Adding Tenths and Hundredths

Adding Tenths and Hundredths 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 6 in this fraction is the denominator.

  The operation used in this equation is addition.

  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.
  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

  • 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.

  • 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 2's, 5's and 10's, but not by 7.

• Identify the correct order or steps to solve.

  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, untill they equal the larger denominator in the other fraction.

  $\mathbf{\frac{50}{100}}$ can be simplified to a smaller fraction by dividing both the numerator and denominator by 50.

  Solution

  To add tenths and hundredths,

  • Check if the two fractions have like denominators.

  • If the fractions do NOT have like denominators, multiply the denominator of the smaller fraction until it is the same. Multiply the numerator by the same.

  • Once all fractions have the same denominator, add the equivalent fractions together to get the sum.

  • Simplify by dividing the numerator and denominator of the sum by a common denominator, if possible.

• Match each addition expression with the correct sum.

  Hints

  30 ÷ 10 = 3
  100 ÷ 10 = 10

  70 ÷ 10 = 7
  100 ÷ 10 = 10

  20 ÷ 20 = 1
  100 ÷ 20 = 50

  Solution

  Problem 1

  • $\frac{10}{100}$ + $\frac{2}{10}$ = ?
  • $\frac{2}{10}$ x $\frac{1}{10}$ = $\frac{20}{100}$
  • $\frac{10}{100}$ + $\frac{20}{100}$ = $\frac{30}{100}$
  • $\frac{30}{100}$ ÷ $\frac{10}{10}$ = $\frac{3}{10}$

  Problem 2

  • $\frac{20}{100}$ + $\frac{5}{10}$ = ?
  • $\frac{5}{10}$ x $\frac{10}{10}$ = $\frac{50}{100}$
  • $\frac{20}{100}$ + $\frac{50}{100}$ = $\frac{70}{100}$
  • $\frac{70}{100}$ ÷ $\frac{10}{10}$ = $\frac{7}{10}$

  Problem 3

  • $\frac{7}{100}$ + $\frac{10}{100}$ = $\frac{17}{100}$

  Problem 4

  • $\frac{10}{100}$ + $\frac{10}{100}$ = ?
  • $\frac{10}{100}$ + $\frac{10}{100}$ = $\frac{20}{100}$
  • $\frac{20}{100}$ ÷ $\frac{20}{20}$ = $\frac{1}{50}$

• Calculate the sum of the equation.

  Hints

  The first step to solve the problem is to identify the unknown amount with a question mark (?).

  In order to add tenths and hundreds, you first have to create like denominators using multiplication. Multiply BOTH the numerator (above) and denominator (below).

  Like denominators: $\mathbf{\frac{10}{20}}$ + $\mathbf{\frac{2}{20}}$

  Different denominators: $\mathbf{\frac{1}{50}}$ + $\mathbf{\frac{1}{10}}$

  Once you have like denominators, you can add your fractions to find the sum. Only add the numerators! (The number above).

  $\mathbf{\frac{30}{100}}$ + $\mathbf{\frac{20}{100}}$ = ?

  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 (above) and denominator (below).

  $\mathbf{\frac{50}{100}}$ ÷ $\mathbf{\frac{50}{50}}$ = ?

  Solution

  • $\frac{3}{100}$ + $\frac{2}{10}$ = ?
  • $\frac{2}{10}$ x $\frac{10}{10}$ = $\frac{20}{100}$
  • $\frac{30}{100}$ + $\frac{20}{100}$ = $\frac{50}{100}$
  • $\frac{50}{100}$ ÷ $\frac{50}{50}$ = $\frac{1}{2}$

• Calculate the sum of the equations.

  Hints

  You will need to first find like denominators 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 by 2.

  A piece of scrap paper to write out each step is recommended for this problem!

  Solution

  Problem 1

  • $\frac{1}{4}$ + $\frac{1}{40}$ = ?
  • $\frac{10}{40}$ + $\frac{1}{40}$ = ?
  • $\frac{10}{40}$ + $\frac{1}{40}$ = $\frac{11}{40}$
  • $\frac{11}{40}$ cannot be simplified.

  Problem 2

  • $\frac{2}{5}$ + $\frac{2}{50}$ = ?
  • $\frac{20}{50}$ + $\frac{2}{50}$ = ?
  • $\frac{20}{50}$ + $\frac{2}{50}$ = $\frac{22}{50}$
  • $\frac{22}{50}$ is equivalant to $\frac{11}{25}$ (divide by 2).

  Problem 3

  • $\frac{2}{30}$ + $\frac{1}{3}$ = ?
  • $\frac{2}{30}$ + $\frac{10}{30}$ = ?
  • $\frac{2}{30}$ + $\frac{10}{30}$ = $\frac{12}{30}$
  • $\frac{12}{30}$ is equivalant to $\frac{6}{15}$ (divide by 2).

  Problem 4

  • $\frac{1}{2}$ + $\frac{3}{10}$ = ?
  • $\frac{5}{10}$ + $\frac{3}{10}$ = ?
  • $\frac{5}{10}$ + $\frac{3}{10}$ = $\frac{8}{10}$
  • $\frac{8}{10}$ is equivalant to $\frac{4}{5}$ (divide by 2).