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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.
### 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.
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