Question

which is greater the sum -3/10 and 7/9 or the sum of 7/8 and -15/24 and by how much?​

Answer 1

Question

Which is greater the sum $\frac{-3}{10}$ and $\frac{7}{9}$ or the sum of $\frac{7}{8}$ and $\frac{-15}{24}$ and by how much?

$\rule{300}{1}$

Answer

To find the answer we must add  $\frac{-3}{10}$ and $\frac{7}{9}$ and also  $\frac{7}{8}$ and $\frac{-15}{24}$ . After that we'll compare the sum of both numbers to find the final answer.

So first, let's add $\frac{-3}{10}+\frac{7}{9}$

$\frac{-3}{10}+\frac{7}{9}$

Step 1: Find the LCM of the denominators.

LCM of 10 and 9 = 10×9 = 90

Step 2: Make the denominators equal.

$\frac{-3\times 9 }{10\times 9 }+\frac{7\times 10 }{9\times 10 }$

$\frac{-27 }{90 }+\frac{70 }{90 }$

Step 3: Add the numerators and let the denominator be the same.

$\frac{-27 }{90 }+\frac{70 }{90 }$

$\frac{43}{90 }$

Now, lets add $\frac{7}{8}+\frac{-15}{24}$

Step 1: Find the LCM of the denominators.

LCM of 8 and 24 = 24

Step 2: Make the denominators equal.

$\frac{7\times 3 }{8\times 3 }+\frac{-15}{24}$

$\frac{21}{24 }+\frac{-15}{24}$

Step 3: Add the numerators and let the denominator be the same.

$\frac{21}{24 }+\frac{-15}{24}$

$\frac{6}{24}$

Step 4: Simplify the fraction.

$\frac{6\div 6 }{24\div 6 }$

$\frac{1 }{4 }$

$\bf \therefore \frac{-3}{10}+\frac{7}{9} = \frac{43}{90} \\ \\ \therefore \frac{7}{8}+\frac{-15}{24} = \frac{1}{4}$

Now we need to compare $\frac{43}{90}$ and $\frac{1 }{4 }$

Step 1: Find the LCM of the denominators.

LCM of 90 and 4 = 180

Step 2: Make the denominators equal.

$\frac{43\times 2 }{90\times 2 } = \frac{86}{180}$

$\frac{1\times 45 }{4\times 45 } = \frac{45}{180}$

Step 3: Compare the fractions.

$\frac{86}{180}>\frac{45}{180}$

$\frac{43}{90} >\frac{1}{4}$

$\bf \therefore \frac{-3}{10}+\frac{7}{9} > \frac{7}{8}+\frac{-15}{24}$

∴ The sum $\bf \frac{-3}{10}$ and $\bf \frac{7}{9}$ is greater than the sum of $\bf \frac{7}{8}$ and $\bf \frac{-15}{24}$.

Now we need to find the difference between them.

We'll take those two numbers we found.

$\frac{86}{180}-\frac{45}{180}$

$\frac{41}{180}$

∴ The difference between them is $\bf \frac{41}{180}$.

$\rule{300}{1}$

Answer 2

Answer:

Which is greater, the sum of −7 10 and 3/−7 or the sum of −1/8 and 15/24 , and by how much?