Question 15 Marks
Find the missing numbers:
(a) 5 glasses of juice shared equally among 4 friends is the same as __________ glasses of juice shared equally among 8 friends. So, $\frac{5}{4}=\frac{?}{8}$
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in __________ bags. So, $\frac{4}{3}=\frac{12}{?}$.
(c) 7 rods divided among 5 children is the same as rods divided among children. So, $\frac{7}{5}=$ __________
(a) 5 glasses of juice shared equally among 4 friends is the same as __________ glasses of juice shared equally among 8 friends. So, $\frac{5}{4}=\frac{?}{8}$
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in __________ bags. So, $\frac{4}{3}=\frac{12}{?}$.
(c) 7 rods divided among 5 children is the same as rods divided among children. So, $\frac{7}{5}=$ __________
Answer
View full question & answer→(a) Here, the amount of juice each friend gets when 5 glasses are shared among 4 friends = $\frac{\text { number of glasses }}{\text { number of friends }}=\frac{5}{4}$
Now to determine how many glasses of juice would be needed to give each of the 8 friends the same amount $=8 \times \frac{5}{4}$
= 10 glasses
So, 10 glasses of juice shared equally among 8 friends is the same as 5 glasses of juice shared equally among 4 friends.
$\therefore \frac{5}{4}=\frac{10}{8}$
(b) Here 4 kg of potatoes divided equally in 3 bags then amount of potatoes per bag = $\frac{4 kg}{3 bags }=\frac{4}{3} kg$ per bag
Let x is the number of bags for 12 kg of potatoes, where each bag has the same amount of potatoes then
$\begin{array}{l}\frac{12 kg}{x \text { bags }}=\frac{4}{3} kg \text { per bag } \\ \Rightarrow 12 \times 3=4 \times x \\ \Rightarrow 36=4 \times \\ \Rightarrow x=\frac{36}{4} \\ \Rightarrow x=9 \\ \therefore \frac{4}{3}=\frac{12}{9}\end{array}$
(c) Dividing 7 rotis among 4 children gives 7 each child = $\frac{7}{5}$ of a roti. We can find an equivalent fraction by multiplying both the numerator and the denominator by the same number. For example, multiplying both by 2.
$\frac{7 \times 2}{5 \times 2}=\frac{14}{10}$
So, 7 rotis divided among 5 children is the same as 14 rotis divided among 10 children
$\therefore \frac{7}{5}=\frac{14}{10}$
Now to determine how many glasses of juice would be needed to give each of the 8 friends the same amount $=8 \times \frac{5}{4}$
= 10 glasses
So, 10 glasses of juice shared equally among 8 friends is the same as 5 glasses of juice shared equally among 4 friends.
$\therefore \frac{5}{4}=\frac{10}{8}$
(b) Here 4 kg of potatoes divided equally in 3 bags then amount of potatoes per bag = $\frac{4 kg}{3 bags }=\frac{4}{3} kg$ per bag
Let x is the number of bags for 12 kg of potatoes, where each bag has the same amount of potatoes then
$\begin{array}{l}\frac{12 kg}{x \text { bags }}=\frac{4}{3} kg \text { per bag } \\ \Rightarrow 12 \times 3=4 \times x \\ \Rightarrow 36=4 \times \\ \Rightarrow x=\frac{36}{4} \\ \Rightarrow x=9 \\ \therefore \frac{4}{3}=\frac{12}{9}\end{array}$
(c) Dividing 7 rotis among 4 children gives 7 each child = $\frac{7}{5}$ of a roti. We can find an equivalent fraction by multiplying both the numerator and the denominator by the same number. For example, multiplying both by 2.
$\frac{7 \times 2}{5 \times 2}=\frac{14}{10}$
So, 7 rotis divided among 5 children is the same as 14 rotis divided among 10 children
$\therefore \frac{7}{5}=\frac{14}{10}$
