What you need to know

Things to remember:

  • We can use estimation to simplify fractions.
  • Try each of our four operations, then compare the answers.
  • Try all four operations might not be necessary.

 

 

Find the missing operation that makes the following true:

 

5 \_\_\_ 2\frac{3}{4} = 7.75

 

This might be obvious, but let’s try all four operations to see what we get.

 

Addition: 5 + 2\dfrac{3}{4} = 7.75

Subtraction: 5 - 2\dfrac{3}{4} =2.25

Multiplication: 5 \times 2\dfrac{3}{4} = 13.75

Division: 5 \div 2\dfrac{3}{4} =1.\overline{81}

 

So, we can see that our missing operation here must have been a +.

 

We don’t always have to try every operation though, if we remember some key points:

Addition:        When adding a positive number to another number, it makes it bigger.

 

Subtraction:   When subtracting a positive number from another number, it makes it smaller.

 

Multiplication: When multiplying by a number bigger than 1, it makes it bigger.

When multiplying by a number smaller than 1, it makes it smaller.

 

Division: When dividing by a number bigger than 1, it makes it smaller.

When dividing by a number smaller than 1, it makes it bigger.

 

The numbers and fraction were quite nice, but how about if they are a bit tougher?

 

Find the missing operation that makes the following true:

 

\dfrac{13}{48} \_\_\_ 3 = \frac{13}{16}

 

Neither of these fractions are particularly nice, but we can estimate find estimate for them to make them a little nicer. We can estimate fractions by changing the numerator and denominator into numbers that let us simplify them down.

 

\dfrac{13}{48}\rightarrow\frac{12}{48}\rightarrow\frac{1}{4}

\dfrac{13}{16}\rightarrow\frac{12}{16}\rightarrow\frac{3}{4}

 

Now that we have our estimates, let’s put them in.

 

\dfrac{1}{4} \_\_\_ 3 = \frac{3}{4}

 

Our estimate is now asking “How do we use 3 to turn \dfrac{1}{4} into \dfrac{3}{4}?” Well, we multiply of course!

 

\dfrac{1}{4} \times 3 = \frac{3}{4}

 

So, our missing operation was a multiplication!

 

\dfrac{13}{48} \times 3= \frac{13}{16}

Example Questions

Question 1: Find the missing operation that makes the following true:

 

\frac{21}{100} \_\_\_ 2 = \frac{21}{50}

Answer

\dfrac{21}{100}\rightarrow\frac{20}{100}\rightarrow\dfrac{1}{5}

\dfrac{21}{50}\rightarrow\frac{20}{50}\rightarrow\dfrac{2}{5}

Our estimate is now asking “How do we use 2 to turn \dfrac{1}{5} into \dfrac{2}{5}?” Well, we multiply, so this must be our missing operation!

\dfrac{21}{100} \times 2 = \dfrac{21}{50}

Question 2: Find the missing operation that makes the following true:

 

\frac{9}{40} \_\_\_ 4 = \frac{9}{10}

Answer

\dfrac{9}{40}\rightarrow\dfrac{10}{40}\rightarrow\dfrac{1}{4}

\dfrac{9}{10}\rightarrow\dfrac{10}{10}\rightarrow 1

Our estimate is now asking “How do we use 4 to turn \dfrac{1}{4} into 1 whole?” Well, we multiply, so this must be our missing operation!

\dfrac{9}{40} \times 4 = \dfrac{9}{10}