# How to Order Fractions?

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## Ordering Fractions

### TranscriptHow to Order Fractions?

“The water glistens on the cave walls tonight.” “Tank, I think this machine is broken.” “We’ll have to get a new one.” We can help Axel find the best deal on a new karaoke machine by… “Ordering Fractions”. We can compare and order fractions with unlike denominators... by creating equivalent fractions with common denominators. An equivalent fraction is a fraction that has the same value but is represented with a different numerator and denominator. Let’s use three-fourths and five-sixths as an example. First, we rename each fraction with a common denominator. To find the common denominator of fractions, we need to think of a multiple that they share. What is one number that is a multiple of BOTH four and six? Twenty-four. This number becomes the denominator for both fractions. To rename the numerators, we multiply the numerator by the SAME number that we multiplied the original denominator by. In three-fourths, we multiply the denominator, four, by six to make twenty-four, so we will also multiply the numerator by six. What is three times six? Eighteen. Three-fourths is the same as eighteen twenty-fourths. In five-sixths, we multiply the six by four to make twenty-four, so we will multiply the five by four. What is five times four? Twenty. Five-sixths is the same as twenty-twenty-fourths. Once we have like denominators, we can order the fractions from least to greatest by looking at the numerators. Eighteen is less than twenty, so three-fourths is less than five-sixths. Axel sees ads for three stores selling karaoke machines. Each store is running a sale with the machine being a fractional amount off the regular price. If we make equivalent fractions and order them, we’ll determine which store has the biggest discount. We have two-thirds, one-half, and four-fifths. First, think of a multiple that three, two, AND five share. Thirty is a multiple that can be made with all three numbers. Now, rewrite all the denominators as thirty. Next, rename the numerators, by multiplying them by the SAME number that we multiplied the original denominator by. Let’s start with the store with two-thirds off the price. What do we multiply three by to make thirty? Ten… so we will multiply the numerator, two, by ten. What is two times ten? Twenty. Two-thirds and twenty-thirtieths are equivalent. In one-half, what do we multiply two by to make thirty? Fifteen. We will multiply the numerator, one, by fifteen and get fifteen. One-half and fifteen-thirtieths are equivalent. Finally, in four-fifths, what do we multiply five by to make thirty? Six. What is six times, the numerator, four? Twenty-four. Four-fifths and twenty-four thirtieths are equivalent. What do we do next? We compare the numerators and order the fractions from least to greatest. The order of the numerators from least to greatest is fifteen, twenty, and twenty-four, so we order the fractions as one-half is less than two-thirds is less than four-fifths. The store with four-fifths off the price has the biggest discount. As Axel and Tank make their purchase, let’s review. Remember… we can compare and order fractions with unlike denominators by creating equivalent fractions with common denominators. First, we rename each fraction with a common denominator. To rename the numerators, we multiply it by the SAME number that we needed to multiply to make the denominator. Once we have like denominators, we can order the fractions from least to greatest by looking at the numerators. We can write the original fractions as an expression using less than or greater than symbols. “The water glistens on the cave walls tonight.” “No fish can be seen.” singing beautifully] “I’m in an aquarium of solitude…” “ and it appears….I’m the KING!” "Ebb and FLOW, ebb and Flow..." "That's so beautiful!"

## How to Order Fractions? exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video How to Order Fractions? .
• ### Match equivalent fractions by multiplying by 4.

Hints

Always multiply the numerator and the denominator by the same number. For this problem the numerator and denominator are both being multiplied by 4.

In this example, both the numerator and denominator are multiplied by 6. This creates the equivalent fraction, $\frac{18}{24}$.

Solution
• $\frac{1}{5}$ = $\frac{4}{20}$, because when the numerator and denominator in $\frac{1}{5}$ are both multipled by 4 we get $\frac{4}{20}$.
• $\frac{1}{4}$ = $\frac{4}{16}$, because when the numerator and denominator in $\frac{1}{4}$ are both multipled by 4 we get $\frac{4}{16}$.
• $\frac{1}{3}$ = $\frac{4}{12}$, because when the numerator and denominator in $\frac{1}{3}$ are both multipled by 4 we get $\frac{4}{12}$.
• $\frac{2}{6}$ = $\frac{8}{24}$, because when the numerator and denominator in $\frac{2}{6}$ are both multipled by 4 we get $\frac{8}{24}$.
• ### Find the equivalent fractions.

Hints

2 fractions are equivalent to $\frac{1}{2}$, and 2 fractions are equivalent to $\frac{1}{3}$.

To see if 2 fractions are equivalent, find a multiple the denominators share. Then multiply the numerator by the same to see if the fractions are equivalent. Example: $\frac{4}{16}$ and $\frac{1}{4}$
Both 4 and 16 fit into 16
4 x $\frac{1}{4}$ = $\frac{4}{16}$
$\frac{4}{16}$ = $\frac{4}{16}$
The fractions are equivalent.

