Multiplication of Integers by a Fraction and a Mixed number: Worded problems

To solve this problem, we need to calculate the average time Chris spends running per kilometer. We are given that Chris runs 2 km in $4\frac{1}{2}$ minutes.

First, let's convert the mixed fraction $4\frac{1}{2}$ into an improper fraction. The whole number 4 and the fraction $\frac{1}{2}$ combine as follows:

$4\frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}$

This means that the total time taken is $\frac{9}{2}$ minutes.

Next, we find the average time Chris runs per kilometer by dividing the total time by the distance:

$\text{Average time per km} = \frac{\text{Total time}}{\text{Total distance in km}} = \frac{\frac{9}{2}}{2}$

To divide by a fraction, we multiply by its reciprocal:

$\frac{\frac{9}{2}}{2} = \frac{9}{2} \times \frac{1}{2} = \frac{9}{4}$

The fraction $\frac{9}{4}$ can be converted back into a mixed number:

$\frac{9}{4} = 2\frac{1}{4}$

Therefore, the average time Chris runs per kilometer is $2\frac{1}{4}$ minutes.

To solve this problem, we will follow these steps:

• Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction.
• Step 2: Divide the improper fraction by 2.
• Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction. This is done by multiplying the whole number 2 by the denominator 2 and adding the numerator 1. Hence, $2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$.
Step 2: Divide $\frac{5}{2}$ by 2. Dividing by 2 is equivalent to multiplying by $\frac{1}{2}$. Therefore, $\frac{5}{2} \div 2 = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$.
Step 3: The fraction $\frac{5}{4}$ is already in its simplest form, but it can also be expressed as a mixed number: $1\frac{1}{4}$.

Therefore, each child will receive $1\frac{1}{4}$ dollars.

To solve this problem, we need to determine how much of the pie each child will receive after Ruth's husband has eaten one piece.

Let's break it down step by step:

• Step 1: Determine the remaining pie.
• The pie was cut into 4 equal pieces, and 1 piece was eaten. So, the fraction of the pie remaining is:
• $\frac{4}{4} - \frac{1}{4} = \frac{3}{4}$
• Step 2: Divide the remaining pie among the 3 children.
• To divide $\frac{3}{4}$ equally among 3 children, we perform:
• $\frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3}$
• When multiplying fractions, multiply the numerators and the denominators:
• $\frac{3 \times 1}{4 \times 3} = \frac{3}{12} = \frac{1}{4}$

Thus, each child will receive $\frac{1}{4}$ of the pie.

Therefore, the solution to the problem is $\frac{1}{4}$, which corresponds to choice 2.

To solve this problem, let's proceed step by step:

• Step 1: Identify the given information:
  We know that there are 4 children and each child eats $\frac{1}{2}$ pizza.
• Step 2: Apply the formula:
  We use the formula: Total pizza consumed = Number of children × Amount of pizza per child. Here, this is $4 \times \frac{1}{2}$.
• Step 3: Perform the calculation:
  Calculate $4 \times \frac{1}{2} = \frac{4}{2} = 2$.

Conclusion:
The total number of pizzas consumed by the children is $2$.

To find out how many kilometers Joel ran on average each minute, we begin with these steps:

• Step 1: Convert the mixed number $1\frac{1}{2}$ km into an improper fraction. The mixed number represents 1 full unit plus half a unit, which is calculated as:

$1\frac{1}{2} = 1 + \frac{1}{2} = \frac{3}{2}$ km

• Step 2: Use the average formula to calculate the distance per minute:

$\text{Average distance per minute} = \frac{\frac{3}{2} \text{ km}}{3 \text{ minutes}}$

Simplifying this expression involves dividing fractions:

$\frac{\frac{3}{2}}{3} = \frac{3}{2} \times \frac{1}{3} = \frac{3}{2 \times 3} = \frac{3}{6} = \frac{1}{2}$ km per minute

Therefore, Joel traveled, on average, $\frac{1}{2}$ km per minute. This matches the provided correct answer, confirming choice 4 is correct.

Let's solve the problem step-by-step:

Step 1: Convert the mixed fraction to an improper fraction.
The mixed number $22\frac{1}{2}$ can be expressed in terms of improper fraction as follows:
First, convert $22\frac{1}{2}$ to an improper fraction:
$22\frac{1}{2} = \frac{2 \times 22 + 1}{2} = \frac{45}{2}$.

Step 2: Use the speed formula.
We know that speed = distance / time. Here, the distance is $\frac{45}{2}$ meters and the time is 7 seconds.
To find meters per second, we calculate:
$\frac{45}{2} \div 7 = \frac{45}{2} \times \frac{1}{7} = \frac{45}{14}$.

Step 3: Simplify the fraction.
The fraction $\frac{45}{14}$ can be simplified. It converts to mixed number as follows:
First, divide 45 by 14 which gives a quotient of 3 and a remainder of 3.
Therefore, $\frac{45}{14} = 3\frac{3}{14}$.

Therefore, Daniel swims $3\frac{3}{14}$ meters per second.