1. [tex]$\frac{1}{6} \times \frac{5}{9}=[/tex]
2. [tex]$\frac{6}{7} \times \frac{2}{9}=[/tex]
3. [tex]$\frac{5}{24} \times \frac{8}{15}=[/tex]
4. [tex]$2 \frac{11}{12} \times \frac{2}{5}=[/tex]
5. [tex]$4 \frac{9}{10} \times 1 \frac{1}{7}=[/tex]
Copy and answer. Write the answer in simplest form.
Answer (2)
The answers to the multiplication problems involving fractions and mixed numbers are: 1. 54 5 , 2. 21 4 , 3. 9 1 , 4. 6 7 , and 5. 5 28 . Each answer is presented in its simplest form after performing the multiplication and simplifying where necessary.
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Multiply the numerators and denominators of the fractions.
Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by the GCD.
For mixed numbers, convert them to improper fractions before multiplying.
The simplified results are: 54 5 , 21 4 , 9 1 , 6 7 , and 5 28 .
Explanation
Problem Analysis We are given a series of multiplication problems involving fractions and mixed numbers. Our goal is to perform each multiplication and simplify the result to its simplest form.
Solution Plan For each problem, we will follow these steps:
If there are mixed numbers, convert them to improper fractions.
Multiply the numerators to get the new numerator.
Multiply the denominators to get the new denominator.
Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by the GCD.
Solving Problem 1
6 1 × 9 5 = 6 × 9 1 × 5 = 54 5 . The GCD of 5 and 54 is 1, so the fraction is already in simplest form.
Solving Problem 3
7 6 × 9 2 = 7 × 9 6 × 2 = 63 12 . The GCD of 12 and 63 is 3. Dividing both numerator and denominator by 3, we get 63 ÷ 3 12 ÷ 3 = 21 4 .
Solving Problem 5
24 5 × 15 8 = 24 × 15 5 × 8 = 360 40 . The GCD of 40 and 360 is 40. Dividing both numerator and denominator by 40, we get 360 ÷ 40 40 ÷ 40 = 9 1 .
Solving Problem 7
2 12 11 × 5 2 . First, convert the mixed number to an improper fraction: 2 12 11 = 12 2 × 12 + 11 = 12 24 + 11 = 12 35 . Now, multiply: 12 35 × 5 2 = 12 × 5 35 × 2 = 60 70 . The GCD of 70 and 60 is 10. Dividing both numerator and denominator by 10, we get 60 ÷ 10 70 ÷ 10 = 6 7 .
Solving Problem 9
4 10 9 × 1 7 1 . First, convert the mixed numbers to improper fractions: 4 10 9 = 10 4 × 10 + 9 = 10 40 + 9 = 10 49 and 1 7 1 = 7 1 × 7 + 1 = 7 7 + 1 = 7 8 . Now, multiply: 10 49 × 7 8 = 10 × 7 49 × 8 = 70 392 . The GCD of 392 and 70 is 14. Dividing both numerator and denominator by 14, we get 70 ÷ 14 392 ÷ 14 = 5 28 .
Final Answers The simplified answers are:
54 5
21 4
9 1
6 7
5 28
Examples
Understanding fraction multiplication is essential in various real-life scenarios. For instance, when baking, you might need to halve a recipe that calls for 3 2 cup of flour. To find the new amount, you multiply 2 1 × 3 2 , resulting in 3 1 cup. Similarly, if you're calculating discounts, like 20% off an item that costs $50 , yo u m u lt i pl y t h e f r a c t i o n re p rese n t in g t h e d i sco u n t ( \frac{20}{100} or \frac{1}{5}$) by the original price to find the amount saved. These calculations are fundamental in everyday problem-solving, from cooking and shopping to managing finances and understanding proportions.
