This is a subtraction problem because we want to know how many goldfish the pet store has left over after the teacher buys the first and takes them away from the store. We take the number of goldfish that the store had and then subtract the number that the teacher bought. $\displaystyle 48-11=37$.

When adding fractions, you must first make sure that the denominators are equal. If they are not equal, then you must make them equal by finding the LCD (lowest common denominator). In this case the LCD is 28. Now set up the new equation:

$\displaystyle \frac{7}{28}+\frac{8}{28}=$ 

Then add the numerators to get:

$\displaystyle \frac{15}{28}$ 

Since the factors cannot be reduced any further, the correct answer is $\displaystyle \frac{15}{28}$. 

In order to find the fraction of students who wanted supreme pizza in the two classes combined, we must add the fractions. To add fractions, however, we must first find a common denominator.  Since $\displaystyle \small 4$ and $\displaystyle \small 6$ share the least common multiple $\displaystyle \small 24$, each fraction can be written with a denominator of $\displaystyle \small 24$.

In order to convert $\displaystyle \small \frac{1}{4}$ into a fraction with a denominator of $\displaystyle \small 24$, we multply the top and bottom by $\displaystyle \small 6$.

$\displaystyle \small \frac{(1\cdot 6)}{(4\cdot 6)}=\frac{6}{24}$

In order to convert $\displaystyle \small \frac{1}{6}$ into a fraction with a denominator of 24, we multiply the top and bottom by $\displaystyle \small 4$.

$\displaystyle \small \frac{(1\cdot 4)}{(6\cdot 4)}=\frac{4}{24}$

Now we add the two fractions, but when we add fractions with the same denominator, we only add the numerators. The denominator will remain the same.

$\displaystyle \small \frac{6}{24}+\frac{4}{24}=\frac{10}{24}$

Next we simplify $\displaystyle \small \frac{10}{24}$ by dividing both the numerator and denominator by $\displaystyle \small 2$.

$\displaystyle \small \frac{(10/2)}{(24/2)}=\frac{5}{12}$

If two negative numbers are multiplied, the answer is always positive (greater than $\displaystyle 0$).

The best way to solve this is to turn both mixed numbers into improper fractions. For $\displaystyle 2\frac{1}{4}$, multiply the denominator of the fraction by the whole number, and then add the numerator to the answer. $\displaystyle 4\times2$ is $\displaystyle 8$, and  $\displaystyle 8+1=9$. This gives us our new numerator, $\displaystyle 9$, which we put over the old denominator, $\displaystyle 4$:

$\displaystyle 2\frac{1}{4}=\frac{9}{4}$.

Using the same process with $\displaystyle 5\frac{2}{3}$, we get $\displaystyle 3\times5+2$, or $\displaystyle 17$, as our new numerator:

$\displaystyle 5\frac{2}{3}=\frac{17}{3}$.

To add $\displaystyle \frac{9}{4}+\frac{17}{3}$, the denominators need to match. Find a common multiple of $\displaystyle 3$ and $\displaystyle 4$. $\displaystyle 12$ works! In order to get $\displaystyle 4$ to equal $\displaystyle 12$, multiply both the numerator, $\displaystyle 9$, and denominator, $\displaystyle 4$, by $\displaystyle 3$:

$\displaystyle \frac{9}{4}\times\frac{3}{3}=\frac{27}{12}$

For the second fraction, multiply both the numerator, $\displaystyle 17$, and denominator, $\displaystyle 3$, by $\displaystyle 4$:

$\displaystyle \frac{17}{3}\times\frac{4}{4}=\frac{68}{12}$

Now we can add the two fractions together:

$\displaystyle \frac{27}{12}+\frac{68}{12}=\frac{95}{12}$

We need to convert this improper fraction back into a mixed number. To do this, divide $\displaystyle 95$ by $\displaystyle 12$ to get $\displaystyle 7$ with a remainder of $\displaystyle 11$. The remainder becomes the numerator of the fraction. $\displaystyle 12$ remains the denominator. Therefore the answer is $\displaystyle 7\frac{11}{12}$.

$\displaystyle \frac{3}{5}+ \frac{3}{10} =$

In order to add fractions, each fraction must have the same denominator. We must convert the fraction $\displaystyle \frac{3}{5}$ into a fraction that has a denominator of 10.

We multiply the numerator and denominator by 2.

$\displaystyle \frac{3}{5}*\frac{2}{2}=\frac{3*2}{5*2}=\frac{6}{10}$

So, now we have $\displaystyle \frac{6}{10} + \frac{3}{10}$

Then we add the numerators together: $\displaystyle 6 + 3 = 9$.

We keep the same denominator (10), and the answer is $\displaystyle \frac{9}{10}$.  

This problem requires adding up all of the different clothing items $\displaystyle (5+4+10)$. The answer is 19.

This problem is asking you to determine the relationship between the two fractions. Think of the fractions as pieces of a pizza. Which fraction has more pieces? $\displaystyle \frac{5}{12}$ does, so that is your answer. Then, you have to pick the correct inequality sign. Since $\displaystyle \frac{5}{12}$ is greater, the point of the inequality sign must be pointing to the lower fraction. Therefore, $\displaystyle <$ is the correct sign.

$\displaystyle \frac{8}{9} + \frac{1}{3} = \frac{8}{9} + \frac{1 \times 3 }{3 \times 3 } = \frac{8}{9} + \frac{ 3 }{9 } = \frac{8+3}{9} = \frac{11}{9}$

First, add feet and inches separately.

     $\displaystyle 4 \textrm{ ft }7\textrm{ in }$

     $\displaystyle 6 \textrm{ ft }11\textrm{ in }$

$\displaystyle + \; \underline{3 \textrm{ ft }5\textrm{ in}}$

     $\displaystyle 13 \textrm{ ft }23\textrm{ in }$

Since 12 inches make one foot,we divide 23 by 12:

$\displaystyle 23 \div 12 = 1 \textrm{ R }11$

23 inches is equal to 1 foot 11 inches. Therefore,

$\displaystyle 13 \textrm{ ft }23\textrm{ in } = 13 \textrm{ ft } + 1 \textrm{ ft } 11\textrm{ in }$, and:

     $\displaystyle 13 \textrm{ ft }$

+   $\displaystyle \underline{1 \textrm{ ft }11\textrm{ in }}$

     $\displaystyle 14 \textrm{ ft }11\textrm{ in }$