Using the property [tex]\frac{a}{b}=\frac{a k}{b k}[/tex], fill in the blanks by substituting proper numbers in the following.

[tex]\frac{5}{7}=\frac{\square}{28}=\frac{35}{\square}=\frac{\square}{3.5}=\frac{30}{\square}[/tex]



Answer :

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]