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Fraction - Addition

Worksheet

\frac{1}{5}+\frac{1}{3}
=3\cdot5\left(\frac{1}{5}\right)+3\cdot5\left(\frac{1}{3}\right)
=\frac{\left(3\left(1\right)+5\left(1\right)\right)}{3\cdot5}
=\frac{3+5}{15}
=\frac{8}{15}

  • To add the fractions 1/5 and 1/3, we need to find a common denominator. A common denominator is a number that both 5 and 3 can divide evenly.

  • First, let’s find the common denominator by multiplying 5 and 3 together. So, 5 x 3 is 15. The common denominator we get is 15.

 

 

  • Now that we have the common denominator, we need to make both fractions have this denominator.

     

  • To do that, we need to multiply the top and bottom of 1/5 by 3. This gives us 3/15.

     

  • Next, we need to multiply the top and bottom of 1/3 by 5. This gives us 5/15.

     

  • Now, we have 3/15 and 5/15. Since the denominators are the same, we can add the numerators (the top numbers) together.

     

  • So, 3/15 + 5/15 equals (3 + 5) / 15 which simplifies to 8/15.

  • Therefore, 1/5 + 1/3 equals 8/15.

  • Step 1: Find a common denominator. In this case, we could use 6 as a common denominator because both 3 and 2 go into 6 evenly.
  • Step 2: Create equivalent fractions with the common denominator. For 1/3, we can multiply both the numerator (top number) and the denominator (bottom number) by 2, resulting in 2/6. For 1/2, we can multiply both the numerator and denominator by 3, giving us 3/6.
  • Step 3: Now that both fractions have the same denominator, we can subtract the numerators. So, 2/6 – 3/6 becomes (2-3)/6 in fraction form.
  • Step 4: Simplify the numerator. 2-3 equals -1, so the fraction becomes -1/6.
  • Therefore, the solution to 1/3 – 1/2 is -1/6. This means if you take away 1/2 from 1/3, you will have -1/6 left.

Worksheet

\frac{1}{3}-\frac{1}{2}
=\frac{2\times1-3\times1}{3\times2}
=\frac{2-3}{6}
=-\frac{1}{6}

To solve this fraction, we need to multiply the numerators (the numbers on top) together and multiply the denominators (the numbers on the bottom) together.

Step 1:
Take the numerator of the first fraction, which is 3, and multiply it by the numerator of the second fraction, which is 10. So, 3 multiplied by 10 is 30.

Step 2:
Next, take the denominator of the first fraction, which is 25, and multiply it by the denominator of the second fraction, which is 9. So, 25 multiplied by 9 is 225.

Step 3:
Now, we have a new fraction with the numerator of 30 and the denominator of 225.

Step 4:
To simplify this fraction, we need to see if there’s any number we can divide both the numerator and denominator by and still get the same fraction.

Step 5:
In this case, we notice that both 30 and 225 are divisible by 5. So, let’s divide both numbers by 5.

Step 6:
When we divide the numerator 30 by 5, we get 6. And when we divide the denominator 225 by 5, we get 45.

Step 7:
Therefore, the simplified fraction of 3/25 multiplied by 10/9 is 6/45.

Worksheet

\frac{3}{25}\times\frac{10}{9}
\frac{\cancel{3}}{25}\times\frac{10}{\cancel{9}} = \frac{1}{5}\times\frac{2}{3}
\frac{1}{5}\times\frac{2}{3}=\frac{2}{15}

The operation of addition in words are represented thus

  • Sum = more than
  • Plus = greater than
  • Gain = larger than
  • Increase= enlarge
  • Rise= grow
  • Expand = augment

 

Sum

In word, the sum of a number and 10

n + 10

Plus

A number plus 20

n + 20

Gain/Increase

A number gained 20 or increaded by 20

n + 20

Enlarge/expanded

50 enlarged or expanded by a number, n.

50 + n

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AlgebraPop fractions solver simplifies the following fraction-related task

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Improper fractions to mixed number

\frac{12}{7}=1\ \frac{5}{7}

Mixed numbers to improper fractions

1\frac{8}{9}=\frac{17}{9}

addition of proper fractions

\frac{1}{3}+\frac{2}{5}=\frac{11}{15}

addition of mixed numbers

2\frac{1}{3}+3\frac{1}{2}=5\frac{5}{6}

Subtraction of fractions

\frac{3}{9}-\frac{1}{2}=-\frac{1}{6}