Comparing Fractions Using Cross Multiplication
Basics on the topic Comparing Fractions Using Cross Multiplication
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Cross Multiplication
When we compare fractions, we are determining which one is greater than, less than, or equal to the other.
Cross multiplication is one method used to compare fractions. To compare using cross multiplication: 1)Multiply the denominator of one fraction with the numerator of the other fraction being compared.
2) Compare the products to determine if the fraction is greater than, less than, or equal to the other.
Transcript Comparing Fractions Using Cross Multiplication
Axel and Tank are in the treasure hunt room at the Sunken Ship Funhouse. They get five minutes in the room to find as many treasure chests with the greater amounts of jewels as they can. "This one has twothirds jewels!" "This one has threefifths! How do we know which one has more?" In order to collect as many jewels as they can, Axel and Tank will be... Comparing Fractions Using Cross Multiplication. When we compare fractions, we are determining which one is greater than, less than, or equal to the other. Cross multiplication is one method used to compare fractions. To compare using cross multiplication, multiply the denominator of one fraction with the numerator of the other fraction being compared. Then, compare the products to determine if the fraction is greater than, less than, or equal to the other. Let’s use the twothirds and threefifths fractions as an example. First, multiply THIS denominator, three, by THIS numerator, three. Three times three is nine. Next, multiply THIS denominator, five, across to THIS numerator, two. Five times two is ten. Now, compare the products. Ten is greater than nine… so twothirds is GREATER than threefifths. Why does cross multiplication work when comparing fractions? When we compare fractions with different denominators, we look to make equivalent fractions with the same denominator. We find the least common multiple that each denominator shares and multiplying the numerator by that same number. In the fractions twothirds and threefifths, the common denominator is fifteen. Since you multiply three times five to make fifteen, multiply the numerator by five. Two times five is TEN. Five times three is fifteen and three times three equals NINE. Tenfifteenths is greater than ninefifteenths...so twothirds is greater than threefifths. In cross multiplication, the product of each side of the fraction is the SAME as the numerators created in the equivalent fractions. This method is useful when you are working with fractions with larger numbers or have multiplestep problems to solve. Now, let's help Axel and Tank compare more fractions using cross multiplication. Compare sevenninths and eighttwelfths. What is nine times eight? Seventytwo. What is twelve times seven? Eightyfour. Is sevenninths less than, greater than, or equal to eighttwelfths? Sevenninths is GREATER than eighttwelfths. Compare fivefourteenths and seventwelfths. Pause the video to solve and press play when you're ready to check the solution. Twelve times five is sixty and fourteen times seven is ninetyeight so, fivefourteenths is LESS than seventwelfths. Looks like time is running out for Axel and Tank's treasure hunt, so let's review. Remember... when we compare fractions, we are determining which one is greater than, less than, or equal to the other. Cross multiplication is one method used to compare fractions. To solve using cross multiplication, multiply the denominator of one fraction with the numerator of the other fraction across the expression. Then, compare the products to determine which fraction is greater than, less than, or equal to the other. This method is useful when you are working with larger fractions or have a multiplestep problem to solve. "Time's up! How do we get out of here?" "This way!"
Comparing Fractions Using Cross Multiplication exercise

Label the picture.
Hints2 x 5 = ? 3 x 3 = ?
Which answer is greater?The symbol < means the left is less than the right.
The symbol > means the left is greater than the right.
The symbol = means both the left and right are equal to each other.Solution To find which fraction is greater, use cross multiplication with the numerators and denominators.
 2 x 5 = 10, and 3 x 3 = 9.
 10 is greater than 9, so $\mathbf{\frac{2}{3}}$ is greater than $\mathbf{\frac{3}{5}}$.

Complete the steps to compare fractions.
HintsCross multiply the numerator and denominator to find which fraction is greater, lesser, or equal.
Shown below is an example.
$\frac{9}{10}$ ? $\frac{4}{5}$
In order to find which is greater, first solve for 9 x 5 and 10 x 4 as this cross multiplys the numerators and denominators. Once we have the answers we can compare those numbers.
The symbol < means the left is less than the right.
The symbol > means the left is greater than the right.
The symbol = means both the left and right are equal to each other.Solution To find which number is greater, first multiply the numerator of the left fraction with the denominator of the right fraction.
 Next, multiply the denominator of the left fraction with the numerator of the right fraction.
 Compare the products of the multiplication equations to find which result is greater.
 45 is greater than 40, so $\frac{9}{10}$ is greater than $\frac{4}{5}$.

