Lesson 7 5Ef609

1. **Problem:** Calculate $0.8 - 0.206$. **Step 1:** Write the subtraction. $$0.8 - 0.206$$ **Step 2:** Align decimals and subtract. $$0.800 - 0.206 = 0.594$$ **Answer:** $0.594$ 2. **Problem:** Which is greater, $\frac{3}{5}$ or $48\%$? **Step 1:** Convert $\frac{3}{5}$ to decimal. $$\frac{3}{5} = 0.6$$ **Step 2:** Convert $48\%$ to decimal. $$48\% = 0.48$$ **Step 3:** Compare decimals. $$0.6 > 0.48$$ **Answer:** $\frac{3}{5}$ is greater. 3. **Problem:** Solve for $a$ in $a - 12 = 52$. **Step 1:** Add $12$ to both sides. $$a - 12 + 12 = 52 + 12$$ $$a = 64$$ **Answer:** $a = 64$ 4. **Problem:** Write an algebraic phrase for "five less than the quotient of a number and six." **Step 1:** Let the number be $x$. **Step 2:** Quotient of number and six is $\frac{x}{6}$. **Step 3:** Five less than that is: $$\frac{x}{6} - 5$$ **Answer:** $\frac{x}{6} - 5$ 5. **Problem:** Find the GCF of $10ab^2c^3$ and $15a^2b^2$. **Step 1:** Factor coefficients: $10 = 2 \times 5$, $15 = 3 \times 5$. **Step 2:** GCF of coefficients is $5$. **Step 3:** For variables, take minimum powers: - $a$: min$(1,2) = 1$ - $b$: min$(2,2) = 2$ - $c$: min$(3,0) = 0$ (no $c$ in second term) **Step 4:** GCF is: $$5 a b^2$$ **Answer:** $5ab^2$ 6. **Problem:** Solve for $x$ in $4x + 16 = 28$. **Step 1:** Subtract $16$ from both sides. $$4x + 16 - 16 = 28 - 16$$ $$4x = 12$$ **Step 2:** Divide both sides by $4$. $$\frac{\cancel{4}x}{\cancel{4}} = \frac{12}{4}$$ $$x = 3$$ **Answer:** $x = 3$ 7. **Problem:** Find the area of the trapezoid with top base $16$ in, bottom base $8$ in, and height $10$ in. **Step 1:** Use trapezoid area formula: $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times \text{height}$$ **Step 2:** Substitute values: $$\text{Area} = \frac{16 + 8}{2} \times 10$$ **Step 3:** Simplify numerator: $$\frac{24}{2} \times 10 = 12 \times 10 = 120$$ **Answer:** $120$ square inches 8. **Problem:** Calculate $-93 + (-54)$. **Step 1:** Add the two negative numbers. $$-93 + (-54) = -(93 + 54) = -147$$ **Answer:** $-147$ 9. **Problem:** Solve and graph $2x + 4 \geq 2$. **Step 1:** Subtract $4$ from both sides. $$2x + 4 - 4 \geq 2 - 4$$ $$2x \geq -2$$ **Step 2:** Divide both sides by $2$. $$\frac{\cancel{2}x}{\cancel{2}} \geq \frac{-2}{2}$$ $$x \geq -1$$ **Answer:** $x \geq -1$ (Graph: number line with a closed circle at $-1$ and shading to the right.) 10. **Problem:** Calculate $-4(-2)(9)$. **Step 1:** Multiply stepwise. $$-4 \times -2 = 8$$ $$8 \times 9 = 72$$ **Answer:** $72$ 11. **Problem:** $60$ is what percent of $80$? **Step 1:** Use formula: $$\text{Percent} = \frac{\text{part}}{\text{whole}} \times 100$$ **Step 2:** Substitute values: $$\frac{60}{80} \times 100 = 0.75 \times 100 = 75$$ **Answer:** $75\%$ 12. **Problem:** Simplify $23t + 18t$. **Step 1:** Combine like terms. $$(23 + 18)t = 41t$$ **Answer:** $41t$ 13. **Problem:** Marcus's net displacement after running various distances. **Step 1:** Add forward distances: $10 + 6 + 23 = 39$ **Step 2:** Add backward distances: $4 + 9 + 3 = 16$ **Step 3:** Net displacement: $$39 - 16 = 23$$ **Answer:** Marcus is $23$ feet forward from starting point. 14. **Problem:** Write $68,270,000$ in scientific notation. **Step 1:** Move decimal to after first digit: $$6.8270000$$ **Step 2:** Count decimal moves: $7$ places. **Answer:** $6.827 \times 10^{7}$ 15. **Problem:** Convert $7$ tons to pounds. **Step 1:** Use conversion: $1$ ton = $2000$ pounds. **Step 2:** Multiply: $$7 \times 2000 = 14000$$ **Answer:** $14000$ pounds 16. **Problem:** Calculate $1.402 + 2$. **Step 1:** Add: $$1.402 + 2 = 3.402$$ **Answer:** $3.402$ 17. **Problem:** Solve for $x$ in $\frac{3x - 2}{5} = -7$. **Step 1:** Multiply both sides by $5$. $$\cancel{5} \times \frac{3x - 2}{\cancel{5}} = -7 \times 5$$ $$3x - 2 = -35$$ **Step 2:** Add $2$ to both sides. $$3x - 2 + 2 = -35 + 2$$ $$3x = -33$$ **Step 3:** Divide both sides by $3$. $$\frac{\cancel{3}x}{\cancel{3}} = \frac{-33}{3}$$ $$x = -11$$ **Answer:** $x = -11$ 18. **Problem:** Simplify $4(3r - 2y + 5) + 2(4r - 7)$. **Step 1:** Distribute: $$4 \times 3r = 12r$$ $$4 \times (-2y) = -8y$$ $$4 \times 5 = 20$$ $$2 \times 4r = 8r$$ $$2 \times (-7) = -14$$ **Step 2:** Combine terms: $$12r - 8y + 20 + 8r - 14$$ **Step 3:** Combine like terms: $$12r + 8r = 20r$$ $$20 - 14 = 6$$ **Answer:** $20r - 8y + 6$ 19. **Problem:** Evaluate $\frac{x}{y} + xy$ if $x = 8$ and $y = 2$. **Step 1:** Substitute values: $$\frac{8}{2} + 8 \times 2$$ **Step 2:** Calculate: $$4 + 16 = 20$$ **Answer:** $20$ 20. **Problem:** Rachael missed $15$ out of $25$ questions. What percent did she miss? **Step 1:** Use formula: $$\text{Percent missed} = \frac{15}{25} \times 100$$ **Step 2:** Calculate: $$0.6 \times 100 = 60$$ **Answer:** $60\%$ missed