Question

compare \\(\frac{4}{10}\\) and \\(\frac{8}{100}\\). complete the sentence describing the comparison. \\(\frac{4}{10}\\) is less than \\(\frac{8}{100}\\). show how you can use multiplication to find an equivalent fraction. \\(\frac{4 \times \square}{10 \times \square} = \frac{?}{100}\\)

Explanation:

Step1: Find the multiplier for the denominator

We know that we want to convert the denominator 10 to 100. To find what we multiply 10 by to get 100, we solve \(10\times x = 100\). Dividing both sides by 10, we get \(x = 10\) (since \(100\div10 = 10\)). So we multiply the denominator by 10.

Step2: Multiply the numerator by the same number

To keep the fraction equivalent, we must multiply the numerator by the same number we multiplied the denominator by (which is 10). So we multiply 4 by 10. Then we calculate the new numerator: \(4\times10 = 40\). So the fraction becomes \(\frac{4\times10}{10\times10}=\frac{40}{100}\).

Answer:

The first box (numerator multiplier) is 10, the second box (denominator multiplier) is 10, and the "?" in the numerator of the result is 40. So filling in the boxes: \(\frac{4\times\boldsymbol{10}}{10\times\boldsymbol{10}}=\frac{\boldsymbol{40}}{100}\)