Multiply $\frac{1}{2}$ and $\frac{1}{3}$ by 5, 4, and 3 to find the equivalent fractions.

Solution
• $\frac{1}{2}$ = $\frac{5}{10}$, because when the numerator and denominator in $\frac{1}{2}$ are both multipled by 5 we get $\frac{5}{10}$.
• $\frac{1}{2}$ = $\frac{4}{8}$, because when the numerator and denominator in $\frac{1}{2}$ are both multipled by 4 we get $\frac{4}{8}$.
• $\frac{1}{3}$ = $\frac{3}{9}$, because when the numerator and denominator in $\frac{1}{3}$ are both multipled by 3 we get $\frac{3}{9}$.
• $\frac{1}{3}$ = $\frac{4}{12}$, because when the numerator and denominator in $\frac{1}{3}$ are both multipled by 4 we get $\frac{4}{12}$.
• ### Find the equivalent fractions.

Hints

Find a number that the numerator and denominator on the left can be multiplied by, to make another fraction on the right.

For example, if we multiply $\frac{4}{5}$ by 2, we would get $\frac{8}{10}$. Or if we multiplied $\frac{4}{5}$ by 3 we would get $\frac{12}{15}$.

What is $\frac{2}{5}$ x 1? Or $\frac{2}{5}$ x 2? Eventually, you will find the equivalent fraction.

You're multiplying the fractions on the left by 2, 3 and 5.

Solution

The above image shows the equivalent fractions. To find each equivalent pair:

• $\frac{1}{2}$ = $\frac{5}{10}$ because when the numerator and denominator in $\frac{1}{2}$ are both multipled by 5 we get $\frac{5}{10}$.
• $\frac{2}{5}$ = $\frac{4}{10}$ because when the numerator and denominator in $\frac{2}{5}$ are both multipled by 2 we get $\frac{4}{10}$.
• $\frac{3}{4}$ = $\frac{9}{12}$ because when the numerator and denominator in $\frac{3}{4}$ are both multipled by 3 we get $\frac{9}{12}$.
• $\frac{3}{6}$ = $\frac{9}{18}$ because when the numerator and denominator in $\frac{3}{6}$ are both multipled by 3 we get $\frac{9}{18}$.
• ### Ordering fractions.

Hints

All of the denominators on the right are 50. Think about how the numerator and denominator in the fraction on the left can be multiplied to make a new fraction with a denominator of 50.

Look at the first question, $\frac{3}{5}$ . Find what factor the denominator (5) in $\frac{3}{5}$ needs to be multiplied by to make 50.

Next, multiply the numerator (3) by this same factor.

The top number in the fraction is the numerator.

The bottom number in the fraction is the denominator.

Solution
• 1) $\frac{3}{5}$ x $\frac{10}{10}$ = $\frac{30}{50}$.
As we need to make the denominator in the second fraction 50, we multiply the first denominator (5) by 10. Whatever we do to the denominator we also do to the numerator, so we multiply the numerator (3) by 10 to get 30.
• 2) $\frac{2}{25}$ x $\frac{2}{2}$ = $\frac{4}{50}$
As we need to make the denominator in the second fraction 50, we multiply the first denominator (25) by 2. Whatever we do to the denominator we also do to the numerator, so we multiply the numerator (2) by 2 to get 4.
• 3) $\frac{4}{10}$ x $\frac{5}{5}$ = $\frac{20}{50}$
As we need to make the denominator in the second fraction 50, we multiply the first denominator (10) by 5. Whatever we do to the denominator we also do to the numerator, so we multiply the numerator (4) by 5 to get 20.
• ### Complete the numerator.

Hints

All of the choices have the same denominator, 20. What multiplied by 5 makes 20? You must also multiply the numerator by this number.

To find the equivalent fraction, solve for the numerator.
Find the answer for 20 ÷ 5, then multiply the numerator (3) by the same number.

Multiply the numerator and denominator by 4.

Solution
• 5 x 4 = 20
• 3 x 4 = 12
• $\frac{12}{20}$ is an equivalent fraction to $\frac{3}{5}$
• ### Ordering different denominators.

Hints

First, find a common multiple of all fractions.

Try multiplying the largest denominator by 2, and see if the product is a number that is a common multiple of the other fractions.

• Next, create equivalent fractions with the same denominator.
• Finally, order the fractions from least to greatest.

6, 4, 8 and 12 are all common multiples of 24. Convert the fractions to have a denominator of 24.

Solution
• $\frac{1}{6}$ x $\frac{4}{4}$ = $\frac{4}{24}$
• $\frac{1}{4}$ x $\frac{6}{6}$ = $\frac{6}{24}$
• $\frac{3}{8}$ x $\frac{3}{3}$ = $\frac{9}{24}$
• $\frac{5}{12}$ x $\frac{2}{2}$ = $\frac{10}{24}$