Question

Choose the fraction that goes in the blank 7/8 > - > 3/5

Answer 1

Answer:

The fraction is $\frac{3}{4}$

Step-by-step explanation:

* Lets explain how to solve the problem

- The fraction m/n has m as a numerator and n as a denominator

- To compare between fractions we must to put all of them with

  same denominator

- We can make that by find the lowest common multiple (L.C.M) of

 the all denominators

- Ex: The L.C.M of the denominators of these fraction

 $\frac{1}{2},\frac{3}{4},\frac{5}{6}$ is 12 because 12 is the first

 common multiple of 2 , 4 , 6

- The fractions will be change:

# $\frac{1}{2}=\frac{6}{12}$ ⇒ we multiplied up and down by 6

  to make the denominator = 12

# $\frac{3}{4}=\frac{9}{12}$ ⇒ we multiplied up and down by 3

  to make the denominator = 12

# $\frac{5}{6}=\frac{10}{12}$ ⇒ we multiplied up and down by 2

  to make the denominator = 12

- The fractions will be $\frac{6}{12},\frac{9}{12},\frac{10}{12}$

* Lets solve the problem

- To chose a fraction between $\frac{7}{8},\frac{3}{5}$, we must

 find The L.C.M for the denominators 8 and 5

∵ The least common multiple of 8 and 5 is 40

∴ The fraction $\frac{7}{8}=\frac{35}{40}$ ⇒ we multiplied up

  and down by 5 to make the denominator = 40

∴ The fraction $\frac{3}{5}=\frac{24}{40}$ ⇒ we multiplied up

  and down by 8 to make the denominator = 40

- Lets find any fraction between $\frac{35}{40}$ and $\frac{24}{40}$

∵ The fraction $\frac{30}{40}$ is between the fractions

    $\frac{35}{40}$ and  $\frac{24}{40}$

∴ $\frac{35}{40}>\frac{30}{40}>\frac{24}{40}$

- Lets reduce the fraction to its simplest form

∵ The simplest form of $\frac{30}{40}$ is $\frac{3}{4}$

   by dividing up and down by 10

∴ $\frac{7}{8}>\frac{3}{4}>\frac{3}{5}$

* The fraction is $\frac{3}{4}$