Practice Solutions

1. $4^2÷8+3{\left(1–2\right)}^4–\left|–5\right|$

$$\begin{gathered} 16÷8+3{\left(–1\right)}^4–5 \\ 16÷8+3\left(1\right)–5 \\ 2+3–5 \\ \overline{)0} \end{gathered}$$

2. $\left|2^3–3^3\right|+15÷5–2+\sqrt{16}$

$$\begin{gathered} \left|8–27\right|+15÷5–2+\sqrt{16} \\ \left|–19\right|+3–2+4 \\ 19+3–2+4 \\ \overline{)24} \end{gathered}$$

3. $\left|5–\left(–2\right)\right|–6\left(–3\right)+3\left|–4\right|÷6$

$$\begin{gathered} \left|5+2\right|–6\left(–3\right)+3\left(4\right)÷6 \\ 7+18+12÷6 \\ 7+18+2 \\ \overline{)27} \end{gathered}$$

4. $–6^2÷3–2^2{\left(83–81\right)}^2$

$$\begin{gathered} –\left(36\right)÷3–4{\left(2\right)}^2 \\ –36÷3–4\left(4\right) \\ –12–16 \\ \overline{)–28} \end{gathered}$$

5. $\sqrt{4^2+3^2}+{\left(2–4\right)}^2$

$$\begin{gathered} \sqrt{16+9}+{\left(–2\right)}^2 \\ \sqrt{25}+4 \\ 5+4 \\ \overline{)9} \end{gathered}$$

6. ${\left(3+\left|7–8\right|·9\right)}^2÷\left(5–\left|–6–11\right|\right)$

$$\begin{gathered} {\left(3+\left|–1\right|·9\right)}^2÷\left(5–\left|–17\right|\right) \\ {\left(3+1·9\right)}^2÷\left(5–17\right) \\ {\left(3+9\right)}^2÷–12 \\ {\left(12\right)}^2÷–12 \\ 144÷–12 \\ \overline{)–12} \end{gathered}$$

7. $\left|78–75\right|·\left(–15\right)+5^2·3÷5$

$$\begin{gathered} \left|3\right|·\left(–15\right)+25·3÷5 \\ 3\left(–15\right)+75÷5 \\ –45+15 \\ \overline{)–30} \end{gathered}$$

8. $–\sqrt{81}÷3+16·\frac{1}{2}÷\sqrt{64}$

$$\begin{gathered} –9÷3+8÷8 \\ –3+8÷8 \\ –3+1 \\ \overline{)–2} \end{gathered}$$

9. $\left(128–\left(5\left(2+1\right)\right)+6\left(10–8\right)\right)÷5$

$$\begin{gathered} \left(128–5\left(3\right)+6\left(2\right)\right)÷5 \\ \left(128–15+12\right)÷5 \\ \left(113+112\right)÷5 \\ 125÷5 \\ \overline{)25} \end{gathered}$$

10. $2^3–\frac{1}{3}\sqrt{81}·4+\frac{4}{5}\sqrt{100}$

$$\begin{gathered} 8–\frac{1}{3}\left(9\right)·4+\frac{4}{5}\left(10\right) \\ 8–3·4+8 \\ 8–12+8 \\ \overline{)4} \end{gathered}$$

11. $\left|13–{\left(8–2\right)}^2+\sqrt{121}\right|$

$$\begin{gathered} \left|13–{\left(6\right)}^2+11\right| \\ \left|13–36+11\right| \\ \left|–23+11\right| \\ \left|–12\right| \\ \overline{)12} \end{gathered}$$

12. $17–30÷2·3+85$

$$\begin{gathered} 17–15·3+85 \\ 17–45+85 \\ \overline{)57} \end{gathered}$$