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Adding and subtracting fractions

Fractions, grade 6 Lesson 4 of 22Learning

Adding and subtracting fractions

You can only add and subtract parts of the same size – so it all starts with the denominator.

Adding with the same denominator
Careful: add only the numerators, not the denominators.

When the denominators are the same, you add parts of the same size: add the numerators, and the denominator stays. 27+37=57\displaystyle {\frac{2}{7}+\frac{3}{7}}={\frac{5}{7}} – two sevenths and three sevenths are five sevenths.

Adding with different denominators

When the denominators are different, first expand to a common denominator, then add: 23+14=812+312=1112\displaystyle {\frac{2}{3}+\frac{1}{4}}={\frac{8}{12}+\frac{3}{12}}={\frac{11}{12}}.

Adding and subtracting mixed numbers

Mixed numbers can be written as improper fractions first: 312−134=72−74=144−74=74=134\displaystyle {3\frac{1}{2}-1\frac{3}{4}}={\frac{7}{2}-\frac{7}{4}}={\frac{14}{4}-\frac{7}{4}}={\frac{7}{4}}={1\frac{3}{4}}.

Exercise 1

Calculate.
Write the result in its simplest form, or as a mixed number.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        d

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          e

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            Exercise 2

            Yoav ate 14\displaystyle \frac{1}{4} of the pizza, and Dana ate 13\displaystyle \frac{1}{3} of it.
            What part of the pizza did they eat together?
            What part is left?
            Write each answer as a fraction in its lowest terms.

            Together

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              Left

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power