Adding Tenth and Hundredth

Adding Tenth and Hundredth exercise

• Identify the different parts of the equation.

  Hints

  The 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.

  Solution

  The 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.

  Solution

  True

  • 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?

  Hints

  In 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.

  Solution

  To add tenths and hundredths,

  1. 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.
  2. 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 $\frac{20}{100}$.
  3. 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 $\frac{50}{100}$.
  4. 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?

  Hints

  Start 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.

  Solution

  Problem 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.

  Problem 2

  • $\frac{20}{100}$ + $\frac{5}{10}$ = ?
  • $\frac{5}{10}$ = $\frac{50}{100}$ 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.

  Problem 3

  • $\frac{7}{10}$ + $\frac{10}{100}$ = ?
  • $\frac{7}{10}$ = $\frac{70}{100}$ 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.

  Problem 4

  • $\frac{6}{10}$ + $\frac{30}{100}$ = ?
  • $\frac{6}{10}$ = $\frac{60}{100}$ 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.

  Hints

  Which 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

  1. $\frac{10}{100}$ + $\frac{2}{10}$ = ?
  2. $\frac{2}{10}$ = $\mathbf{\frac{20}{100}}$ if the numerator and denominator are both multiplied by 10.
  3. $\frac{10}{100}$ + $\frac{20}{100}$ = $\mathbf{\frac{30}{100}}$
  4. $\frac{30}{100}$ = $\mathbf{\frac{3}{10}}$ if the numerator and denominator are both divided by 10.

• Calculate the sum of the equations.

  Hints

  You 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.

  Solution

  Problem 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.

  Problem 2

  • $\frac{2}{5}$ + $\frac{2}{50}$ = ?
  • $\frac{2}{5}$ = $\frac{20}{50}$ 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.

  Problem 3

  • $\frac{2}{30}$ + $\frac{1}{3}$ = ?
  • $\frac{1}{3}$ = $\frac{10}{30}$ 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.