Arithmetic › Order of operations

Multiplication and division chains

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1. Division and multiplication order ●○○○○ 10 ptsEvaluate $25 \div 5 \times 5$.
2. Division and multiplication from left to right ●○○○○ 10 ptsEvaluate $10 \div 2 \times 3 + 6$.
3. Chained multiplication and division of decimals ●○○○○ 10 ptsCalculate $427 \div 2.68 \times 16 \times 26.8 \div 42.7 \times 16$.
4. Multiplying and dividing in base 4 ●●○○○ 20 ptsCompute $120_4\times13_4\div2_4$. Express your answer in base 4.
5. Binary multiplication and division ●●○○○ 20 ptsFind $10110_2\times10100_2\div10_2$. Express your answer in base 2.
6. Smallest result from changing multiplications to divisions ●●●○○ 50 ptsIn the expression $9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$, some of the "$\times$" signs are changed to "$\div$" so that the final result is still a natural number $N$. Find the smallest possible $N$.
7. Smallest integer from parenthesized division chain ●●●○○ 50 ptsIn the expression $10 : 9 : 8 : 7 : 6 : 5 : 4 : 3 : 2 : 1$, parentheses are placed so that the value of the expression is an integer. What is the smallest number that could have been obtained?
8. Distinct values from parenthesised divisions ●●●○○ 50 ptsHow many different values can be obtained by placing parentheses in all possible ways in the expression $2:3:5:7:11:13:17:19:23:29$, where $:$ denotes division?
9. Smallest integer from parenthesised divisions ●●●●○ 100 ptsIn the expression $10:9:8:7:6:5:4:3:2:1$, where $:$ denotes division, parentheses are placed so that the value of the expression is an integer. What is the smallest value that could have been obtained?

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