Here are the step-by-step solutions for each expression. I have followed the order of operations (PEMDAS/BODMAS): first Parentheses, then Exponents, then Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).
1) $39 - \frac{7}{8} \times 16$
* First, multiply $\frac{7}{8}$ by $16$. Since $16 \div 8 = 2$, this becomes $7 \times 2 = 14$.
* Now subtract: $39 - 14 = 25$.
2) $(-8.1) \div 3 - 2.63$
* First, divide $-8.1$ by $3$. This equals $-2.7$.
* Now subtract: $-2.7 - 2.63$.
* Think of this as adding two negative numbers: $-(2.7 + 2.63) = -5.33$.
3) $36.5 - 4 \times 3.14 - (-9.06)$
* First, multiply $4 \times 3.14 = 12.56$.
* The expression is now: $36.5 - 12.56 - (-9.06)$.
* Subtracting a negative is the same as adding: $36.5 - 12.56 + 9.06$.
* Subtract first: $36.5 - 12.56 = 23.94$.
* Add next: $23.94 + 9.06 = 33$.
4) $\frac{3}{4} \times 8 + \left(-\frac{2}{5}\right) \cdot 6$
* First part: $\frac{3}{4} \times 8$. Since $8 \div 4 = 2$, this is $3 \times 2 = 6$.
* Second part: $-\frac{2}{5} \times 6 = -\frac{12}{5}$. Converting to decimal, $-\frac{12}{5} = -2.4$.
* Add them together: $6 + (-2.4) = 6 - 2.4 = 3.6$.
5) $28 - \frac{6}{7} \div \left(\frac{2}{7}\right)$
* First, handle the division. Dividing by a fraction is the same as multiplying by its reciprocal.
* $\frac{6}{7} \div \frac{2}{7} = \frac{6}{7} \times \frac{7}{2}$. The $7$s cancel out, leaving $\frac{6}{2} = 3$.
* Now subtract: $28 - 3 = 25$.
6) $4.2 \times 8 - (-0.09)$
* First, multiply $4.2 \times 8$. ($4 \times 8 = 32$ and $0.2 \times 8 = 1.6$, so $32 + 1.6 = 33.6$).
* The expression is now: $33.6 - (-0.09)$.
* Subtracting a negative becomes addition: $33.6 + 0.09 = 33.69$.
7) $11.7 + 3.9 \times 5.6 + (-17)$
* First, multiply $3.9 \times 5.6$.
* $39 \times 56 = 2184$.
* There are two decimal places total, so the result is $21.84$.
* Now add from left to right: $11.7 + 21.84 = 33.54$.
* Finally, add $-17$ (which is subtracting 17): $33.54 - 17 = 16.54$.
8) $42 \times \frac{3}{7} - 36 \times \frac{1}{2}$
* First part: $42 \times \frac{3}{7}$. Divide $42$ by $7$ to get $6$, then multiply by $3$: $6 \times 3 = 18$.
* Second part: $36 \times \frac{1}{2}$. Half of $36$ is $18$.
* Subtract: $18 - 18 = 0$.
9) $(-2) \times 3 + \left(\frac{3}{4}\right)$
* First, multiply $-2 \times 3 = -6$.
* Now add $\frac{3}{4}$ (which is $0.75$).
* $-6 + 0.75 = -5.25$ (or $-5 \frac{1}{4}$).
10) $7 - 2.5 + (-6.8) - 1.3$
* Work from left to right.
* $7 - 2.5 = 4.5$.
* $4.5 + (-6.8)$ is the same as $4.5 - 6.8 = -2.3$.
* $-2.3 - 1.3 = -3.6$.
Final Answer:
1) 25
2) -5.33
3) 33
4) 3.6
5) 25
6) 33.69
7) 16.54
8) 0
9) -5.25
10) -3.6
Parent Tip: Review the logic above to help your child master the concept of rational number worksheet.
