Fractions and mixed numbers

When the denominators are the same, add the numerators and keep the denominator unchanged.

For example, 2/7 + 3/7 = 5/7. Do not add the denominators: you are still counting sevenths. If the numerator equals the denominator, the fraction is one whole.

A denominator of 10 means tenths, so write one digit after the decimal point. A denominator of 100 means hundredths, so write two digits after it.

For example, 7/10 = 0.7, 7/100 = 0.07, and 35/100 = 0.35. Remember the zero when there are fewer than ten hundredths.

Compare the whole parts first. The larger whole part gives the larger mixed number.

If the whole parts are equal, compare the fractions. Their denominators are the same here, so compare the numerators. If both whole and fractional parts match, the numbers are equal.

Multiply the previous term by two. Check that doubling your term gives the following term.

Starting with the first term, repeatedly add the stated step. Compare each expected term with the displayed term in that position.

Determine which of the two alternating steps comes next. Add only that step’s fraction.

A mixed number consists of a whole-number part and a fractional part. Only the fractional part determines how it is rounded.

1. Compare the numerator with half of the denominator.
2. If the fractional part is less than one half, keep the whole-number part unchanged.
3. If the fractional part is equal to or greater than one half, add 1 to the whole-number part.

Rule: less than one half rounds down; equal to or greater than one half rounds up.

Subtract the stated fraction from the last term. Exchange one whole for fractional parts if needed.

Add the stated fraction to the last term. Convert a full denominator of parts into one whole.

When the denominators are the same, subtract the second numerator from the first. Keep the denominator unchanged.

For example, 6/9 − 2/9 = 4/9. You are subtracting equal-sized parts, so do not subtract the denominators.