Common Denominators: Worded problems

To solve this problem, we need to determine how much of the cake is left after Jorge consumes part of it. We know the following:

• The cake initially has 8 slices, with only 3 slices left, meaning $\frac{3}{8}$ of the cake remains.
• Jorge eats $\frac{1}{4}$ of the entire original cake.

We need to find $\frac{1}{4}$ in terms of eighths to subtract it from $\frac{3}{8}$:

$\frac{1}{4} = \frac{2}{8}$ since multiplying both the numerator and the denominator by 2 converts it.

Thus, the amount of cake Jorge eats from the original amount available is equivalent to $\frac{2}{8}$ of the cake.

Now, we perform the subtraction to find the remaining portion of the cake:

$\frac{3}{8} - \frac{2}{8} = \frac{1}{8}$

Therefore, the amount of cake left after Jorge eats his portion is $\frac{1}{8}$ of the original cake. Thus, the final solution is:

$\frac{1}{8}$.

To determine how much of the doughnuts they eat in total, let's find the sum of the fractions that represent their consumption.

First, consider Jessy's consumption of the strawberry doughnut: $\frac{1}{6}$.

Next, consider James's consumption of the chocolate doughnut: $\frac{1}{3}$.

To add these fractions, we need a common denominator. The denominators are 6 and 3. The least common multiple of these is 6.

Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 6:

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

Now we have the fractions $\frac{1}{6}$ and $\frac{2}{6}$.

We can add them since they have the same denominator:

$\frac{1}{6} + \frac{2}{6} = \frac{1 + 2}{6} = \frac{3}{6}$

Therefore, in total, Jessy and James eat:

$\frac{3}{6}$ of the doughnuts.

The correct answer choice is the one that corresponds to $\frac{3}{6}$, which is Choice 2.

Thus, the solution to this problem is that they eat $\frac{3}{6}$ of the doughnuts in total.

To solve this problem, we need to express the portions eaten by the husband and the son as fractions of their respective pizzas and then add these fractions.

First, let's express the husband's consumption as a fraction. The husband eats 1 slice from the first pizza, which is divided into 3 equal slices. Therefore, the husband eats:

$\frac{1}{3}$ of the first pizza.

Next, express the son's consumption as a fraction. The son eats 2 slices from the second pizza, which is divided into 9 equal slices. Therefore, the son eats:

$\frac{2}{9}$ of the second pizza.

Now, to add these fractions, we need a common denominator. The denominators here are 3 and 9. The least common denominator for these is 9. So, we convert $\frac{1}{3}$ to have a denominator of 9:

$\frac{1}{3} = \frac{3 \times 1}{3 \times 3} = \frac{3}{9}$.

Now, add the fractions:

$\frac{3}{9} + \frac{2}{9} = \frac{5}{9}$.

Therefore, the total amount the husband and the son eat in total is $\frac{5}{9}$ of the combined pizzas.

Thus, the correct answer is $\frac{5}{9}$.

To solve this problem, we'll determine the fraction of the track John covers at a speed of 34 km/h.

• Step 1: Understand that John runs three segments of the track:
  • 50 meters at 38 km/h
  • 25 meters at 36 km/h
  • 25 meters at 34 km/h
• Step 2: Identify that the question specifically asks about the third segment, which is 25 meters.
• Step 3: Calculate the fraction of the track these 25 meters represent out of 100 meters: $\text{Fraction at 34 km/h} = \frac{25 \text{ meters}}{100 \text{ meters}} = \frac{1}{4}$
• Step 4: The calculation shows that John covers $\frac{1}{4}$ of the track at a speed of 34 km/h.
• Step 5: Double-check by verifying the simplification and ensuring the calculation matches the track setup and speed descriptions.

Therefore, the solution to the problem is $\frac{1}{4}$.