Question

Step 4: Find the numerator and the denominator.

61
×
64
×
1
10
×
1
10

​
×
1
10
×
1
10

?
×
1
10
×
1
10
=
?
×
1
​
RESET STEP
61
( 60 + 1 )
×
64
( 60 + 4 )
​
=
60 × 60
​
=
60 × 4
​
=
1 × 60
+
​
=
1 × 4
​

Answer 1

To find the numerator and the denominator for the expression you've provided, we can first break down the multiplication:

Given the expression:

\[
61 \times 64 \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}
\]

We can express the four factors of \(\frac{1}{10}\) as:

\[
\frac{1}{10^4}
\]

Now, let’s compute the numerator before solving the entire multiplication step by step:

**Step 1: Compute the product of 61 and 64:**

We can use the distributive property (or FOIL method) to multiply \(61\) and \(64\):

\[
61 \times 64 = (60 + 1)(60 + 4)
\]

Applying the distributive property:

\[
= 60 \times 60 + 60 \times 4 + 1 \times 60 + 1 \times 4
\]
\[
= 3600 + 240 + 60 + 4
\]
\[
= 3904
\]

So the numerator is **3904**.

**Step 2: Compute the entire fraction:**

The complete expression is now:

\[
\frac{3904}{10^4}
\]

The denominator \(10^4\) equals \(10000\).

So, the denominator is **10000**.

Thus, the final result, with **numerator** and **denominator** identified, is:

**Numerator:** \(3904\)

**Denominator:** \(10000\)