Adding Tenth and Hundredth
Basics on the topic Adding Tenth and Hundredth
Adding Fractions – Tenths and Hundredths
Sometimes, a problem may ask you to add two fractions that don’t share the same denominator such as adding tenths and hundredths. But how do you add tenths and hundredths? Find out all you need to know about adding fractions with uneven denominators with the example in this text and by watching the video.
Adding Tenths and Hundredths– Example
How do you add fractions with uneven denominators? When adding fractions with tenths and hundredths, first, set up the problem.
Next, look at the denominator, the bottom number, of both fractions. Since they’re not the same, we need to convert one fraction to have the same denominator as the other.
To do this, we can multiply the fractions with the ten denominator by ten to make one hundred. When we do this, we also need to multiply the numerator, the top number, by ten as well.
Now both denominators are one hundred, we can solve the problem!
Adding Tenths and Hundredths – Summary
Remember, when adding tenths and hundredths fractions, make sure you have the same denominators before solving the problem. The denominator of the sum will always remain the same, and you only need to add together the numerators.
Below, you can see the necessary steps to adding fractions with uneven denominators.
Step #  What to do 

1  Set up the problem and look at the denominators. 
2  Multiply the smaller denominator until it matches the other denominator. Remember to multiply the numerator as well. 
3  Once both denominators are the same, add the numerators. The sum is your result. 
After watching this video, you will find more interactive exercises, worksheets and further activities on adding tenths and hundredths with questions and answers.
Transcript Adding Tenth and Hundredth
Axel has decided to bake a delicious cake with leftover ingredients. "Hey Tank, I need you to calculate how much flour is left." "And while you're at it, do the same for the sugar, please!" Let's help Tank calculate the total flour and sugar Axel has to bake with by adding tenths and hundredths. A tenth represents one part of a whole divided into ten equal parts. We can represent tenths as a fraction by writing the parts we have for the numerator, over a denominator of ten. A hundredth represents one part of a whole divided into one hundred equal parts. We can represent hundredths as a fraction by writing the parts we have for the numerator, over a denominator of one hundred. Let's practise adding the leftover bags of flour together. One bag has seventyseven hundredths of flour and the other bag has onetenth. We are solving seventyseven hundredths plus onetenth. First, make sure both fractions have the same denominator. Tenths and hundredths are not the same so we need to multiply the tenths fraction by ten so that both fractions have a common denominator. Ten times ten is one hundred. Since we multiplied the denominator of the tenths fraction by ten we must do the same for its numerator. One times ten is ten. One tenth and ten hundredths are equivalent fractions. Now, we can add the fractions because both denominators are one hundred! The denominator remains one hundred since we are adding. Then, add the numerators. Seventyseven plus ten equals eightyseven. Axel has eightyseven hundredths of flour to bake with. Now we know how to add tenths and hundredths, let's help Tank solve how much sugar Axel has to bake with! One bag of sugar has thirtyhundredths left and the other bag has twotenths left. We are solving thirty hundredths plus twotenths. What is the first step? Make sure the fractions have the same denominator. How can we make the denominator of both fractions the same? Multiply the numerator and denominator of the tenths fraction by ten. Ten times ten is one hundred. Two times ten is twenty. Two tenths and twenty hundredths are equivalent fractions. What is the final step? Add the fractions. The denominator remains onehundred. Thirty plus twenty equals fifty. We can simplify fiftyhundredths because fifty goes into both fifty and one hundred. Fifty goes into one hundred two times. Fifty goes into fifty once. Axel has half a bag of sugar for baking his cake! While Axel bakes the cake, let's review! Remember, when adding tenths and hundredths first, make sure both fractions have the same denominator. Second, keep the denominator the same in the sum, since this never changes when adding fractions. Third, add together the numerators. Don't forget to simplify when possible! "It's ready, Tank!" "Oh boy, I have been dreaming of this cake all day!"
Adding Tenth and Hundredth exercise

