Addition of Fractions: Worded problems

To solve this problem, we'll find out how much of the paper roll Danny used by adding the fractions representing the parts used for the book and notebook covers.

• Step 1: Identify the fractions used.
• Step 2: Determine the common denominator for the fractions $\frac{1}{6}$ and $\frac{2}{3}$.
• Step 3: Convert $\frac{2}{3}$ to the common denominator.
• Step 4: Add the fractions.
• Step 5: Simplify the result if needed.

Let's work through these steps:

Step 1: Danny used the fractions $\frac{1}{6}$ and $\frac{2}{3}$.

Step 2: The denominators are 6 and 3. The least common denominator is 6.

Step 3: Convert $\frac{2}{3}$ to a fraction with a denominator of 6.

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Step 4: Add the fractions $\frac{1}{6}$ and $\frac{4}{6}$.

$\frac{1}{6} + \frac{4}{6} = \frac{1 + 4}{6} = \frac{5}{6}$

Step 5: The fraction $\frac{5}{6}$ is already in its simplest form.

Therefore, Danny used $\frac{5}{6}$ of the paper roll in total.

The correct answer is $\frac{5}{6}$.

To solve this problem, we'll add the fractions representing the portions of pizza each person eats.

• Step 1: Identify the fractions to add. Daniel eats $\frac{1}{4}$ of the pizza, and Mariano eats $\frac{1}{4}$ of the pizza.
• Step 2: Since the fractions have the same denominator, add the numerators: $1 + 1 = 2$.
• Step 3: Keep the denominator the same, which is $4$.
• Step 4: The resulting fraction is $\frac{2}{4}$.
• Step 5: Simplify the fraction $\frac{2}{4}$ by dividing the numerator and the denominator by their greatest common divisor, which is $2$.

Thus, $\frac{2}{4} = \frac{1}{2}$.

Therefore, the total amount of pizza eaten by Daniel and Mariano together is $\frac{1}{2}$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the area covered by the banana plantation.

• Step 2: Identify the area covered by the watermelon plantation.

• Step 3: Sum the two areas to find the total area covered by both plantations.

Now, let's work through each step:
Step 1: The banana plantation covers $\frac{3}{8}$ of the field.
Calculate its area: $10,000 \times \frac{3}{8} = 10,000 \times 0.375 = 3,750 \, \text{m}^2$.

Step 2: The watermelon plantation covers $\frac{1}{4}$ of the field.
Calculate its area: $10,000 \times \frac{1}{4} = 10,000 \times 0.25 = 2,500 \, \text{m}^2$.

Step 3: Add these areas to find the total area covered by both plantations:
$3,750 \, \text{m}^2 + 2,500 \, \text{m}^2 = 6,250 \, \text{m}^2$.

Therefore, the total surface area covered by the banana and watermelon plantations is 6,250$\text{m}^2$.

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

• Step 1: Calculate the number of blue balls.

We know that $\frac{1}{5}$ of the 15 balls are blue. Thus, the number of blue balls is calculated as:

$\text{Number of blue balls} = \frac{1}{5} \times 15 = 3$

• Step 2: Calculate the number of red balls.

Similarly, $\frac{1}{3}$ of the 15 balls are red. So, the number of red balls is:

$\text{Number of red balls} = \frac{1}{3} \times 15 = 5$

• Step 3: Find the total number of balls that are either red or blue.

Sum the number of blue balls and the number of red balls:

$\text{Total number of red or blue balls} = 3 + 5 = 8$

Therefore, there are a total of 8 balls in the jar that are either red or blue.

To solve this problem, we'll follow these steps:

• Determine the amount of apple juice.
• Determine the amount of pineapple juice.
• Add the two amounts to find the total quantity.

Now, let's work through each step:

Step 1: Determine the amount of apple juice.

The juice is made up of $\frac{1}{2}$ of apple juice. Therefore, the amount of apple juice is calculated as follows:

Step 2: Determine the amount of pineapple juice.

The juice is made up of $\frac{1}{4}$ of pineapple juice. Therefore, the amount of pineapple juice is calculated as follows:

Step 3: Add the two amounts to find the total quantity of apple and pineapple juices.

Therefore, the total amount of apple and pineapple juice together is $\text{450 ml}$, which corresponds to choice 2. Hence, the final answer is:

The correct answer to the problem is $450$.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the weight of the chocolate cookies.
• Step 2: Calculate the weight of the coconut.
• Step 3: Add these two weights to find the total weight of both components.

Step 1: Calculate the weight of the chocolate cookies:
The fraction of the total ingredients that are chocolate cookies is $\frac{3}{7}$. Thus, the weight of the chocolate cookies is:

Step 2: Calculate the weight of the coconut:
The fraction of the total ingredients that are coconut is $\frac{1}{3}$. Thus, the weight of the coconut is:

Step 3: Add these two weights together:
To find the total weight of the chocolate cookies and coconut, we sum the individual weights:

Therefore, the total weight of chocolate cookies and coconut in the cake is 160 grams.

