Here are the step-by-step solutions for each problem on the worksheet.
1. Find the unit rate.
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Problem: 550 ml for 5 oranges.
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Step 1: To find the unit rate (how much is in *one* orange), divide the total amount by the number of items.
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Calculation: $550 \div 5 = 110$.
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Result: There are 110 ml per orange.
2. Evaluate the expression for x = 6 and y = 4.
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Problem: $xy - 3y$
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Step 1: Substitute the numbers into the expression. Replace $x$ with 6 and $y$ with 4.
* Expression becomes: $(6)(4) - 3(4)$
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Step 2: Multiply the first part: $6 \times 4 = 24$.
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Step 3: Multiply the second part: $3 \times 4 = 12$.
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Step 4: Subtract the results: $24 - 12 = 12$.
3. Use the following function rule to find f(9).
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Problem: $f(x) = 2x - 9$
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Step 1: The notation $f(9)$ means you need to plug in 9 wherever you see an $x$.
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Step 2: Substitute 9 into the equation: $2(9) - 9$.
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Step 3: Multiply first: $2 \times 9 = 18$.
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Step 4: Subtract: $18 - 9 = 9$.
4. What % of 60 is 27?
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Problem: Find the percentage.
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Step 1: Set up the fraction: $\frac{27}{60}$.
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Step 2: Divide 27 by 60 to get a decimal.
* $27 \div 60 = 0.45$
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Step 3: Convert the decimal to a percentage by multiplying by 100.
* $0.45 \times 100 = 45\%$
5. Solve for y.
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Problem: $5y - (-2) < 17$
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Step 1: Simplify the left side. Subtracting a negative is the same as adding.
* $5y + 2 < 17$
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Step 2: Isolate the term with $y$ by subtracting 2 from both sides.
* $5y < 17 - 2$
* $5y < 15$
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Step 3: Divide both sides by 5 to solve for $y$. Since we are dividing by a positive number, the inequality sign stays the same.
* $y < \frac{15}{5}$
* $y < 3$
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Final Answer:
1. 110 ml/orange
2. 12
3. 9
4. 45%
5. y < 3
Parent Tip: Review the logic above to help your child master the concept of fun worksheet for 8th graders.
