Remainder Practice Problems: Fractions, Decimals & Mixed Numbers

Let's begin:

Step 1: Upon examination, the diagram divides the rectangle into 7 vertical sections.

Step 2: The entire shaded region spans the full width, essentially covering all sections, so the shaded number is 7.

Step 3: The fraction of the total rectangle that is shaded is $\frac{7}{7}$.

Step 4: Simplifying, $\frac{7}{7}$ becomes $1$.

Therefore, the solution is marked by the choice: Answers a + b.

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

First, examine the grid and count the total number of sections. Observing the grid, there is a total of 6 columns, each representing equal-sized portions along the grid, as evidenced by vertical lines.

Next, count how many of these sections are colored. The entire portion from the first column to the fourth column is colored. This means we have 4 out of 6 sections that are marked red.

We can then express the colored area as a fraction: $\frac{4}{6}$.

The problem involves finding the fraction represented by shaded parts in a drawing. Here's a step-by-step guide to solve it:

• Step 1: Count the total number of sections in the drawing. There are 7 blocks arranged linearly.
• Step 2: Since each block appears to be fully shaded, count those shaded. Each of the 7 blocks is shaded.
• Step 3: The fraction is formed by placing the number of shaded sections over the total sections. Thus, the fraction is $\frac{7}{7}$.

The fraction for the shaded portion of the drawing is $\frac{7}{7}$, which is a complete whole, as every block is shaded.

Therefore, the solution to the problem is $\frac{7}{7}$.

The task is to determine which of the given figures correctly represents the decimal fraction 0.1.

To interpret 0.1, we recognize it as $\frac{1}{10}$. This indicates that in a graphical representation of 10 equal parts, 1 part should be shaded. Each figure is assumed to be divided into such equal parts.

Let's analyze the options:

• Choice 1: Shows 10 equal divisions with 1 part shaded. This potentially represents 0.1 since it shades exactly 1 of 10 parts.
• Choice 2: Shows 10 equal divisions with more than 1 part shaded. Thus, it represents more than 0.1.
• Choice 3: Shows 10 equal divisions with numerous parts shaded. It represents a number greater than 0.1.
• Choice 4: Shows a full shading, representing 1 (i.e., shading all 10 parts), clearly not 0.1.

Hence, the correct choice that correspond to 0.1 is Choice 1. This figure accurately shades exactly 1 out of 10 equal segments.

Therefore, the solution to the problem indicates that choice 1 correctly represents the decimal fraction 0.1.

To convert the improper fraction $\frac{13}{11}$ into a mixed number, we need to perform division to separate the whole number from the fractional part.

• Step 1: Divide the numerator by the denominator. - Perform the division: $13 \div 11 = 1$. Since 13 is not a multiple of 11, we obtain a quotient and a remainder. - The division gives a quotient of 1 and a remainder of 2 (since $13 - 11 \times 1 = 2$).
• Step 2: Express the remainder as part of the fraction. - The remainder is 2, and this will be the numerator of the fractional part. - The denominator remains the same, 11.
• Step 3: Write the mixed number. - Combine the whole number and the fraction. - The mixed number is $1\frac{2}{11}$.

Now, let's verify our solution with the given choices. The correct option matches Choice 2, which is $1\frac{2}{11}$.

Therefore, the fraction $\frac{13}{11}$ as a mixed number is $1\frac{2}{11}$.