For example: \(\dfrac{2}{22}\)
Here, the GCF of \(2\) and \(22\) is \(2.\) Thus, we will divide both numerator and denominator by \(2.\)
\(\dfrac{2\div2}{22\div2}=\dfrac{1}{11}\)
Hence, the simplest form of \(\dfrac{2}{22}\) is \(\dfrac{1}{11}\).
Note: The values of a ratio and of simplified form are always same.
A \(\dfrac{1}{8}\)
B \(\dfrac{2}{3}\)
C \(\dfrac{3}{2}\)
D \(\dfrac{12}{1}\)
For example: \(\dfrac{1}{2}\) and \(\dfrac{3}{6}\)
If we simplify \(\dfrac{3}{6}\), it becomes \(\dfrac{1}{2}\).
Thus, \(\dfrac{1}{2}\) and \(\dfrac{3}{6}\) are equivalent ratios.
The equivalent ratios of a ratio can be obtained by multiplying both numerator and denominator by a non-zero number.
For example: \(\dfrac{1}{3}\)
To obtain the equivalent ratio of \(\dfrac{1}{3}\), multiply both \(1\) and \(3\) by a non-zero number.
Let it be \(3.\)
Then, \(\dfrac{1×3}{3×3}=\dfrac{3}{9}\)
Thus, the equivalent ratio of \(\dfrac{1}{3}\) is \(\dfrac{3}{9}\).
The equivalent ratios of a ratio can be obtained by dividing both numerator and denominator by a non-zero number.
For example: \(\dfrac{22}{6}\)
To obtain the equivalent ratio of \(\dfrac{22}{6}\), divide both \(22\) and \(6\) by a non-zero number.
The GCF of \(22\) and \(6\) is \(2.\)
Thus, \(\dfrac{22\div2}{6\div2}=\dfrac{11}{3}\)
Thus, the equivalent ratio of \(\dfrac{22}{6}\) is \(\dfrac{11}{3}\).
A \(\dfrac{1}{3}\)
B \(\dfrac{4}{12}\)
C \(\dfrac{1}{6}\)
D \(\dfrac{12}{36}\)
Step 1: Write the ratio in fraction form.
Step 2: Simplify the fraction, if possible.
Step 3: Convert the fraction to a decimal.
For example: We want to convert \(3:6\) in decimal form.
Step 1: We write the given ratio, \(3:6\) in fraction form.
\(3:6=\dfrac{3}{6}\)
Step 2: Now, we have to simplify the fraction, if possible.
The GCF of \(3\) and \(6\) is \(3\).
Thus \(\dfrac{3\div3}{6\div3}=\dfrac{1}{2}\)
Step 3: We will convert the fraction to a decimal by dividing \(1\) by \(2\).
Thus, \(3:6=0.5\)
A \(0.5\)
B \(0.6\)
C \(0.7\)
D \(0.8\)
Step 1: Write the ratios in fraction form.
Step 2: Simplify the fractions, if possible.
Step 3: Convert the fractions to decimals.
For example: \(2:4\) and \(4:5\) are to be compared.
Step 1: We write the given ratios, \(2:4\) and \(4:5\) in fraction form.
\(2:4=\dfrac{2}{4}\) and \(4:5=\dfrac{4}{5}\)
Step 2: Now, we simplify the fractions, if possible.
The GCF of \(2\) and \(4\) is \(2\).
Thus, \(\dfrac{2\div2}{4\div2}=\dfrac{1}{2}\)
The GCF of \(4\) and \(5\) is \(1\).
Thus, \(\dfrac{4}{5}\) is already in its simplest form.
Step 3: We convert the fractions to decimals by dividing \(1\) by \(2\) and \(4\) by \(5\).
Thus, \(\dfrac{1}{2}=0.5\) and \(\dfrac{4}{5}=0.8\)
Now, compare both the ratios.
\( 0.5<0.8\)
Thus, \(\dfrac{2}{4}<\dfrac{4}{5}\)
or \(2:4<4:5\).
A \(\text{2 to 4}\)
B \(\text{1 to 5}\)
C \(\text{Both are equal}\)
D
Total balls \(=15\), White balls \(=5\), Black balls \(=15-5=10\)
Here, the ratio can be written in statement form as follows-
(i) For every \(5\) white balls there are \(10\) black balls in the bag.
(ii) By the equivalent ratio, \(\dfrac{5}{10}=\dfrac{10}{20}\)
Thus, there are \(10\) white balls for every \(20\) black balls.
(iii) There are \(5\) white balls for total \(15\) balls in the bag.
A There are \(7\) red squares for every \(9\) green squares in the box.
B There are \(7\) red squares for total \(16\) squares in the box.
C There are \(9\) green squares for total \(16\) squares in the box.
D There are \(9\) red squares for every \(7\) green squares in the box.