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Scaling by simple fractions

Scaling by simple fractions

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Tutor: Labib

Summary

Scaling by simple fractions

​​In a nutshell

Simple fractions only have a fractional part. Simple fractions can be used to scale other numbers up or down. This helps you to quickly compare different expressions without performing complex calculations. 



Fractions relative to 1

By comparing the numerator (the top number of a fraction) and the denominator (the bottom number of a fraction), you can identify whether it is greater than, equal to, or less than 11.


Example 1

Identify whether the following fractions: 12,33,54\dfrac 12, \dfrac 33,\dfrac 54are greater than, equal to, or less than 11.


​  a) 12=\begin{aligned} & a) \space \dfrac 12 = \end{aligned}  The numerator is less than the denominator.

12<1\underline{\dfrac 12 \lt 1}​​


b) 33=\begin{aligned} &b) \space \dfrac 33 = \end{aligned} The numerator is equal to the denominator.

33=1\underline{\dfrac 33 = 1}​​


c) 54=\begin{aligned} &c)\space \dfrac 54 = \end{aligned} The numerator is greater than the denominator.

54>1\underline{\dfrac 54 \gt 1}



Scaling with simple fractions

By comparing simple fractions, expressions can be sorted from largest to smallest without performing multiplication. 


Example 2

Andy and Janet host a bake sale with 4040 cakes each. Andy manages to sell 25\dfrac 25 of his cakes while Janet sells 35\dfrac 35​. Who sold more cakes?  


Form expressions for the number of cakes Andy and Janet have sold.

Andy: 40×2540 \times \dfrac{2}{5}


Janet40×3540 \times \dfrac{3}{5} ​​


Compare the expressions using scaling. 

35\dfrac{3}{5}  is greater than 25\dfrac 25 as the numerator is larger.


​Therefore, Janet sold more cakes. 


Note: If you wish to multiply a number by a fraction, multiply the number by the numerator and then divide by the denominator. 



Example 3

Arrange the following expressions in order of size, from largest to smallest:


34×9947×3434×53\dfrac 34 \times \dfrac99 \quad\quad\quad\quad \dfrac 47 \times \dfrac34 \quad\quad\quad\quad \dfrac 34\times \dfrac 53​​


Rearrange all the expressions to be in terms of a common multiple.


34×9934×4734×53\dfrac 34 \times \dfrac99 \quad\quad\quad\quad \dfrac 34 \times \dfrac47 \quad\quad\quad\quad \dfrac 34\times \dfrac 53


Compare the uncommon multiples in each expression by checking whether the fractions are smaller than, greater than or equal to 11​. 


53>99>47\dfrac 53 > \dfrac99 > \dfrac47​​


Rearrange the expressions.

34×5334×9934×47\underline{\dfrac 34 \times \dfrac53 \quad\quad\quad\quad \dfrac 34 \times \dfrac99 \quad\quad\quad\quad \dfrac 34\times \dfrac 47}​​


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FAQs - Frequently Asked Questions

How do you multiply a number by a fraction?

What are simple fractions?

How do you know if a fraction is less than 1?

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