Add and subtract mixed numbers

Combine whole parts and fractional parts

For 12/3 + 23/4, first make the parts the same size: thirds and quarters can both be expressed as twelfths. Then

Seventeen twelfths include one more whole and five twelfths. Keep that extra whole. Adding denominators would invent a new part size and give the wrong amount.

You can also change both mixed numbers into improper fractions: 5/3 + 11/4 = 20/12 + 33/12 = 53/12 = 45/12. The two methods count the same twelfths.

If matching the part sizes needs practice, revisit Add unlike fractions.

Exchange a whole when subtracting

A ribbon is 31/4 m long. Cut off 12/3 m. Change the fractional parts to twelfths: 33/12-18/12.

Three twelfths are too few to remove eight twelfths. Exchange one whole for twelve twelfths: 33/12 = 215/12. Now subtract to get 17/12 m.

Check by adding the cut and the remainder: 18/12 + 17/12 = 2 + 15/12 = 33/12 m. An exchange changes the representation, not the ribbon length.

Check your understanding 1 Where did the whole go?

Find 41/6-23/4. Show the exchange or use improper fractions.

Your difference and exchange or improper-fraction method

Show answer

Use twelfths: 42/12 = 314/12. Subtract 29/12 to get 15/12. Alternatively (50-33)/12 = 17/12.

Read the whole before the fraction

Check your understanding 2 Separate a comparison from a total

A bag holds 21/2 kg of rice. Another holds 3/4 kg less. Find the mass of the second bag, then the combined mass. Check the stated difference between the bags.

Your two masses and difference check

Show answer

Second bag: 22/4-3/4 = 13/4 kg. Together: 21/2 + 13/4 = 41/4 kg. Check 13/4 + 3/4 = 21/2 kg. The phrase “less” compares the second bag with the first; it does not describe their total.