6th Grade Math Final Review Worksheet with problems on fractions, statistics, unit rates, and geometry.

Here are the step-by-step solutions for the problems shown on the worksheet.

1. Fraction Addition
To add fractions with different denominators (bottom numbers), you first need to make the denominators the same.
* The problem is: $\frac{5}{6} + \frac{1}{2}$
* Change $\frac{1}{2}$ so it has a denominator of 6. Since $2 \times 3 = 6$, multiply the top and bottom by 3: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
* Now add them: $\frac{5}{6} + \frac{3}{6} = \frac{8}{6}$.
* Simplify the fraction. Both numbers can be divided by 2: $\frac{4}{3}$. This can also be written as the mixed number $1 \frac{1}{3}$.

2. Mean, Median, and Mode
The data set is: 19, 25, 21, 22, 20, 26, 26, 17.
First, let's put them in order from least to greatest:
17, 19, 20, 21, 22, 25, 26, 26

* Mean (Average): Add all the numbers together and divide by how many numbers there are (8).
* Sum: $17 + 19 + 20 + 21 + 22 + 25 + 26 + 26 = 176$
* Divide: $176 \div 8 = 22$
* Median (Middle): Find the middle number. Since there are 8 numbers (an even amount), take the two middle ones (21 and 22) and find their average.
* $(21 + 22) \div 2 = 21.5$
* Mode (Most Frequent): Look for the number that appears the most often.
* 26 appears twice. All others appear once. So, the mode is 26.

3. Unit Rates
A unit rate tells you how much for *one* single item or hour. You find it by dividing.

* Jamil earned \$36 for 4 hours:
* $\$36 \div 4 \text{ hours} = \$9$ per hour.
* We traveled 350 miles in 7 hours:
* $350 \text{ miles} \div 7 \text{ hours} = 50$ miles per hour.
* 20 pens cost \$4.80:
* $\$4.80 \div 20 \text{ pens} = \$0.24$ per pen.

4. Evaluate the Expression
Follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Expression: $3^2 + 2 \times 20 - 4^2$

1. Exponents: Calculate $3^2$ ($3 \times 3 = 9$) and $4^2$ ($4 \times 4 = 16$).
* New expression: $9 + 2 \times 20 - 16$
2. Multiplication: Calculate $2 \times 20 = 40$.
* New expression: $9 + 40 - 16$
3. Addition/Subtraction: Go from left to right.
* $9 + 40 = 49$
* $49 - 16 = 33$

5. Surface Area of a Rectangular Prism
Formula: $SA = 2(lw + lh + wh)$
Dimensions: Length ($l$) = 5 cm, Width ($w$) = 3 cm, Height ($h$) = 2 cm.

1. Find the area of the three pairs of faces:
* $l \times w = 5 \times 3 = 15$
* $l \times h = 5 \times 2 = 10$
* $w \times h = 3 \times 2 = 6$
2. Add them up: $15 + 10 + 6 = 31$
3. Multiply by 2: $31 \times 2 = 62$
The surface area is 62 square centimeters.

6. Reflection Across the Y-Axis
Point B is located at coordinates $(2, 4)$.
When you reflect a point across the y-axis (the vertical line), the x-coordinate changes its sign (positive becomes negative), but the y-coordinate stays the same.
* Original: $(2, 4)$
* New x: $-2$
* New y: $4$
New coordinates: $(-2, 4)$

7. Frequency Table Percentage
Question: What percentage of students scored at least 85?
"At least 85" means any score of 85 or higher. Looking at the table, we look at the rows for "85-89" and "90-100".

1. Count the students in those groups:
* 85-89: 20 students
* 90-100: 10 students
* Total students with 85+: $20 + 10 = 30$
2. Find the total number of students in the whole class by adding the frequency column:
* $1 + 3 + 8 + 20 + 10 = 42$ total students.
3. Calculate the percentage:
* $(30 \div 42) \times 100 \approx 71.4\%$

8. Greatest Number of Bouquets
Kenyan has 24 red flowers and 36 yellow flowers. He wants identical bouquets with no flowers left over. This requires finding the Greatest Common Factor (GCF) of 24 and 36.

* Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
* Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The largest number that fits into both is 12.
Therefore, the greatest number of bouquets he can make is 12.
*(Note: Each bouquet would have 2 red flowers and 3 yellow flowers).*

Final Answer:
1. 1 1/3 (or 4/3)
2. Mean: 22, Median: 21.5, Mode: 26
3. $9/hour; 50 mph; $0.24/pen
4. 33
5. 62 cm²
6. (-2, 4)
7. Approximately 71.4%
8. 12 bouquets