Adding Tenths and Hundredths — Let's Practice!

Adding Tenths and Hundredths — Let's Practice! exercise

• Identify the expressions that are equivalent.

  Hints

  To compare the expressions, you must first create like-denominators.

  The fractions, $\frac{55}{100}$ and $\frac{3}{100}$ share like denominators. The fractions, $\frac{55}{100}$ and $\frac{3}{10}$ do not.

  Solution

  When you add tenths and hundredths you need to first make sure the denominators are the same. By multiplying the numerator and the denominator of $\frac{3}{10}$ you make $\frac{30}{100}$, which you can then add to $\frac{35}{100}$. The same applies with $\frac{5}{10}$, $\frac{3}{10}$, and $\frac{4}{10}$.

  • $\frac{3}{10}$ x 10 = $\frac{30}{100}$ = $\frac{35}{100}$ + $\frac{30}{100}$
  • $\frac{5}{10}$ x 10 = $\frac{50}{100}$ = $\frac{3}{100}$ + $\frac{50}{100}$
  • $\frac{6}{10}$ x 10 = $\frac{60}{100}$ = $\frac{60}{100}$ + $\frac{2}{100}$
  • $\frac{4}{10}$ x 10 = $\frac{40}{100}$ = $\frac{40}{100}$ + $\frac{45}{100}$

• Identify the expressions that are equivalent.

  Hints

  To compare the expressions, you must first create like-denominators.

  To compare the expressions, you must first create like-denominators.
  The fractions, $\frac{55}{100}$ and $\frac{33}{100}$ share like denominators. The fractions, $\frac{55}{100}$ and $\frac{33}{10}$ do not.

  When creating like denominators don't forget to divide or multiply the numerator as well!

  Solution

  • $\frac{50}{100}$ ÷ 10 = $\frac{5}{10}$
  • $\frac{20}{100}$ ÷ 10 = $\frac{2}{10}$
  • $\frac{40}{100}$ ÷ 10 = $\frac{4}{10}$
  • $\frac{10}{100}$ ÷ 10 = $\frac{1}{10}$

• Solve the equations.

  Hints

  Use a pencil and paper to help you keep track of the steps.

  With the equation, $\frac{35}{100}$ + $\frac{3}{10}$, and $\frac{3}{100}$ + $\frac{5}{10}$, it is easiest to multiply to create like denominators.

  With the equation, $\frac{30}{100}$ + $\frac{2}{10}$, it is easiest to divide to create like denominators.

  Do NOT simplify the fractions!

  Solution

  • $\frac{35}{100}$ + $\frac{3}{10}$ = $\frac{35}{100}$ + $\frac{30}{100}$ = $\frac{65}{100}$
  • $\frac{3}{100}$ + $\frac{5}{10}$ = $\frac{3}{100}$ + $\frac{50}{100}$ = $\frac{53}{100}$
  • $\frac{30}{100}$ + $\frac{2}{100}$ = $\frac{3}{10}$ + $\frac{2}{10}$ = $\frac{5}{10}$

• Simplify the solutions.

  Hints

  In the solution to $\frac{40}{100}$ + $\frac{40}{100}$, both 80 and 100 can be divided by 10. This solution can then be further simplified by dividing by 2.

  Simplify the answer as many times as necessary.

  Solution

  • $\frac{40}{100}$ + $\frac{40}{100}$ = $\frac{80}{100}$
  • $\frac{80}{100}$ ÷ $\frac{10}{10}$ = $\frac{8}{10}$
  • $\frac{8}{10}$ ÷ $\frac{2}{2}$ = $\frac{4}{5}$

• Convert the tenths fraction to hundredths using multiplication.

  Hints

  Always remember to multiply both the numerator (above) and denominator (below) by the same number.

  Multiply or divide to create like denominators before attempting to solve.

  Solution

  • 7 x 10 = 70, 10 x 10 = 100
  • $\frac{70}{100}$ + $\frac{8}{100}$ = $\frac{78}{100}$

• Solve the equations.

  Hints

  In the equation, $\frac{20}{100}$ + $\frac{5}{10}$, $\frac{20}{100}$ can be divided by 10 to make equal denominators.

  Remember to simplify as many times as necessary. If there is a common denominator between the numerator and denominator, divide again!

  Solution

  • $\frac{20}{100}$ + $\frac{5}{10}$ = $\frac{2}{10}$ + $\frac{5}{10}$ = $\frac{7}{10}$
  • $\frac{30}{100}$ + $\frac{2}{10}$ = $\frac{3}{10}$ + $\frac{2}{10}$ = $\frac{5}{10}$ = $\frac{1}{2}$
  • $\frac{3}{10}$ + $\frac{50}{100}$ = $\frac{3}{10}$ + $\frac{5}{10}$ = $\frac{8}{10}$ = $\frac{4}{5}$
  • $\frac{4}{10}$ + $\frac{20}{100}$ = $\frac{4}{10}$ + $\frac{2}{10}$ = $\frac{6}{10}$ = $\frac{3}{5}$