Answer :
Sure, let's solve these problems step-by-step.
1. The first part is finding the missing denominator in the equivalent fraction [tex]\(\frac{6}{5} = \frac{30}{\square}\)[/tex].
- Start with the original fraction [tex]\(\frac{6}{5}\)[/tex].
- We need to find the denominator that makes [tex]\(\frac{30}{\square}\)[/tex] equivalent to [tex]\(\frac{6}{5}\)[/tex].
- To find this, we can use cross multiplication:
[tex]\[
6 \times \square = 5 \times 30
\][/tex]
- This simplifies to:
[tex]\[
6 \times \square = 150
\][/tex]
- Solve for the square by dividing both sides by 6:
[tex]\[
\square = \frac{150}{6} = 25
\][/tex]
- So, the missing number in the fraction is 25.
2. The second part is finding the missing numerator in the equivalent fraction [tex]\(\frac{4}{\square} = \frac{32}{40}\)[/tex].
- Start with the equivalent fractions [tex]\(\frac{4}{\square}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex].
- We want to find the missing denominator for [tex]\(\frac{4}{\square}\)[/tex] that makes it equivalent to [tex]\(\frac{32}{40}\)[/tex].
- We'll use cross multiplication again:
[tex]\[
4 \times 40 = \square \times 32
\][/tex]
- Simplify this to:
[tex]\[
160 = 32 \times \square
\][/tex]
- Solve for the square by dividing both sides by 32:
[tex]\[
\square = \frac{160}{32} = 5
\][/tex]
- So, the missing numerator in the fraction is 5.
Therefore, the solutions are:
- The missing denominator in [tex]\(\frac{6}{5} = \frac{30}{\square}\)[/tex] is 25.
- The missing numerator in [tex]\(\frac{4}{\square} = \frac{32}{40}\)[/tex] is 5.
1. The first part is finding the missing denominator in the equivalent fraction [tex]\(\frac{6}{5} = \frac{30}{\square}\)[/tex].
- Start with the original fraction [tex]\(\frac{6}{5}\)[/tex].
- We need to find the denominator that makes [tex]\(\frac{30}{\square}\)[/tex] equivalent to [tex]\(\frac{6}{5}\)[/tex].
- To find this, we can use cross multiplication:
[tex]\[
6 \times \square = 5 \times 30
\][/tex]
- This simplifies to:
[tex]\[
6 \times \square = 150
\][/tex]
- Solve for the square by dividing both sides by 6:
[tex]\[
\square = \frac{150}{6} = 25
\][/tex]
- So, the missing number in the fraction is 25.
2. The second part is finding the missing numerator in the equivalent fraction [tex]\(\frac{4}{\square} = \frac{32}{40}\)[/tex].
- Start with the equivalent fractions [tex]\(\frac{4}{\square}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex].
- We want to find the missing denominator for [tex]\(\frac{4}{\square}\)[/tex] that makes it equivalent to [tex]\(\frac{32}{40}\)[/tex].
- We'll use cross multiplication again:
[tex]\[
4 \times 40 = \square \times 32
\][/tex]
- Simplify this to:
[tex]\[
160 = 32 \times \square
\][/tex]
- Solve for the square by dividing both sides by 32:
[tex]\[
\square = \frac{160}{32} = 5
\][/tex]
- So, the missing numerator in the fraction is 5.
Therefore, the solutions are:
- The missing denominator in [tex]\(\frac{6}{5} = \frac{30}{\square}\)[/tex] is 25.
- The missing numerator in [tex]\(\frac{4}{\square} = \frac{32}{40}\)[/tex] is 5.
