Daily Math Review Worksheets - Math Buzz (Level E) - Free Printable

Here are the step-by-step solutions for each part of the worksheet.

Part 1: Volume of the Rectangular Prism

To find the volume, we split the L-shaped figure into two separate rectangular prisms (Prism A and Prism B).

Step 1: Identify dimensions for Prism A (the vertical part)
* Looking at the left side of the shape, the total height is 20 mm.
* The bottom section (Prism B) has a height of 5 mm.
* So, the height of just the top part (Prism A) is $20 - 5 = \mathbf{15}$ mm.
* The width of this vertical column is given at the top as 6 mm.
* The depth (length going back) is given as 3 mm.
* Dimensions for Prism A: $15 \times 6 \times 3$

Step 2: Calculate Volume of Prism A
* $15 \times 6 = 90$
* $90 \times 3 = \mathbf{270}$ cubic mm

Step 3: Identify dimensions for Prism B (the horizontal bottom part)
* The problem states to partition the shape. Since we took the full height for Prism A, Prism B is the remaining block at the bottom.
* The height is given on the left as 5 mm.
* The depth is the same as the rest of the shape: 3 mm.
* To find the length: The total width at the bottom is 18 mm. The vertical column (Prism A) takes up 6 mm of that width. So, the remaining length for Prism B is $18 - 6 = \mathbf{12}$ mm. (This matches the label "12 mm" in the middle of the diagram).
* Dimensions for Prism B: $5 \times 12 \times 3$

Step 4: Calculate Volume of Prism B
* $5 \times 12 = 60$
* $60 \times 3 = \mathbf{180}$ cubic mm

Step 5: Find Total Volume
* Add the two volumes together: $270 + 180 = \mathbf{450}$ cubic mm

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Part 2: Evaluate Expressions

Given values: $x = 8$ and $y = 24$.

Expression 1: $(12x - 3y) \div 6$
1. Substitute the numbers: $(12 \times 8 - 3 \times 24) \div 6$
2. Multiply inside the parentheses first:
* $12 \times 8 = 96$
* $3 \times 24 = 72$
3. Subtract: $96 - 72 = 24$
4. Divide by 6: $24 \div 6 = \mathbf{4}$

Expression 2: $160 \div (4x + 2y)$
1. Substitute the numbers: $160 \div (4 \times 8 + 2 \times 24)$
2. Multiply inside the parentheses first:
* $4 \times 8 = 32$
* $2 \times 24 = 48$
3. Add inside the parentheses: $32 + 48 = 80$
4. Divide: $160 \div 80 = \mathbf{2}$

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Part 3: Multiply Decimals

Problem: $3.5 \times 8.3$

1. Ignore the decimals for a moment and multiply $35 \times 83$.
* $35 \times 3 = 105$
* $35 \times 80 = 2800$
* $105 + 2800 = 2905$
2. Count the decimal places in the original problem:
* $3.5$ has 1 decimal place.
* $8.3$ has 1 decimal place.
* Total decimal places needed in the answer: $1 + 1 = \mathbf{2}$.
3. Place the decimal point in 2905 so there are 2 digits to the right: 29.05

Answer: 29.05

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Part 4: Divide with Powers of 10

Rule: When dividing by $10$, $100$, or $1000$, move the decimal point to the left.
* $10^1$ means move left 1 spot.
* $10^2$ means move left 2 spots.
* $10^3$ means move left 3 spots.

Column 1:
1. $54.7 \div 10^1$: Move decimal left 1 spot $\rightarrow$ 5.47
2. $54.7 \div 10^2$: Move decimal left 2 spots $\rightarrow$ 0.547
3. $54.7 \div 10^3$: Move decimal left 3 spots $\rightarrow$ 0.0547

Column 2:
1. $36.98 \div 10^1$: Move decimal left 1 spot $\rightarrow$ 3.698
2. $36.98 \div 10^2$: Move decimal left 2 spots $\rightarrow$ 0.3698
3. $36.98 \div 10^3$: Move decimal left 3 spots $\rightarrow$ 0.03698

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Final Answer:

Volume Section:
* Prism A: $15 \times 6 \times 3 = 270$
* Prism B: $5 \times 12 \times 3 = 180$
* Volume = $450$ cubic mm

Evaluate Expressions:
* $(12x - 3y) \div 6 =$ 4
* $160 \div (4x + 2y) =$ 2

Multiply:
* $3.5 \times 8.3 =$ 29.05

Divide:
* $54.7 \div 10^1 =$ 5.47
* $54.7 \div 10^2 =$ 0.547
* $54.7 \div 10^3 =$ 0.0547
* $36.98 \div 10^1 =$ 3.698
* $36.98 \div 10^2 =$ 0.3698
* $36.98 \div 10^3 =$ 0.03698