How to ADD any two MIXED-FRACTIONS QUICKLY

Many Standardized Math Tests have problems that have MIXED-FRACTIONS to be solved by ADDITION, directly or indirectly, and since the tests are timed it is very important that these operations are done QUICKLY.

Things You'll Need

• Pencil and
• Paper

Instructions

1. 

   Given the ADDITION problem, as shown in the Image to the left, we can find the SUM of the MIXED-FRACTIONS by first ADDING the WHOLE NUMBERS of the MIXED-FRACTIONS. Please click on the Image to get a better view.

2. 

   The sum of the WHOLE NUMBERS ( 8 ), will now be added to the sum of the two PROPER FRACTIONS as shown in the Image on the left. To add the PROPER FRACTIONS, we multiply the Numerator of the first fraction with the Denominator of the second fraction, that is( 2 x 9 ) = 18. Please click on the Image to get a better view.

3. 

   We then multiply the Numerator of the second fraction with the
   Denominator of the first fraction, that is ( 4 x 5 ) = 20, as shown in the Image on the left. Please click on the Image to get a better view.

4. 

   Then multiply the Denominators of the two fractions, that is ...
   ( 5 x 9 ) = 45, as shown in the Image on the left. Please click on the Image to get a better view.

5. 

   We now take the sum of the first two products ( 18 + 20 ) = 38, and
   write it as the Numerator of the answer, and 45 as the Denominator of the answer. Please see the Image on the left. Please click on the Image to get a better view.

6. 

   The answer to the SUM of the two MIXED-FRACTION is....
   the Mixed fraction 8 and ( 38 / 45 ), as shown in the Image on the left. Please click on the Image to get a better view.

7. 

   In the case that the SUM of the two PROPER FRACTIONS is an IMPROPER FRACTION, then change the IMPROPER FRACTION to a MIXED-FRACTION, then ADD the WHOLE NUMBER part of this MIXED-FRACTION to the WHOLE NUMBER of the first answer. Please click the image on the left to see the example.

Tips & Warnings

• Another method is to first change both MIXED-FRACTIONS to IMPROPER FRACTIONS and then ADD them by following the instructions stated in STEPS # 3,# 4 and # 5.