Match the fractions and expressions.
HintsCross multiply the numerator and denominator to find which fraction is greater than, less than, or equal to.
Shown below is an example.
Example:
 $\frac{4}{9}$ and $\frac{3}{5}$
 4 x 5 = 20, 9 x 3 = 18
 20 > 18
 So, $\frac{4}{9}$ > $\frac{3}{5}$
Solution$\frac{9}{10}$ and $\frac{4}{5}$
9 x 5 = 45
10 x 4 = 40
45 < 40$\frac{2}{5}$ and $\frac{7}{9}$
2 x 9 = 18
7 x 5 = 35
18 < 35$\frac{6}{3}$ and $\frac{4}{9}$
6 x 9 = 54
3 x 4 = 12
54 < 12$\frac{2}{10}$ and $\frac{8}{14}$
2 x 14 = 28
10 x 8 = 80
28 < 80 
Highlight the correct expressions.
HintsCross multiply the numerator and denominator to find which fraction is greater than, less than, or equal to.
Shown below is an example.
The symbol < means the left is less than the right.
The symbol > means the left is greater than the right.
The symbol = means both the left and right are equal to each other.Solution1) 4 x 5 = 20, 6 x 3 = 18. 20 is greater than 18, so $\mathbf{\frac{4}{6}}$ is greater than $\mathbf{\frac{3}{5}}$.
2) 7 x 10 = 70, 9 x 6 = 54. 70 is greater than 54, so $\mathbf{\frac{7}{9}}$ is greater than $\mathbf{\frac{6}{10}}$.
3) 2 x 10 = 20, 3 x 8 = 24. 20 is less than 24, so $\mathbf{\frac{2}{3}}$ is less than $\mathbf{\frac{8}{10}}$.
4) 2 x 10 = 20, 6 x 5 = 30. 20 is less than 30, so $\mathbf{\frac{2}{6}}$ is less than $\mathbf{\frac{5}{10}}$. 
Compare the fractions.
HintsThe symbol < means the left is less than the right.
The symbol > means the left is greater than the right.
The symbol = means both the left and right are equal to each other.In order to find which fraction is greater than, less than, or equal to, cross multiply the numerator and denominator. Then compare the products.
In this example, 10 is greater than 9. So, $\mathbf{\frac{2}{3}}$ is greater than $\mathbf{\frac{3}{5}}$.Solution $\mathbf{\frac{7}{9}}$ and $\mathbf{\frac{8}{12}}$
 7 x 12 = 84
 9 x 8 = 72
 84 > 72
 $\mathbf{\frac{7}{9}}$ > $\mathbf{\frac{8}{12}}$

Complete the blanks with >, =, or <.
HintsCross multiply the numerator and denominator to find which fraction is greater, lesser, or equal.
Example:
 $\frac{4}{9}$ and $\frac{3}{5}$
 4 x 5 = 20, 9 x 3 = 18
 20 < 18
 So, $\frac{4}{9}$ > $\frac{3}{5}$
Solution1) $\frac{5}{11}$ and $\frac{2}{3}$
5 x 3 = 15
11 x 2 = 22
15 < 22
$\frac{5}{11}$ < $\frac{2}{3}$2) $\frac{7}{12}$ and $\frac{6}{7}$
7 x 7 = 49
12 x 6 = 72
49 < 72
$\frac{7}{12}$ < $\frac{6}{7}$3) $\frac{16}{20}$ < $\frac{8}{10}$
16 x 10 = 160
20 x 8 = 160
160 = 160
$\frac{16}{20}$ = $\frac{8}{10}$4) $\frac{13}{15}$ < $\frac{8}{9}$
13 x 9 = 117
15 x 8 = 120
117 < 120
$\frac{13}{25}$ < $\frac{8}{9}$