

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

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-Canceling for Multiplying Fractions (0:23)

Cross-canceling is a useful trick that simplifies fraction multiplication before multiplying, making calculations easier.

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

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? (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? (2:18)

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.