Here are the step-by-step solutions for each problem on the worksheet.
1. Greatest Common Factor
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Step 1: Look at the numbers 48 and 72. The largest number that divides evenly into both is 24.
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Step 2: Look at the variables $x^2$ and $x^3$. The highest power they both share is $x^2$.
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Step 3: Combine them to get $24x^2$.
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Answer: C
2. Sale Price Calculation
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Step 1: Find 20% of the original price ($16.00). You can do this by multiplying: $16 \times 0.20 = 3.20$. This is the discount amount.
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Step 2: Subtract the discount from the original price: $16.00 - 3.20 = 12.80$.
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Answer: C
3. Multiplying Expressions
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Step 1: Distribute the $-3x$ to both terms inside the parentheses.
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Step 2: Multiply $-3x$ by $x$ to get $-3x^2$.
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Step 3: Multiply $-3x$ by $-4$. Remember that a negative times a negative is a positive, so you get $+12x$.
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Result: $-3x^2 + 12x$
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Answer: D
4. Simplifying Fractions
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Step 1: Divide the numbers: $24 \div 6 = 4$.
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Step 2: Divide the $x$ terms: $x^2 \div x = x$. (One $x$ cancels out).
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Step 3: Divide the $y$ terms: $y \div y^3 = \frac{1}{y^2}$. (Two $y$'s remain in the denominator).
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Result: $\frac{4x}{y^2}$
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Answer: C
5. Solving Equations
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Goal: Isolate $x$ in the equation $3x - 2 = 10$.
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Step 1: Undo the subtraction by adding 2 to both sides.
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Step 2: Undo the multiplication by dividing both sides by 3.
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Answer: A
6. Geometry Angles
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Step 1: Since lines NP and ST are parallel, the angle labeled $40^\circ$ and angle $\angle NXS$ are "alternate interior angles." This means $\angle NXS$ is also $40^\circ$.
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Step 2: Angle $\angle NXS$ and angle $x$ form a straight line along line MQ. Angles on a straight line add up to $180^\circ$.
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Step 3: Calculate $x$: $180^\circ - 40^\circ = 140^\circ$.
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Answer: C
7. Inequalities
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Step 1: Translate "The sum of a number ($n$) and its square ($n^2$)" into math: $n + n^2$.
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Step 2: Translate "is less than or equal to" into symbols: $\le$.
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Step 3: Translate "negative three": $-3$.
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Result: $n + n^2 \le -3$
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Answer: D
8. Temperature Conversion
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Step 1: Plug the Fahrenheit temperature (50) into the formula: $C = (50 - 32) \times \frac{5}{9}$.
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Step 2: Solve the part in the parentheses first: $50 - 32 = 18$.
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Step 3: Multiply by the fraction: $18 \times \frac{5}{9}$.
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Step 4: It is easier to divide 18 by 9 first, which gives 2. Then multiply by 5: $2 \times 5 = 10$.
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Answer: D
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Final Answer:
1. C
2. C
3. D
4. C
5. A
6. C
7. D
8. D
Parent Tip: Review the logic above to help your child master the concept of ged math worksheets pdf with answers.
