Work out and simplify where possible.
a) $8 \times \frac{1}{5}$
b) $\frac{1}{8} \times 15$
Answer (1)
Multiply 8 by 5 1 to get 5 8 .
Simplify 5 8 to 1 5 3 .
Multiply 8 1 by 15 to get 8 15 .
Simplify 8 15 to 1 8 7 .
The answers are 5 8 and 8 15 .
Explanation
Problem Analysis We are asked to calculate and simplify the following expressions: a) 8 × 5 1 b) 8 1 × 15 We will perform the multiplication and simplify the results where possible.
Calculations a) To calculate 8 × 5 1 , we multiply the whole number 8 by the fraction 5 1 . This can be written as: 8 × 5 1 = 1 8 × 5 1 = 1 × 5 8 × 1 = 5 8 The fraction 5 8 is an improper fraction, which means the numerator is greater than the denominator. We can convert it to a mixed number by dividing 8 by 5. The quotient is 1 and the remainder is 3. So, 5 8 = 1 5 3 .
b) To calculate 8 1 × 15 , we multiply the fraction 8 1 by the whole number 15. This can be written as: 8 1 × 15 = 8 1 × 1 15 = 8 × 1 1 × 15 = 8 15 The fraction 8 15 is also an improper fraction. We can convert it to a mixed number by dividing 15 by 8. The quotient is 1 and the remainder is 7. So, 8 15 = 1 8 7 .
Results The results of the calculations are: a) 8 × 5 1 = 5 8 = 1 5 3 b) 8 1 × 15 = 8 15 = 1 8 7
Examples
Understanding fractions and multiplication is essential in everyday life. For instance, when you're baking a cake and need to use half of a recipe that calls for 2/3 cup of flour, you're essentially multiplying fractions. Knowing how to perform these calculations accurately ensures your cake turns out just right! Similarly, if you're splitting a pizza with friends and each person gets 1/8 of the pizza, multiplying fractions helps you determine how much pizza each person receives.
