Certainly! I'll guide you through the steps to find the missing number in the equivalent fractions.
We are given the equation:
[tex]\[
\frac{16}{40} = \frac{?}{100}
\][/tex]
To find the value of the missing number in the second fraction, we need to determine what value should be in place of "?" to make the two fractions equivalent.
Step-by-Step Solution:
1. Understand the Concept of Equivalent Fractions:
Equivalent fractions have the same value when simplified, even though they may look different. In other words, they represent the same part of a whole.
2. Set Up the Equation:
We are given:
[tex]\[
\frac{16}{40} = \frac{?}{100}
\][/tex]
3. Cross-Multiply to Find the Missing Numerator:
To solve for "?" (the numerator in the second fraction), we can use the cross-multiplication method. Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the two products equal to each other.
This gives us:
[tex]\[
16 \times 100 = 40 \times ?
\][/tex]
4. Perform the Multiplication:
Calculate the left side of the equation:
[tex]\[
16 \times 100 = 1600
\][/tex]
5. Solve for the Missing Number:
Set up the equation from the cross-multiplication:
[tex]\[
1600 = 40 \times ?
\][/tex]
To isolate "?", divide both sides of the equation by 40:
[tex]\[
? = \frac{1600}{40}
\][/tex]
6. Calculate the Division:
Perform the division:
[tex]\[
\frac{1600}{40} = 40
\][/tex]
Therefore, the missing number is:
[tex]\[
? = 40
\][/tex]
So, the equivalent fraction to [tex]\(\frac{16}{40}\)[/tex] with a denominator of 100 is:
[tex]\[
\frac{40}{100}
\][/tex]
This matches our equivalent fraction given in the problem. The missing number is indeed 40.
