Sure, I'll walk you through the solution for each phrase step-by-step.
### Phrase 1: 16 more than the quotient of 84 and 12
First, we calculate the quotient of 84 and 12:
[tex]\[
\frac{84}{12} = 7
\][/tex]
Then, we add 16 to this quotient:
[tex]\[
7 + 16 = 23
\][/tex]
So, the expression is:
[tex]\[
\frac{84}{12} + 16
\][/tex]
And the result is:
[tex]\[
23.0
\][/tex]
### Phrase 2: 14 less than the product of 12 and 7
First, we calculate the product of 12 and 7:
[tex]\[
12 \times 7 = 84
\][/tex]
Then, we subtract 14 from this product:
[tex]\[
84 - 14 = 70
\][/tex]
So, the expression is:
[tex]\[
12 \times 7 - 14
\][/tex]
And the result is:
[tex]\[
70
\][/tex]
### Phrase 3: The quotient of 63 and 9 multiplied by 7
First, we calculate the quotient of 63 and 9:
[tex]\[
\frac{63}{9} = 7
\][/tex]
Then, we multiply this quotient by 7:
[tex]\[
7 \times 7 = 49
\][/tex]
So, the expression is:
[tex]\[
\left( \frac{63}{9} \right) \times 7
\][/tex]
And the result is:
[tex]\[
49.0
\][/tex]
### Phrase 4: The difference of 54 and 32 multiplied by the difference of 8 and 2
First, we calculate the difference of 54 and 32:
[tex]\[
54 - 32 = 22
\][/tex]
Then, we calculate the difference of 8 and 2:
[tex]\[
8 - 2 = 6
\][/tex]
Next, we multiply these differences:
[tex]\[
22 \times 6 = 132
\][/tex]
So, the expression is:
[tex]\[
(54 - 32) \times (8 - 2)
\][/tex]
And the result is:
[tex]\[
132
\][/tex]
### Phrase 5: [tex]\( \frac{1}{3} \)[/tex] of 36 multiplied by the difference of 15 and 2
First, we calculate [tex]\( \frac{1}{3} \)[/tex] of 36:
[tex]\[
\frac{1}{3} \times 36 = 12
\][/tex]
Then, we calculate the difference of 15 and 2:
[tex]\[
15 - 2 = 13
\][/tex]
Next, we multiply these results:
[tex]\[
12 \times 13 = 156
\][/tex]
So, the expression is:
[tex]\[
\left( \frac{1}{3} \right) \times 36 \times (15 - 2)
\][/tex]
And the result is:
[tex]\[
156.0
\][/tex]
### Phrase 6: The difference of 28 and 4 divided by 6
First, we calculate the difference of 28 and 4:
[tex]\[
28 - 4 = 24
\][/tex]
Then, we divide this difference by 6:
[tex]\[
\frac{24}{6} = 4
\][/tex]
So, the expression is:
[tex]\[
\frac{28 - 4}{6}
\][/tex]
And the result is:
[tex]\[
4.0
\][/tex]
There you go! The detailed solutions for each phrase.