The mother spends time preparing both salad and french fries. We need to sum up these two times:

Given the times:

• Salad: $\frac{1}{6}$ hour
• French fries: $\frac{2}{3}$ hour

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

Convert $\frac{2}{3}$ to a fraction with a denominator of 6:

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Now, add the fractions:

$\frac{1}{6} + \frac{4}{6} = \frac{1 + 4}{6} = \frac{5}{6}$

Therefore, the total time the mother spends preparing food is $\frac{5}{6}$ of an hour.

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'll follow these steps:

• Step 1: Identify the total fraction Marcos wants in cash, which is $\frac{1}{2}$ of his money.
• Step 2: Determine the fraction he has already withdrawn, which is $\frac{1}{6}$.
• Step 3: Calculate the additional fraction he needs to withdraw. This is done by subtracting the withdrawn fraction from the desired cash fraction: $\frac{1}{2} - \frac{1}{6}$.

Now, let's perform the calculations:

Step 3:

Convert the fractions $\frac{1}{2}$ and $\frac{1}{6}$ to have a common denominator:

The least common denominator (LCD) of 2 and 6 is 6.

$\frac{1}{2} = \frac{3}{6}$ (since $1 \times 3 = 3$ and $2 \times 3 = 6$)

$\frac{1}{6}$ is already with denominator 6, so it remains $\frac{1}{6}$.

Subtract the two fractions:

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

Simplify $\frac{2}{6}$ by dividing the numerator and the denominator by 2:

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

Therefore, Marcos needs to withdraw an additional $\frac{1}{3}$ of his money to have half of his money in cash.

Therefore, the correct answer to the problem is $\frac{1}{3}$.

To solve this problem, we need to determine how much of her homework Sarah has completed by adding the fractions $\frac{2}{3}$ and $\frac{1}{5}$.

First, find the least common denominator (LCD) for the fractions. The denominators are 3 and 5. The LCD of 3 and 5 is 15.

Next, convert each fraction to an equivalent fraction with the denominator of 15:

• $\frac{2}{3}$ becomes $\frac{2 \times 5}{3 \times 5} = \frac{10}{15}$
• $\frac{1}{5}$ becomes $\frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

Now, add the two fractions:

$\frac{10}{15} + \frac{3}{15} = \frac{10 + 3}{15} = \frac{13}{15}$

Thus, Sarah has completed $\frac{13}{15}$ of her total homework.

The correct answer is therefore $\frac{13}{15}$.

To solve this problem, we will add the fractions of the work Sarah completed in the first and second hours:

• Step 1: Identify the fractions: Sarah completed $\frac{2}{8}$ of the work in the first hour and $\frac{1}{4}$ of the work in the second hour.
• Step 2: Convert the fractions to have the same denominator. The denominators are 8 and 4, respectively. The least common denominator (LCD) of 8 and 4 is 8.
• Step 3: Convert $\frac{1}{4}$ to a fraction with a denominator of 8. Since $\frac{1}{4} = \frac{2}{8}$, we convert it as follows: $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$
• Step 4: Add the fractions with the common denominator: $\frac{2}{8} + \frac{2}{8} = \frac{2 + 2}{8} = \frac{4}{8}$
• Step 5: Simplify the resulting fraction. Divide the numerator and the denominator by their greatest common divisor, which is 4: $\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}$

Therefore, Sarah completed $\frac{1}{2}$ of the assignment in total.

To solve the problem of determining how long Ned spends doing his homework, we need to add the times he spent on language and science homework.

Given:
- Language homework: $\frac{1}{8}$ of an hour
- Science homework: $\frac{6}{8}$ of an hour

Since both times have the same denominator, adding them is straightforward:

$\frac{1}{8} + \frac{6}{8} = \frac{1+6}{8} = \frac{7}{8}$

Therefore, Ned spends $\frac{7}{8}$ of an hour doing his homework.

To solve this problem, we will add the fractions representing the amount of paper Daniel uses:

• Step 1: Identify the fractions of the paper roll used.
  Daniel uses $\frac{2}{5}$ of the roll for the book and $\frac{3}{4}$ for the notebook.
• Step 2: Find a common denominator.
  The denominators are 5 and 4. The least common multiple of 5 and 4 is 20. Hence, the common denominator will be 20.
• Step 3: Convert each fraction to have this common denominator.
  • For $\frac{2}{5}$, convert it to $\frac{2}{5} \times \frac{4}{4} = \frac{8}{20}$.
  • For $\frac{3}{4}$, convert it to $\frac{3}{4} \times \frac{5}{5} = \frac{15}{20}$.
• Step 4: Add the two fractions.
  Add $\frac{8}{20} + \frac{15}{20} = \frac{23}{20}$.
• Step 5: Interpret the result.
  The result $\frac{23}{20}$ implies that Daniel used more than one whole roll, specifically $\frac{23}{20}$ of the paper roll in total.

Therefore, the solution to the problem is $\frac{23}{20}$.

