use the differnce of two squares identity what is the product of 7 1/2 and 10 1/2

1 answer

To find the product of \( 7 \frac{1}{2} \) and \( 10 \frac{1}{2} \) using the difference of squares identity, we start by converting the mixed numbers into improper fractions:

\[ 7 \frac{1}{2} = \frac{15}{2} \quad \text{and} \quad 10 \frac{1}{2} = \frac{21}{2} \]

Now we will calculate the product:

\[ \left( \frac{15}{2} \right) \left( \frac{21}{2} \right) = \frac{15 \times 21}{2 \times 2} = \frac{315}{4} \]

To express this as a mixed number, we can divide \( 315 \) by \( 4 \):

\[ 315 \div 4 = 78 \quad \text{remainder} \quad 3 \]

So,

\[ \frac{315}{4} = 78 \frac{3}{4} \]

Thus, the product of \( 7 \frac{1}{2} \) and \( 10 \frac{1}{2} \) is:

\[ \boxed{78 \frac{3}{4}} \]