Daniell421
18

# find the sum of 2/100+20/100+2/10= show work

$\frac{2}{100} + \frac{20}{100} + \frac{2}{10} =$ ? First, we have to find the common denominator before we can do anything else. Two of the fractions are already the same; their denominators are a 100. For the third fraction, $\frac{2}{10}$, we can easily transform 10 to a 100 by multiplying it by 10. REMEMBER: when you multiply (or subtract, or divide, etc.) the denominator or the numerator, you have to multiply BOTH by the same number. For example, if you multiply the denominator by 3, than you also have to multiply the numerator by 3. So, first we multiply $\frac{2}{10}$ by 10 so we can make our denominator 100 (so we will be able to begin adding) So we multiply the numerator, 2, by 10 and the denominator, 10, by 10: $\frac{2}{10}$ × $\frac{10}{10}$ = $\frac{20}{100}$ (Note: You don't have to write the multiplication by 10 as a fraction, you can simply just write a small "× 10" in front of each, or you may not have to write it at all if you like) So now that we have a common denominator, we have: $\frac{2}{100} + \frac{20}{100} + \frac{20}{100} =$ ? Now we can start adding from left to right in order, since it is all addition: $\frac{2}{100} + \frac{20}{100} + \frac{20}{100}$ $\frac{22}{100} + \frac{20}{100}$ $\frac{22}{100} + \frac{20}{100} = \frac{42}{100}$ So our answer is $\frac{42}{100}$, but we're not finished yet. We have to simplify. Simplifying means writing the equation/answer in the simplest form until it can no longer be simplified. Both 42 and 100 are even numbers, so they can both be divided by 2. Which is easier if you don't want to use a bigger number that will get us to the simplest form faster: $\frac{42}{100}$ ÷ $\frac{2}{2}$ = $\frac{21}{50}$ As you can see, $\frac{21}{50}$ is our simplest form, and you can write it in decimal form if you like, which can get by dividing the numerator by the denominator: 21 ÷ 50 = 0.42 ⇒ $\frac{21}{50} = 0.42$ There is also another way you solve this equation; instead of multiplying the original equation to find the common denominator, you can find another, smaller common denominator by dividing. For this equation, you may find this method easier, however both methods seem to be in the same level of easiness: You can either divide the whole equation by 2, then multiply the last fraction by 5, or you may divide the first two fractions by 2, and multiply the last fraction by 5, the latter being exactly the same except for it being one step less than the former. Here is the first method (*dividing the whole equation by 2, then multiplying the last fraction by 5): $\frac{2}{100}$ ÷ 2 = $\frac{1}{50}$ $\frac{20}{100}$ ÷ 2 = $\frac{10}{50}$ $\frac{2}{10}$ ÷ 2 = $\frac{1}{5}$ $\frac{1}{5}$ × 10 = $\frac{10}{50}$ $\frac{1}{50} + \frac{10}{50} + \frac{10}{50}$ $\frac{11}{50} + \frac{10}{50}$ = $\frac{21}{50}$ The second method (dividing the first two fractions by 2 and multiplying the third fraction by 5): $\frac{2}{100} + \frac{20}{100} + \frac{2}{10}$ $\frac{2}{100}$ ÷ 2 =  $\frac{1}{50}$ $\frac{20}{100}$ ÷ 2 = $\frac{10}{50}$ $\frac{2}{10}$ × 5 = $\frac{10}{50}$ $\frac{1}{50} + \frac{10}{50}$ + $\frac{10}{50}$ $\frac{11}{50}$ + $\frac{10}{50}$ = $\frac{21}{50}$ *I have attached a drawing to show you how it is usually written when dividing a whole equation by a number(s).