Identify the different parts of the equation.
HintsThe numerator is above the fraction bar, and indicates how many pieces of the whole are being used in this fraction.
The operation used in this equation is addition.
The 6 in this fraction is the denominator.
SolutionThe numerator is always above the fraction bar, and indicates how many pieces of the whole we are using in this fraction.
The denominator is always below the fraction bar, and shows how many pieces the whole has been divided into.
The sum is the answer to an addition problem and comes after the equals sign.
There is no multiplication or subtraction used in this equation. 
Identify the statements that accurately describe tenths and hundredths.
Hints$\mathbf{\frac{1}{10}}$ is one piece from a group of 10.
$\mathbf{\frac{1}{100}}$ is one piece from a group of 100.
There are three correct answers.
SolutionTrue
 A tenth represents one part of a whole, divided into 10 equal pieces.
 A hundredth represents one part of a whole divided into 100 equal parts.
 One hundredth can by written as a fraction by writing 1 as the numerator and 100 as the denominator.
False
 One tenth can be written as a fraction, by writing 10 as the numerator and 1 as the denominator. In a fraction, the numerator, or number on top, shows how many of something there is. So the fraction one tenth must be written as $\mathbf{\frac{1}{10}}$.
 10 and 100 can both be divided by 7. 10 and 100 can both be divided by two, five and ten but not by 7.

How do we add tenths and hundredths?
HintsIn order to add tenths and hundredths, the denominator must first be the same. In the fraction $\frac{1}{10}$, 10 is the denominator.
To make common denominators, the best strategy is to multiply smaller numbers, like 10, until they equal the larger denominator in the other fraction.
If we multiply the numerator and denominator of $\frac{2}{10}$ by 10, we get $\frac{20}{100}$.
$\mathbf{\frac{50}{100}}$ can be simplified to a smaller fraction by dividing both the numerator and denominator by 50.
SolutionTo add tenths and hundredths,
 Check if the two fractions have the same denominator. For example, if we are adding $\frac{2}{10}$ + $\frac{30}{100}$ we can check and see that the denominators are not the same.
 If the fractions do NOT have the same denominators, multiply the denominator of the smaller fraction until it is the same. Multiply the numerator by the same. For example, we would multiply the numerator and the denominator of $\frac{2}{10}$ by 10 to get $\frac{20}{100}$.
 Once all fractions have the same denominator, add the equivalent fractions together to get the sum. For example, we would add $\frac{20}{100}$ + $\frac{30}{100}$ to get $\frac{50}{100}$.
 Simplify by dividing the numerator and denominator of the sum by a common denominator, if possible. For example, if we divide the numerator and denominator of $\frac{50}{100}$ by 50, we get $\frac{1}{2}$.

Can you solve the problems?
HintsStart by making sure both fractions in the equation have the same denominator. You will need to multiply or divide by ten.
Once you have added the fractions with the same denominator, make sure to simplify.
For example, $\frac{60}{100}$ becomes $\frac{3}{5}$ by dividing both the numerator and denominator by 20.
SolutionProblem 1
 $\frac{20}{100}$ + $\frac{2}{10}$ = ?
 $\frac{2}{10}$ = $\frac{20}{100}$ if the numerator and denominator are both multiplied by 10.
 $\frac{20}{100}$ + $\frac{20}{100}$ = $\frac{40}{100}$
 $\frac{40}{100}$ = $\frac{2}{5}$ if the numerator and denominator are both divided by 20.
 $\frac{20}{100}$ + $\frac{5}{10}$ = ?
 $\frac{5}{10}$ = $\frac{50}{100}$ if the numerator and denominator are both multiplied by 10.
 $\frac{20}{100}$ + $\frac{50}{100}$ = $\frac{70}{100}$
 $\frac{70}{100}$ = $\frac{7}{10}$ if the numerator and denominator are both divided by 10.
 $\frac{7}{10}$ + $\frac{10}{100}$ = ?
 $\frac{7}{10}$ = $\frac{70}{100}$ if the numerator and denominator are both multiplied by 10.
 $\frac{70}{100}$ + $\frac{10}{100}$ = $\frac{80}{100}$
 $\frac{80}{100}$ = $\frac{4}{5}$ if the numerator and denominator are both divided by 20.
 $\frac{6}{10}$ + $\frac{30}{100}$ = ?
 $\frac{6}{10}$ = $\frac{60}{100}$ if the numerator and denominator are both multiplied by 10.
 $\frac{60}{100}$ + $\frac{30}{100}$ = $\frac{90}{100}$
 $\frac{90}{100}$ = $\frac{9}{10}$ if the numerator and denominator are both divided by 10.

