Math is EDUCATIONAL!!

Multiplying two fractions is easier than adding, taking and dividing fractions. To multiply two fractions together all you need to do be able to do is times the numerators together, and times the denominators together. The numerator is the top part of the fraction, and the denominator is the bottom part of the fraction.

Example 1

Work out 2/7 × 3/5

= 6/35 (Since 2×3=6 and 7×5=35).

Let’s take a look at another example when you have to times another fraction by a whole number.

Example 2

Work out 5 × 3/8.

First write 5 as 5/1.

So we have 5/1 × 3/8.

= 15/8 (since 5×3=15 and 8×1=8)

Let’s take another example of timesing 3 fractions together.

Example 3

Work out 1/3 × 1/2 × 2/9.

To do this all you do is times all the numerators, and times all the denominators.

= 2/54 (since 1×1×2=2, and 3×2×9 is 54)

= 1/27  (simplify the fraction by dividing by 2)

Our last example looks at multiplying two mixed fractions together. When you multiply two mixed fractions together, the easiest way to do this will be to convert the mixed fractions to improper fractions.

Example 4

Work out 2 1/3 × 1 1/5.

First of all you will need to write the two mixed fractions to improper fractions.

Therefore our question can be written as:

7/3 × 6/5.

Now it’s the same as before. Times the numerators, and times the denominators!

42/15 (since 7 × 6 =42, and 3 × 5 =15).

= 14/5 (simplify you final answer by dividing by 3)

You may want to convert your final answer back into a mixed fraction = 2 4/5.

Step 1

A quick reminder; the top number is called the numerator, and the bottom number is called the denominator. It may not seem important to you right now, but in the future you may well change your mind!

Step 2

Let’s start with the problem 2/3 + 4/9. Now, adding fractions is as simple as adding straight across, numerator to numerator and denominator to denominator. But wait; the denominators must be the same! Uh oh…ours are a 3 and a 9! So what can you do? Take a look at the 3 and the 9. Do you spot any similarities?

Step 3

That’s it! Both 3 and 9 share the factors 1 (which is a given) and 3. So therefore, 3 is their GCF, or Greatest Common Factor (pretty self-explanatory; the greatest factor that both numbers share). Now we must figure out how to get the denominators to match. Hm…so how can you get 3 to become a 9? Aha! By multiplying by 3! Be sure that you multiply both the numerator AND denominator by the same amount, so keep the fraction equivalent. Like you will learn later on (around 7th/8th grade), what you do to one side, you must do to the other.

Step 4

3*2=6, and 3*3=9, so the new fraction is 6/9. Now the problem is 6/9+4/9. Now you can add the numerators straight across! Be sure that you don’t add the denominators, though! So 6+4=10, and the fraction becomes 10/9, which, if you prefer a mixed number, is 1 1/9. Congratulations! You have just completed a fraction addition problem! Soon you will be moving on to the other operations of subtraction, multiplication, and division.

Fractions of amounts questions.

1) Work out 1/5 of .

2) Work out 4/7 of 42 g.

3) Work out 5/6 of 24 ml.

4) Work out 2/9 of 45 kg

5) Work out 2/3 of 24 m.

6) In a jar there are 30 sweets. 4/5 of the sweets are toffees. Work out the amount of toffees in the jar.

7) Andy receives pocket money per week. He spends 2/3 of his pocket money on buying books. How much money does he spend on buying books?

At a school play there is an audience of 420 people. 2/7 of the people in the audience are over the age of 60. How many people are over the age of 60 in the house?

9) On a coach there are 24 people. 5/8 of the people on the coach are women and the rest are men. Work out the amount of men on the coach.

10) Gavin is a semi-professional pool player. Last year he played 720 pool games. Out of these games Gavin won 5/8 of the games. Work out the amount of games Gavin won last year.

Answers.

Score 1 mark for each correct answer.  Award ½ of a mark for the correct working out but the wrong answer.

1) 35 ÷ 5 =

2) (42 ÷ 7) × 4 = 24 g

3) (24 ÷ 6) × 5 = 20 ml

4) (45 ÷ 9) × 2 = 10 g

5) (24 ÷ 3) × 2 = 16 m

6) (30 ÷ 5) × 4 = 24 sweets

7) (12 ÷ 3) × 2 =

(420 ÷ 7) × 2 = 120 people

9) (24 ÷ × 3 = 9 people

10) (720 ÷ × 5 = 450 games

If you score 9 or 10 marks award a grade A.

7 or 8 marks award a grade B.

 5 or 6 marks award a grade C.

Less than 5 marks award a grade D.

For extra help try these:

Fractions of amounts 1.

Fractions of amounts 2.

Related Math Articles

Step 1

The key thing to remember is the phrase “Reverse-reverse”. Think of the Cha-cha Slide, if it helps. “Reverse-reverse” is the rule for dividing fractions, which you will soon understand more deeply.

Step 2

Let’s use the problem 1/2 / 1/8 (one half divided by one eighth). Wait! Unlike in multiplication, you can’t do this straight across. A few adjustments, so to say, must be made, but later on, you will be able to  So how do you do it? By reversing the operation and the numerator and denominator of the second fraction. Division becomes multiplication. The denominator, 8, is now the numerator, and the numerator, 1, is now the denominator, for a fraction of 8/1 (eight over one). If you would like, you can also simply think of it as “opposite reciprocal”. Look below to see the example, and watch as the operation switches from division to multiplication and 1/8 (one eighth) becomes 8/1, or eight.

1                 1                1            8

-         /        -       =        -      *     -

2                 8                2            1

Step 3

And now that you have the problem set up correctly, you can multiply straight across! 1 x 8 = 8, and 2 x 1 = 2, so you get 8/2 or 4. Congratulations! You are now able to divide fractions! Soon, you can move past this building block onto more complicated math; fun!

1            8            8            4

-      *      -      =     -      =    -      =      4

2            1            2            1

Tips and Warnings

Don’t rule out the power of making kinetic connections; aka getting up and moving! If you’re a teacher, especially, use this in a lesson plan: get up and start dancing to the Cha-cha Slide! Pay special attention to the “reverse reverse” part; the “reverse reverse” in the song is similar to the “reverse reverse” when you switch the operation (division to multiplication) and flip the second fraction (use its reciprocal).