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Understanding Fractions

One of the most important things in understanding fractions is to learn how to express it. For the fraction 3/5 the numerator is 3 and the denominator is 5. It is read as three-fifths, and the fraction shows that of the 5 equal parts available, 3 parts have been selected or shaded or picked.

Examples:

  1. Write a fraction which has numerator of 5 and the denominator of 6.

    Ans: 5/6

  2. Shade five-sevenths in the box below.

    shape with 7 parts

    The answer is:

    shape with 5 out of 7 parts shaded

  3. A bag has 5 oranges, 10 bananas, 6 pears, 4 apples and 1 pineapple. What fraction of the fruit is

    i)  bananas?

    Total number of fruits = 5 + 10 + 6 + 4 + 1  =  26

    Fraction of bananas = 10/26

    ii) oranges?

    Fraction of oranges = 5/26

    iii) not pears?

    There are 6 pears, so the number of fruits that are not pears = 26 – 6 = 20

    Fraction of fruits that are not pears = 20/26

  4. How many fifths are there in a whole?

    Since the whole has 5 parts, there are 5 fifths in the whole.

  5. Tom has 3/5 of French stamps. What fraction of stamps does he have from other countries?

    3/5 are French stamps means for every 5 stamps, 3 are French stamps, while the rest of the stamps are from other countries. So the fraction of stamps from other countries = 2/5 

  6. How many sixths are in two wholes?

    Each whole has 6 equal parts, so two wholes have 6 x 2 = 12 equal parts.

    Therefore there are 12 sixths in two wholes.

  7. Sara kept 2/7 of her library books. What fraction of books did Sara return?

    Of the 7 books that Sara borrowed, she kept 2, so she returned 7 – 2 = 5 books.

    So fraction of books returned = 5/7  

  8. James has 20 chocolates. He gives half of these chocolates to his sister Jenny, and eats half of what’s left with him. What fraction of the 20 chocolates in now left with James?

    Jenny got half of 20 chocolates = 10 chocolates.

    James now has 20 – 10 = 10 chocolates. 

    He ate half of these chocolates (10 ÷ 2) = 5

    Now chocolates left with James = 20 – 10 – 5  =  5

    So fraction of chocolates left with James = 5/20 

  9. Two friends spent half their pocket money in a toy shop. Did they spend the same amount of money? Explain.

    We cannot say whether they spent the same amount of money because we don’t know whether they both had the same amount of pocket money to start with.

    Even though they are both spending and equal share (in this case half) from their respective pocket monies, they may or may not have the same pocket money.