Examples with solutions for All Operations in Fractions: Only addition and subtraction

Exercise #1

23+21545= \frac{2}{3}+\frac{2}{15}-\frac{4}{5}=

Video Solution

Step-by-Step Solution

Let's try to find the lowest common denominator between 3, 15, and 5

To find the lowest common denominator, we need to find a number that is divisible by 3, 15, and 5

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

2×53×5+2×115×14×35×3=1015+2151215 \frac{2\times5}{3\times5}+\frac{2\times1}{15\times1}-\frac{4\times3}{5\times3}=\frac{10}{15}+\frac{2}{15}-\frac{12}{15}

Now we'll add and then subtract:

10+21215=121215=015 \frac{10+2-12}{15}=\frac{12-12}{15}=\frac{0}{15}

We'll divide both the numerator and denominator by 0 and get:

015=0 \frac{0}{15}=0

Answer

0 0

Exercise #2

1228+14= \frac{1}{2}-\frac{2}{8}+\frac{1}{4}=

Step-by-Step Solution

To solve the expression 1228+14 \frac{1}{2} - \frac{2}{8} + \frac{1}{4} , we must first find a common denominator for the fractions involved.

Step 1: Identify a common denominator. The denominators are 2, 8, and 4. The smallest common multiple of these numbers is 8.

Step 2: Convert each fraction to have the common denominator of 8.

  • The fraction 12 \frac{1}{2} can be written as 48 \frac{4}{8} because 1×4=4 1 \times 4 = 4 and 2×4=8 2 \times 4 = 8 .
  • The fraction 28 \frac{2}{8} is already expressed with 8 as the denominator.
  • The fraction 14 \frac{1}{4} can be written as 28 \frac{2}{8} because 1×2=2 1 \times 2 = 2 and 4×2=8 4 \times 2 = 8 .

Step 3: Substitute these equivalent fractions back into the original expression:

4828+28 \frac{4}{8} - \frac{2}{8} + \frac{2}{8}

Step 4: Perform the subtraction and addition following the order of operations:

  • Subtract: 4828=28 \frac{4}{8} - \frac{2}{8} = \frac{2}{8}
  • Add: 28+28=48 \frac{2}{8} + \frac{2}{8} = \frac{4}{8}

Step 5: Simplify the result:

48 \frac{4}{8} simplifies to 12 \frac{1}{2} by dividing the numerator and denominator by 4.

Therefore, the value of the expression is 12 \frac{1}{2} .

Answer

12 \frac{1}{2}

Exercise #3

13+71525= \frac{1}{3}+\frac{7}{15}-\frac{2}{5}=

Video Solution

Step-by-Step Solution

Let's try to find the lowest common denominator between 3, 15, and 5

To find the lowest common denominator, we need to find a number that is divisible by 3, 15, and 5

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

1×53×5+7×115×12×35×3=515+715615 \frac{1\times5}{3\times5}+\frac{7\times1}{15\times1}-\frac{2\times3}{5\times3}=\frac{5}{15}+\frac{7}{15}-\frac{6}{15}

Now we'll add and then subtract:

5+7615=12615=615 \frac{5+7-6}{15}=\frac{12-6}{15}=\frac{6}{15}

We'll divide both numerator and denominator by 3 and get:

6:315:3=25 \frac{6:3}{15:3}=\frac{2}{5}

Answer

25 \frac{2}{5}