To solve this problem, we need to add the fractions of the packet that Dana eats over the three days.

Let's outline our steps:

• Step 1: Find the common denominator for the fractions $\frac{1}{2}$, $\frac{1}{3}$, and $\frac{1}{4}$.
• Step 2: Convert each fraction to an equivalent fraction with the common denominator.
• Step 3: Add the fractions together.

Step 1: Determine the least common denominator (LCD).
The denominators are 2, 3, and 4. The least common multiple (LCM) of these numbers is 12. Hence, the common denominator is 12.

Step 2: Convert each fraction:
- $\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$
- $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Step 3: Add the fractions:
$\frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{6+4+3}{12} = \frac{13}{12}$

The amount Dana eats over the three days is $\frac{13}{12}$ of the packet.

This means that Dana ate more than a whole packet (since $\frac{13}{12}$ is more than 1).

Therefore, the solution to the problem is $\frac{13}{12}$.

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 add the fractions representing the parts of the bag Daniela ate each day.

Step 1: Identify the fractions.

• First day: $\frac{5}{6}$
• Second day: $\frac{1}{8}$

Step 2: Find a common denominator for the two fractions. The denominators are 6 and 8. The least common multiple (LCM) of 6 and 8 is 24.

Step 3: Convert each fraction to have the common denominator of 24.

• Convert $\frac{5}{6}$ to ?/24: $\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$
• Convert $\frac{1}{8}$ to ?/24: $\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$

Step 4: Add the converted fractions.

$\frac{20}{24} + \frac{3}{24} = \frac{20 + 3}{24} = \frac{23}{24}$

Step 5: Confirm that this result fits within the options provided. The correct answer matches choice 4.

Therefore, the total part of the bag Daniela ate is $\frac{23}{24}$.

To solve this problem, we will follow these steps:

• Step 1: Identify the denominators of the fractions, which are 3 and 7.
• Step 2: Find the least common multiple (LCM) of these denominators.
• Step 3: Rewrite each fraction using this common denominator.
• Step 4: Add the modified fractions together.
• Step 5: Simplify the final result if possible.

Let's apply these steps:

Step 1: The denominators are 3 and 7.

Step 2: The LCM of 3 and 7 is 21.
21 is the smallest number that both 3 and 7 divide without a remainder.

Step 3: Convert each fraction to have a denominator of 21:
For $\frac{2}{3}$: Multiply both numerator and denominator by 7 to get $\frac{14}{21}$.
For $\frac{2}{7}$: Multiply both numerator and denominator by 3 to get $\frac{6}{21}$.

Step 4: Add the fractions:
$\frac{14}{21} + \frac{6}{21} = \frac{14 + 6}{21} = \frac{20}{21}$.

Step 5: The fraction $\frac{20}{21}$ is already in its simplest form.

Therefore, Chris spends a total of $\frac{20}{21}$ of an hour preparing food.

To find the total time Pete spends on his homework, we'll follow these steps:

• Step 1: Identify the given fractions representing time intervals: $\frac{3}{4}$ and $\frac{2}{5}$.
• Step 2: Find the least common denominator (LCD) of the fractions.
• Step 3: Convert fractions to have the same denominator.
• Step 4: Add the converted fractions.
• Step 5: Simplify the resulting fraction if necessary.

Let's now work through each step:

Step 1: We have the fractions $\frac{3}{4}$ (Spanish homework) and $\frac{2}{5}$ (Science assignments).

Step 2: The least common denominator of 4 and 5 is 20.

Step 3: Convert each fraction:

• Convert $\frac{3}{4}$ to a fraction with denominator 20: $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$.
• Convert $\frac{2}{5}$ to a fraction with denominator 20: $\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$.

Step 4: Add the fractions: $\frac{15}{20} + \frac{8}{20} = \frac{23}{20}$.

Step 5: The fraction $\frac{23}{20}$ is already in its simplest form.

Therefore, Pete spends a total of $\frac{23}{20}$ hours on homework.

Thus, the correct answer is choice 4: $\frac{23}{20}$.

To solve this problem, we'll proceed with the following steps:

• Step 1: Calculate the total amount of potato chips eaten over two days.
• Step 2: Subtract the eaten amount from the whole (1) to find what's left.

Step 1: Addition of Fractions
Combine the fractions of chips eaten on both days:

$\frac{5}{6} + \frac{1}{8}$

Find a common denominator for the fractions. The least common multiple of 6 and 8 is 24. Convert each fraction:

$\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$

$\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$

Add the converted fractions:

$\frac{20}{24} + \frac{3}{24} = \frac{20 + 3}{24} = \frac{23}{24}$

This means Daniela ate $\frac{23}{24}$ of the package.

Step 2: Subtract from the whole
The whole package is represented by 1. To find out how much is left, subtract what she ate from 1:

$1 - \frac{23}{24} = \frac{24}{24} - \frac{23}{24} = \frac{1}{24}$

Therefore, the solution to the problem is that Daniela has $\frac{1}{24}$ of the package left to eat.