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7.06 Add and subtract mixed numbers

Lesson

Are you ready?

Do you remember how to add and subtract proper fractions?

Find the value of $\frac{2}{3}+\frac{5}{12}$23+512.

Learn

A mixed number such as $2\frac{3}{4}$234 is made up of a whole part (in this case $2$2) and a fractional part (in this case $\frac{3}{4}$34). We can think of it as the sum of the two parts, $2+\frac{3}{4}$2+34. With the properties of addition as well, we can follow a series of steps to add (and subtract) mixed numbers.

Let's look at an example of $2\frac{3}{4}+3\frac{5}{8}$234+358:

Step 1. We can rewrite this as four terms, by splitting each mixed number into its parts:

$2\frac{3}{4}+3\frac{5}{8}$234+358 $=$= $2+\frac{3}{4}+3+\frac{5}{8}$2+34+3+58

Step 2. We can now add the whole parts together, and separately add the fractional parts together. Adding the wholes first:

$2+\frac{3}{4}+3+\frac{5}{8}$2+34+3+58 $=$= $5+\frac{3}{4}+\frac{5}{8}$5+34+58

Step 3. To add the fractional parts together, we will first rewrite them to have a common denominator. In this case we can get a common denominator of $8$8, by multiplying numerator and denominator of $\frac{3}{4}$34 by $2$2:

$5+\frac{3}{4}+\frac{5}{8}$5+34+58 $=$= $5+\frac{6}{8}+\frac{5}{8}$5+68+58

Step 4. We can now add the fractional parts:

$5+\frac{6}{8}+\frac{5}{8}$5+68+58 $=$= $5+\frac{11}{8}$5+118

Step 5. Since this fractional part $\frac{11}{8}$118 is larger than one whole, we can't just combine the parts to make a mixed number. We can instead rewrite the improper fraction $\frac{11}{8}$118 as its own mixed number:

$5+\frac{11}{8}$5+118 $=$= $5+1\frac{3}{8}$5+138

Step 6. Finally, we can combine the whole parts to get:

$5+1\frac{3}{8}$5+138 $=$= $6\frac{3}{8}$638

So we have that $2\frac{3}{4}+3\frac{5}{8}=6\frac{3}{8}$234+358=638.

Sometimes we don't need all of the steps in this process, depending on the particular fractions.

Apply

Question 1

Find the value of $5\frac{5}{8}+\frac{1}{8}$558+18.

Question 2

Find the value of $2\frac{3}{4}-1\frac{7}{12}$2341712.

Remember!

To add or subtract mixed numbers, we can:

  • split each mixed number into a sum of its whole part and fractional part
  • add or subtract the whole parts and the fractional parts separately
    • make sure that the fractional parts have a common denominator
  • combine the two parts of the answer into a single fraction or mixed number

Outcomes

5.NF.A.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 or 3/5 + 7/10 = 6/10 + 7/10 = 13/10.

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