Calculate the sum of the equation.
HintsWhich symbol is missing from the equation in step 1?
In order to add tenths and hundredths, you first have to make sure that the fractions in the equations have the same denominators using multiplication. Multiply BOTH the numerator (above) and denominator (below).
Same denominators: $\mathbf{\frac{10}{20}}$ + $\mathbf{\frac{2}{20}}$
Different denominators: $\mathbf{\frac{1}{50}}$ + $\mathbf{\frac{1}{10}}$
Once both fractions have the same denominators, you can add your fractions to find the sum by adding the numerators (top number).
$\mathbf{\frac{10}{100}}$ + $\mathbf{\frac{20}{100}}$ = ?
Once you have added your fractions and have the sum, check if the sum can be simplified, or made smaller, using division. Divide BOTH the numerator (top number) and denominator (bottom number).
Solution $\frac{10}{100}$ + $\frac{2}{10}$ = ?
 $\frac{2}{10}$ = $\mathbf{\frac{20}{100}}$ if the numerator and denominator are both multiplied by 10.
 $\frac{10}{100}$ + $\frac{20}{100}$ = $\mathbf{\frac{30}{100}}$
 $\frac{30}{100}$ = $\mathbf{\frac{3}{10}}$ if the numerator and denominator are both divided by 10.

Calculate the sum of the equations.
HintsYou will need to first make sure both fractions in the equation have the same denominator before you can solve these equations.
For the equation $\frac{2}{30}$ + $\frac{1}{3}$, the common denominator is 3. How many times must you multiply 3 to equal 30?
Don't forget to simplify fractions when you can!
Example: $\frac{2}{10}$ can be simplified to $\frac{1}{5}$ by dividing both the numerator and denominator by 2.You can always use a pencil and paper to help with your working.
SolutionProblem 1
 $\frac{1}{4}$ + $\frac{1}{40}$ = ?
 $\frac{1}{4}$ = $\frac{10}{40}$ if the numerator and denominator are both multiplied by 10.
 $\frac{10}{40}$ + $\frac{1}{40}$ = $\frac{11}{40}$
 This cannot be simplified further.
 $\frac{2}{5}$ + $\frac{2}{50}$ = ?
 $\frac{2}{5}$ = $\frac{20}{50}$ if the numerator and denominator are both multiplied by 10.
 $\frac{20}{50}$ + $\frac{2}{50}$ = $\frac{22}{50}$
 $\frac{22}{50}$ = $\frac{11}{25}$ if the numerator and denominator are both divided by 2.
 $\frac{2}{30}$ + $\frac{1}{3}$ = ?
 $\frac{1}{3}$ = $\frac{10}{30}$ if the numerator and denominator are both multiplied by 10.
 $\frac{2}{30}$ + $\frac{10}{30}$ = $\frac{12}{30}$
 $\frac{12}{30}$ = $\frac{2}{5}$ if the numerator and denominator are both divided by 6.
Problem 4
 $\frac{1}{2}$ + $\frac{3}{10}$ = ?
 $\frac{1}{2}$ = $\frac{5}{10}$ if the numerator and denominator are both multiplied by 5.
 $\frac{5}{10}$ + $\frac{3}{10}$ = $\frac{8}{10}$
 $\frac{8}{10}$ = $\frac{4}{5}$ if the numerator and denominator are both divided by 2.
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