Question
Find ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}.$
✓
Answer
The LCM of the denominators 5 and 4 of both the fraction is 20.
We can write:
$\frac{3}{5}=\frac{3\times4}{5\times4}=\frac{12}{20}$
$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$
Since the intergers between the numerators 12 and 15 are not sufficient, we will multiply both the fraction by 5.
$\frac{12}{20}=\frac{12\times5}{200\times5}=\frac{60}{100}$
$\frac{15}{20}=\frac{15\times5}{20\times5}=\frac{75}{100}$
There are 14 integers between 60 and 75. They are 61, 62, 63,........... 73 and 74.
Therefore, $\frac{60}{100},\frac{61}{100},\frac{62}{100},...........\frac{73}{100}$ and $\frac{74}{100}$ are the 14 fractions.
We can take any 10 of these.
We can write:
$\frac{3}{5}=\frac{3\times4}{5\times4}=\frac{12}{20}$
$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$
Since the intergers between the numerators 12 and 15 are not sufficient, we will multiply both the fraction by 5.
$\frac{12}{20}=\frac{12\times5}{200\times5}=\frac{60}{100}$
$\frac{15}{20}=\frac{15\times5}{20\times5}=\frac{75}{100}$
There are 14 integers between 60 and 75. They are 61, 62, 63,........... 73 and 74.
Therefore, $\frac{60}{100},\frac{61}{100},\frac{62}{100},...........\frac{73}{100}$ and $\frac{74}{100}$ are the 14 fractions.
We can take any 10 of these.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Verify the property: x × (y × z) = (x × y) × z by taking:
$\text{x}=\frac{1}{2},\text{y}=\frac{5}{-4},\text{z}=\frac{-7}{5}$
→$\text{x}=\frac{1}{2},\text{y}=\frac{5}{-4},\text{z}=\frac{-7}{5}$
Find the amount and the compound interest on Rs. 8000 for $1\frac{1}{2}$years at 10% per annum, compounded half-yearly.
→Write the cubes of 5 natural numbers which are of the form $3 n+1$ (e.g. $4,7,10, \ldots$ ) and verify the following:
'The cube of a natural number of the form $3 n+1$ is a natural number of the same form i.e. when divided by 3 it leaves the remainder $1^{\prime}$.
→'The cube of a natural number of the form $3 n+1$ is a natural number of the same form i.e. when divided by 3 it leaves the remainder $1^{\prime}$.
If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain percent earned by the dealer.
Referring the given figure of a parallelogram, write the answers of questions given below.
i. If l(WZ) = 4.5 cm, then l(XY) = ?
ii. If l(YZ) = 8.2 cm, then l(XW) = ?
iii. If l(OX) = 2.5 cm, then l(OZ) = ?
iv. If l(WO) = 3.3 cm, then l(WY) = ?
v. If m∠WZY = 120°, then m∠WXY = ? and m∠XWZ = ?
i. If l(WZ) = 4.5 cm, then l(XY) = ?
ii. If l(YZ) = 8.2 cm, then l(XW) = ?
iii. If l(OX) = 2.5 cm, then l(OZ) = ?
iv. If l(WO) = 3.3 cm, then l(WY) = ?
v. If m∠WZY = 120°, then m∠WXY = ? and m∠XWZ = ?
If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14.
Find the cube root of the following rational numbers:
0.003375
0.003375
Divide the sum of $\frac{13}{5}$ and $\frac{-12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{1}{-2}$.
→Ratna obtained a loan of Rs. 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to discharge her debt?
Solve the following equation and also check your result in case:
$\frac{2}{3\text{x}}-\frac{3}{2\text{x}}=\frac{1}{12}$
→$\frac{2}{3\text{x}}-\frac{3}{2\text{x}}=\frac{1}{12}$