1.3 D) Ordering Fractions
Place the following fractions in ascending order.
To answer this question, we are going to be creating equivalent fractions where all of the denominators are the same. The new denominator for the fractions will be the lowest common multiple between all of the denominators involved; the lowest common multiple is the smallest number that is a multiple of two or more given numbers. There are 3 different denominators; 2, 4 and 8. The lowest common multiple between these 3 numbers is the lowest number that 2, 4 and 8 go into, which is 8. The next step is to create equivalent that all have 8 as their denominator.
Whenever we are creating equivalent fractions, we multiply the numerator and the denominator of the fraction by the same value. The first fraction is ½. The denominator of this fraction is 2 and the denominator of the new fraction will be 8. To find out what we have multiplied the denominator by, we divide the new denominator (8) by the original denominator (2), which is 4. We now multiply the original numerator by 4. The equivalent fraction to ½ becomes 4/8.
We now do the same for the other 4 fractions in the question. The second and fifth fraction already have the denominator of 8, which means that we do not need to do anything to them.
The third and fourth fractions have the denominator 4. We want the denominator of the new fraction to be 8, which means that we multiply the original denominator by 2 (8 ÷ 4 = 2). Therefore, we multiply the numerators of the original fractions by 2. This results in the third fraction being 6/8 and the fourth fraction being 2/8.
We now have all of the fractions with a denominator of 8.
We are now able to order the fractions by looking at the numerators of the fractions. The question asks us to order the fractions in ascending order (smallest to largest). This means that we order the fractions from the smallest to the largest numerators.
The final step is to make sure that we give the original fractions rather than the equivalent fractions.
Place the fractions below in descending order.
The first step is to create equivalent fractions with the same denominators. The denominators of the new fractions are going to be the lowest common multiple of all of the current denominators. Therefore, we are looking for the lowest number that 10, 3, 15, 30, 2 and 5 go into. It is usually best to start with the highest current denominator and see whether all of the other denominators are a factor of the highest current denominator. The highest current denominator is 30; 10 is a factor of 30, 3 is a factor of 30, 15 is a factor of 30, 2 is a factor of 30 and 5 is a factor of 30. Therefore, the lowest common multiple for all of the denominators is 30.
The next step is to create equivalent fractions with 30 as the denominators.
In order to get the denominator of the first fraction to equal 30, we need to multiply the numerator and the denominator by 3 (new denominator ÷ original denominator: 30 ÷ 10 = 3). Therefore, the first fraction becomes 9/30.
We need to multiply the numerator and denominator of the second fraction by 10, which means that the fraction becomes 20/30.
The numerator and denominator of the third fraction need to be multiplied by 2, which means that the fraction becomes 22/30.
The fourth fraction already has a denominator of 30, which means that we do not need to do anything to it.
The numerator and denominator of the fifth fraction need to be multiplied by 15, which means that the fraction becomes 15/30.
We need to multiply the numerator and denominator of the final fraction by 6 and this means that it becomes 24/30.
The original and new fractions are given below.
The question is asking us to place the fractions in descending order. As all of the denominators of the fractions are the same, we can order the fractions in descending order by placing the fraction with the highest numerator first and the lowest numerator last.
The final step is to make sure that we write the original fractions and not the equivalent fractions.