Sure, let's solve each part of the problem step-by-step:
Let's consider the given fraction [tex]\(\frac{5}{7}\)[/tex].
### Part i) Finding the missing number for the expression [tex]\(\frac{5}{7} = \frac{\square}{28}\)[/tex]:
We know that:
[tex]\[
\frac{5}{7} = \frac{x}{28}
\][/tex]
To find [tex]\(x\)[/tex], we need to recognize that the fractions are equivalent if the numerators and denominators are multiplied by the same factor.
First, determine the factor that converts [tex]\(7\)[/tex] into [tex]\(28\)[/tex]:
[tex]\[
28 \div 7 = 4
\][/tex]
Thus, we need to multiply both the numerator and denominator of [tex]\(\frac{5}{7}\)[/tex] by 4:
[tex]\[
\frac{5 \times 4}{7 \times 4} = \frac{20}{28}
\][/tex]
So, the missing number is:
[tex]\[
\boxed{20}
\][/tex]
### Part ii) Finding the missing number for the expression [tex]\(\frac{5}{7} = \frac{35}{\square}\)[/tex]:
We know that:
[tex]\[
\frac{5}{7} = \frac{35}{y}
\][/tex]
To find [tex]\(y\)[/tex], we need to determine what factor converts [tex]\(5\)[/tex] into [tex]\(35\)[/tex]:
[tex]\[
35 \div 5 = 7
\][/tex]
Thus, we need to multiply both the numerator and denominator of [tex]\(\frac{5}{7}\)[/tex] by 7:
[tex]\[
\frac{5 \times 7}{7 \times 7} = \frac{35}{49}
\][/tex]
So, the missing number is:
[tex]\[
\boxed{49}
\][/tex]
### Part iii) Finding the missing number for the expression [tex]\(\frac{5}{7} = \frac{\square}{3.5}\)[/tex]:
We know that:
[tex]\[
\frac{5}{7} = \frac{z}{3.5}
\][/tex]
To find [tex]\(z\)[/tex], we need to determine what factor converts [tex]\(7\)[/tex] into [tex]\(3.5\)[/tex]:
[tex]\[
3.5 \div 7 = 0.5
\][/tex]
Thus, we need to multiply both the numerator and denominator of [tex]\(\frac{5}{7}\)[/tex] by 0.5:
[tex]\[
\frac{5 \times 0.5}{7 \times 0.5} = \frac{2.5}{3.5}
\][/tex]
So, the missing number is:
[tex]\[
\boxed{2.5}
\][/tex]
### Part iv) Finding the missing number for the expression [tex]\(\frac{5}{7} = \frac{30}{\square}\)[/tex]:
We know that:
[tex]\[
\frac{5}{7} = \frac{30}{w}
\][/tex]
To find [tex]\(w\)[/tex], we need to determine what factor converts [tex]\(5\)[/tex] into [tex]\(30\)[/tex]:
[tex]\[
30 \div 5 = 6
\][/tex]
Thus, we need to multiply both the numerator and denominator of [tex]\(\frac{5}{7}\)[/tex] by 6:
[tex]\[
\frac{5 \times 6}{7 \times 6} = \frac{30}{42}
\][/tex]
So, the missing number is:
[tex]\[
\boxed{42}
\][/tex]
In summary, the missing numbers are:
[tex]\[
\frac{5}{7} = \frac{20}{28} = \frac{35}{49} = \frac{2.5}{3.5} = \frac{30}{42}
\][/tex]
