Adding and Subtracting Unlike Fractions

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Adding Unlike Fractions
To add unlike fractions (fractions with different denominators), create new fractions with like denominators, then add and simplify.

How do we add the two fractions shown below?

Figure 1.

Multiply each fraction by a fraction that has the same denominator as the fraction it's being multiplied by. Sound confusing? Look below:

Figure 2.

We can multiply by (8/8) and (5/5) because they're equal to 1, and don't change the overall value.

Figure 3.

Subtracting Unlike Fractions
To subtract unlike fractions (fractions with different denominators), create new fractions with like denominators, then subtract and simplify.

How do we subtract the two fractions shown below?

Figure 4.

Again, multiply each fraction by a fraction that has the same denominator as the fraction it's being multiplied by. Sound confusing? Look below:

Figure 5.

We can multiply by (8/8) and (5/5) because they're equal to 1, and don't change the overall value.

Figure 6.