### Math Notes

Subjects
Basic Mathematics Solved Problems | Topics - Contents

# Multiplication of Fractions

#### Multiplication of Proper and Improper Fractions

1. Multiply Numerator to Numerator and Denominator to denominator
2. Reduce the fraction
Examples:
1. Perform the indicated operation: $$\frac{13}{11} \:x\: \frac{2}{3}$$
1. $$\frac{13}{11} \:x\: \frac{2}{3}$$ = $$\frac{13x2}{11x3}$$ = $$\frac{26}{33}$$
2. Since the numerator and denominator has no common factors, then the fraction is in its simplest form.
2. Perform the indicated operation: $$\frac{16}{11} \:x\: \frac{9}{4}$$
1. $$\frac{16}{11} \:x\: \frac{9}{4}$$ = $$\frac{16x9}{11x4}$$ = $$\frac{144}{44}$$
2. Simplify / Reduce:
3. $$\frac{144}{44}$$ = $$\frac{2x2x2x2x3x3}{2x2x11}$$
4. $$\frac{16}{11} \:x\: \frac{9}{4}$$ = $$\frac{2x2x3x3}{11}$$
5. $$\frac{16}{11} \:x\: \frac{9}{4}$$ = $$\frac{36}{11}$$
3. You can also simplify the fraction before multiplying mexample: $$\frac{16}{11} \:x\: \frac{9}{4}$$
1. $$\frac{16}{11} \:x\: \frac{9}{4}$$ = $$\frac{16x9}{11x4}$$
2. Factor every number with its prime factors.
3. $$\frac{16x9}{11x4}$$ =$$\frac{2x2x2x2 \:x\:3x3}{11x2x2}$$
4. Cancel / divide similar factors

5. $$\frac{16x9}{11x4}$$ =$$\frac{2x2 \:x\:3x3}{11}$$
6. Multiply the remaining numbers.

7. $$\frac{16x9}{11x4}$$ =$$\frac{36}{11}$$

#### Multiplication of mixed fractions

1. Transform mixed fraction to its equivalent improper fraction.
2. Use the procedures for multiplying improper fractions.