askvity

How to Solve a Fraction Number?

Published in Fractions 3 mins read

Solving a fraction number depends on the operation you want to perform (addition, subtraction, multiplication, or division) or whether you want to simplify it. Here's a breakdown of how to tackle each scenario:

1. Simplifying Fractions

  • Find the Greatest Common Factor (GCF): Identify the largest number that divides evenly into both the numerator (top number) and the denominator (bottom number).

  • Divide: Divide both the numerator and the denominator by the GCF. This results in an equivalent fraction in its simplest form.

    • Example: Simplify 6/8. The GCF of 6 and 8 is 2. Dividing both by 2 gives 3/4.

2. Adding or Subtracting Fractions

  • Find a Common Denominator: Fractions must have the same denominator before they can be added or subtracted. Find the Least Common Multiple (LCM) of the denominators. This LCM will be the new common denominator.

  • Convert Fractions: Multiply both the numerator and denominator of each fraction by the factor that makes the original denominator equal to the common denominator.

  • Add or Subtract Numerators: Once the denominators are the same, add or subtract the numerators. Keep the denominator the same.

  • Simplify (if possible): Simplify the resulting fraction to its lowest terms.

    • Example: 1/4 + 2/3. The LCM of 4 and 3 is 12.
      • Convert 1/4 to 3/12 (multiply top and bottom by 3).
      • Convert 2/3 to 8/12 (multiply top and bottom by 4).
      • Add the numerators: 3/12 + 8/12 = 11/12.

3. Multiplying Fractions

  • Multiply Numerators: Multiply the numerators of the two fractions.

  • Multiply Denominators: Multiply the denominators of the two fractions.

  • Simplify (if possible): Simplify the resulting fraction to its lowest terms.

    • Example: 2/5 3/4 = (23) / (5*4) = 6/20. Simplify 6/20 to 3/10.

4. Dividing Fractions

  • Invert and Multiply: Invert (flip) the second fraction (the divisor) and then multiply the first fraction by the inverted second fraction. "Invert" means to swap the numerator and the denominator.

  • Multiply: Perform the multiplication as described above.

  • Simplify (if possible): Simplify the resulting fraction to its lowest terms.

    • Example: 1/2 รท 3/4. Invert 3/4 to get 4/3. Then, 1/2 4/3 = (14) / (2*3) = 4/6. Simplify 4/6 to 2/3.

Fractions with Negative Numbers

The same rules apply, but you need to be mindful of the signs. As the reference video clip shows, adding and subtracting fractions with negative numbers requires careful attention to whether the result is positive or negative.

Example from the YouTube video: Combining 9/12 + 20/12 - 42/12. 9 + 20 = 29. 29 - 42 = -13. The result is -13/12.

In summary, solving fraction problems involves finding common denominators for addition/subtraction, multiplying numerators and denominators for multiplication, inverting and multiplying for division, and simplifying the final result whenever possible.

Related Articles